tag:blogger.com,1999:blog-48938626523255683862019-10-21T21:29:16.603+05:30Satyam Mathematicsupto class 8th maths,11th maths, 12th mathematics,B.sc.(Graduation)mathematics,M.sc.( post Graduation) mathematics,competition like,bank, clerk,ssc,and other competition, this website's main goal is to solve problems in mathematics, mental ability,reasoning.many students face to solve mathematics problems.we help them. satyam coaching centrehttp://www.blogger.com/profile/12788483628699913686noreply@blogger.comBlogger57125SatyamMathematicshttps://feedburner.google.comtag:blogger.com,1999:blog-4893862652325568386.post-1721911355624580782019-10-15T23:11:00.000+05:302019-10-15T23:11:51.982+05:30Mathematics Is More Interesting Subject Than Any Other Subject<div dir="ltr" style="text-align: left;" trbidi="on"><h1 style="text-align: left;"><b><i><u>Mathematics Is More Interesting Subject Than Any Other Subject</u></i></b></h1><h2 style="text-align: left;"><b><i><u>1. Introduction to Mathematics is a more interesting subject than other subjects (Introduction to Mathematics Is More Interesting Subject Than Any Other Subject) -</u></i></b></h2><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><a href="https://1.bp.blogspot.com/-0Jz_x0WWKZ0/XaUuNnoVwfI/AAAAAAAAMns/Vyx4jxJnkeIiZPPRZl2xqGn6tsH6ClNHwCEwYBhgL/s1600/Mathematics_Is_More_Interesting_Subject_Than_Any_Other_Subject.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img alt="Mathematics Is More Interesting Subject Than Any Other Subject" border="0" data-original-height="183" data-original-width="275" height="425" src="https://1.bp.blogspot.com/-0Jz_x0WWKZ0/XaUuNnoVwfI/AAAAAAAAMns/Vyx4jxJnkeIiZPPRZl2xqGn6tsH6ClNHwCEwYBhgL/s640/Mathematics_Is_More_Interesting_Subject_Than_Any_Other_Subject.jpg" title="Mathematics Is More Interesting Subject Than Any Other Subject" width="640" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><h4><span style="font-size: large;"><i><u>Mathematics Is More Interesting Subject Than Any Other Subject</u></i></span></h4></td></tr></tbody></table><b><i>It has been said in this article that the mathematics subject is simpler than other subjects. We keep repeatedly appealing in our posts that if interest, curiosity and perseverance along with patience in mathematics can make mathematics simple for those students. You have to memorize the content in other subjects, but in Maths up to class XII (students) remember the formulas properly and know how to use them properly, then at the same time they have interest, curiosity, perseverance, patience. And if concentration is practiced, then his maths subject becomes simple.</i></b><br /><h2 style="text-align: left;"><b><i><u>2. Interest in Mathematics</u></i></b></h2><b><i>To inculcate interest in mathematics, it is necessary to teach children through multiplication, counting, poetry and music. Gradually, when the children have knowledge of counting, mountains and numbers, then they should try to understand the meaning of the words of mathematics. This requires both time and practice. Maturity begins in the child when the brain is together with learning to speak. By presenting some models of mathematics, it should help them to speak and pronounce them clearly. Gradually, interest in children will start to awaken.</i></b><br /><h3 style="text-align: left;"><b><i><u><span style="font-size: large;">3.Curiosity in Mathematics</span></u></i></b></h3><b><i>Just like when a new thing, thing or book is brought, the child repeatedly tries to use it, see and read it. Similarly, in order to increase curiosity in mathematics of the child, new maths should be presented before him, so that the instinct of curiosity can be instilled in them. For example, knowledge of the first digit, counting, multiplication, addition, rest, multiplication, division, etc. should be presented to the children respectively so that they can generate curiosity.</i></b><br /><h3 style="text-align: left;"><b><i><u><span style="font-size: large;">4.Drill in Mathematics -</span></u></i></b></h3><b><i>In order to practice mathematics, children should initially give some small questions in the form of exercises. In addition, while solving the questions in a new way, some questions should be made for frequent practice. When one gets complete knowledge on any method, then it is beneficial to ask questions to check the memory in between and it always proves beneficial. To check the method done in a given period, the teacher gets to know the position of the child and this again awakens the memory of the students. The work of previous period can be repeated by simple question papers and examples.</i></b><br /><b><i>If a teacher does not pay attention to the work done by the child, it means that in the next class, the child does not have to teach it himself. The teaching of that teacher is limited to that level only. In this case, he does not pay attention to the future of the child. To improve in this situation, the head teacher of mathematics should be alert. He should keep in mind that every mathematics teacher should take the examination of the child at the beginning of innovative questions. It is possible in a school where only one teacher teaches children, but where the children finish one school and enter another school, the teachers do not understand their responsibility. In small classes, children are sent to another class before they can be fully practiced in any new method. Due to this the foundation of such boys is weakened and the child seems to have difficulty in understanding the new method. Therefore, the importance of practice is as much at this level as it is at other levels. The teacher likes to use new methods but it hurts children. Before starting any new method, it is necessary to fully understand the former method. This is possible only if sufficient practice of each new method is practiced in the classroom. There are students in the school who can solve the higher method questions and cannot solve the general law questions under them. The only reason for this is the lack of practice in those methods. Because of this, students do not fully understand those simple questions. In this way, when students sit in an exam, they fail to solve simple questions and due to this failure their interest in mathematics is diverted. In this way, those students who do full practice in every field of mathematics always get success.</i></b><br /><b><i>The practice of Mathematics, despite being so important, stumbles in the eyes for some reasons. This gives a lot of scope for excuses to the noodle teacher while the teachers of other subjects get tired of tearing the throat. Mathematics teachers play peacefully in the shadow of their practice work. It does not work under the guise. Because of this the practice method has become infamous. But actually it is not good to teach an important and laborious subject like mathematics without practice. This method has to be used but the teacher should also be well aware of his duties. He should observe that when the child is practicing, he should observe all the children in the class and wherever the child is stuck, he should remove his difficulties. By doing this, all the children will be interested in practice and will be able to take full advantage.</i></b><br /><h3 style="text-align: left;"><b><i><u><span style="font-size: large;">(4.) Patience and Meditation -</span></u></i></b></h3><b><i>Along with interest, curiosity and practice, patience and meditation are also necessary. If we do not have patience and focus in our life, then with the help of interest and curiosity and practice, we will not be able to heal for a long time. Now the question arises why it is necessary to have meditation with patience. If there is no patience then we will be hasty and if we solve any question in haste, then we will make a mistake. Meditation is necessary because if we do not meditate, the mind will not concentrate and the mind will not concentrate, then it will not take mind to solve the questions and practice of mathematics, ie the mind will be moving. Therefore meditation is necessary with patience. Just as both the wheels of the vehicle are capable of running, similarly patience and attention are both necessary. Without patience, we will not be able to do any mathematics question or task successfully. Do the maths methodically and remain fully active till it is completed, do not leave it in the middle. It is necessary to have patience. If you do not have patience, you will run away in the middle, leave the work. We start following any good rule, but we are unable to keep up with lack of patience. Without patience, you cannot even meditate and when meditation is broken, work cannot be done in the same manner. Today, there is an incompleteness of mathematics in our life, it is a mess and the root cause of it is lack of patience and attention. As soon as you plant, fruits do not come in it, rather it is necessary to be patient till the fruit comes. Fruits come on time only, after which the fruits come after that, you have to be patient for that long no matter how much water and fertilizer is put together. One of the characteristics of the patient and meditator is that he is lazy,</i></b><br /><b><i>One is not passive and weak but is alert, active and diligent. Keeps making effort.</i></b><br /><b><i>To make patience and meditation a part of life, the beginning of the morning should be done with meditation. Retiring from Nityakarmo in the morning, after concentrating the mind for a while, one should meditate on the sun in the form of light or the lamp or the light of 7. Initially, the mind will wander here and there, but by practicing patience, we will keep practicing continuously, if we do it regularly and daily, then meditation will be practiced. There is a need to start with strong determination. As the practice progresses, the mind will concentrate and become peaceful. It is also important to keep patience. Interest, curiosity will remain and you will be strengthened only if you are patient, otherwise the immediate interest and curiosity will end. Only by having patience will you be able to use other qualities.</i></b><br /><h3 style="text-align: left;"><b><i><u><span style="font-size: large;">(5.) Passion in Mathematics -</span></u></i></b></h3><b><i>It is necessary to have passion and passion to be successful in a subject like Mathematics. You throw yourself completely. Finally, you will get the right result. If there will be no passion and passion, and when you want to do any work, you will do it and when you do not like it, you will not do it. Therefore, it is also necessary to have passion and passion, only then you will be able to practice a subject like mathematics properly and well.</i></b><br /><b><i>Lastly, if you like this article, then share and like it with your friends. If you have any problem or any suggestion, then comment and tell. Read the article completely.</i></b><br /><h3 style="text-align: left;"><b><i><u><span style="font-size: large;">6. Enumeration is more interesting subject than other subjects (Mathematics is more interesting subject than any other subject) -</span></u></i></b></h3><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><a href="https://1.bp.blogspot.com/-Fmf6gJahTW4/XZFsIgiOAHI/AAAAAAAAMdY/_8PYjlUsdH4ceYK4vDOa4xpKqrq9YACqACLcBGAsYHQ/s640/Mathematics-Is-More-Interesting-Subject-Than-Any-Other-Subject.webp" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img alt="Mathematics Is More Interesting Subject Than Any Other Subject" border="0" data-original-height="183" data-original-width="275" height="425" src="https://1.bp.blogspot.com/-Fmf6gJahTW4/XZFsIgiOAHI/AAAAAAAAMdY/_8PYjlUsdH4ceYK4vDOa4xpKqrq9YACqACLcBGAsYHQ/s640/Mathematics-Is-More-Interesting-Subject-Than-Any-Other-Subject.webp" title="Mathematics Is More Interesting Subject Than Any Other Subject" width="640" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><h4><span style="font-size: large;"><i><u>Mathematics Is More Interesting Subject Than Any Other Subject</u></i></span></h4></td></tr></tbody></table><b><i>Mathematics Is More Interesting Subject Than Any Other Subject</i></b><br /><b><i>Sat, 29 Jul 2017 The two-day senior class teachers' workshop on Science and Mathematics at DAV Barkakana started on Saturday. DAV Director cum Principal Dr. Urmila Singh, Principal HK Jha, Principal UK Rai, Principal Rani Jaiswal, Principal SR Prasad etc. were present on the occasion. The guests were welcomed with a bouquet. After this, the workshop was duly inaugurated by lighting the lamp together and with the DAV anthem. Dr. Singh said that there is no other subject more interesting than mathematics. Once interest is generated towards it, students dedicate their whole life towards it. It is important that students are interested in this, because students are counting on days to get rid of it due to their interest in mathematics. Therefore, teachers should try to generate interest in students towards mathematics. The stage operations teacher Himadri Biswas did. Maths as Resource Person - HG Tiwari, D Pandey, Manoj Kumar, AK Dubey, SR Prasad, Comestry-UK Roy, Ravi Kumar, VN Pandey, AN Pathak, Arvind Singh, Bio-Alok Kumar, RD Mukhopadhyay, Dr Kumar Anand , Gajendra Kumar, Mo Ashif, Sudhir Mishra etc. were present. The two-day workshop was attended by Physics, Chemistry, Bio and Math teachers from DAV Koderma, Bachra, Hazaribagh, Urimari, Tapin North, Kedala, Ghato, Ara, Bharenchanagar, Rajarappa, Barkakana etc.</i></b></div><img src="http://feeds.feedburner.com/~r/SatyamMathematics/~4/VyUta4Bsm7c" height="1" width="1" alt=""/>satyam coaching centrehttp://www.blogger.com/profile/12788483628699913686noreply@blogger.com0https://www.satyammathematics.com/2019/10/mathematics-is-more-interesting-subject-than-any-other-subject.htmltag:blogger.com,1999:blog-4893862652325568386.post-35599537599261180522019-10-05T20:06:00.005+05:302019-10-05T20:06:59.276+05:30Basic Education And Teaching Mathematics<div dir="ltr" style="text-align: left;" trbidi="on"><h1 style="text-align: left;"><b><i><u>Basic Education And Teaching Mathematics</u></i></b></h1><h2 style="text-align: left;"><b><i><u>1.Introduction to Basic Education and Mathematics Teaching -</u></i></b></h2>This article states that basic education is imparted through three mediums - Nature, Society, and Craft. The child's life is spent in early life in the lap of nature and his life in the family After spending time comes in contact with the society. Therefore, in basic education, balance is established in nature, family and society. Mathematics establishes relationships in nature, family and society that are helpful in industry. The child needs knowledge of natural phenomena like sun, moon, time of stars, their position and direction, seasons and rain etc. All this is possible only through mathematics. Thus mathematics is very helpful in understanding natural phenomena. Home and society related problems such as eating, drinking, clothes and building houses, accounting of expenses incurred in transactions, details of income expenditure incurred in marriage, shraddh and other social festivals are all faced. Problems can also be solved through mathematics. Thus, social problems also require mathematics. Mathematics is used step by step in the industry. Use of area according to area of fields, measurement of seeds and weighing of products produced from them, market rate of storages, stores, sale, paper, wood, iron, zinc, tin, etc., color, chemical ratio etc. , The calculation of profit and loss, etc. is not possible without solving mathematics. Hence mathematics is well used in all four mediums - nature, family, society and industry.<br /><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><span style="margin-left: auto; margin-right: auto;"><a href="https://www.satyammathematics.com/" target="_blank"><img alt="Basic Education And Teaching Mathematics" border="0" data-original-height="168" data-original-width="299" height="359" src="https://1.bp.blogspot.com/-zLDrMy8sSPs/XZio7eMv0xI/AAAAAAAAMg8/14bnt3e5VD4wS8SjSd8tCrKXv_Djx1HUACLcBGAsYHQ/s640/Basic_Education-And-Teaching-Mathematics.jpg" title="Basic Education And Teaching Mathematics" width="640" /></a></span></td></tr><tr><td class="tr-caption" style="text-align: center;"><h4><span style="font-size: large;"><i><u><a href="https://www.satyammathematics.com/" target="_blank">Basic Education And Teaching Mathematics</a></u></i></span></h4></td></tr></tbody></table>Apart from this, it is also taken care in basic education that whatever knowledge the child acquires, he should get it on the basis of various activities. In this, education is given in such a way that the correlation between knowledge and activity is maintained. Enumeration is very useful in connecting various actions and the knowledge arising from them. Just as slurry is helpful in connecting one brick with another brick in building construction, in the same way mathematics also helps in linking different actions and knowledge. Therefore, understanding the usefulness of mathematics in basic education should be included in the curriculum.<br />If you like this article, then share and like it with your friends and if you have any problem or any suggestion, then comment and tell. Also read the article.<br /><h2 style="text-align: left;"><b><i><u>2.Objectives to Teach Mathematics in Basic Education -</u></i></b></h2>The aim of teaching mathematics in basic education is to enable students to be able to solve their industry and domestic and social life measurement problems quickly. Therefore, in basic education, the emphasis is on the practical and cultural value of mathematics. Disciplinary value of mathematics is not taken care of at all.<br />Therefore, the teacher should keep the following objectives in mind while teaching mathematics in basic education -<br />(1.) The child should have a thorough knowledge of the marks used in daily life.<br />(2.) The ability to solve many number and geometry problems arising in industry and daily life should be achieved quickly and accurately.<br />(3.) Children should be given opportunities to think on a subject themselves, to be focused, to make successful efforts on it and to express it in subtle terms through words, signs or pictures.<br /><h3 style="text-align: left;"><b><i><u><span style="font-size: large;">3. Mathematics Curriculum in Basic Education </span></u></i></b></h3>The knowledge of mathematics required by the child in a particular situation should be taught to the child at that time. By doing this, the child is interested in learning mathematics. Thus, the current requirement and interest of the child is the basic principle of making a mathematics course in basic education.<br />This course is very flexible. It has a subtle outline of the course. While teaching, teachers are free to choose any subject from the course and according to the interest of the children. There is no place for Theoretical and Artificial Mathematics in the syllabus. Special emphasis is given in this that mathematics should be related to daily life. Self Dr. Zakir Hussai had said in the basic plan of basic education that basic education should not be confined to theoretical marks but it should be very closely related to practical problems that arise while learning basic art skills. Therefore, in basic mathematics, basic questions related to work and time, and factors of meaningless algebra, etc., do not have a place at all in the curriculum of mathematics in basic education. In this, the same mathematics is respected, which is necessary in social and entertainment related activities and practical life in handicraft.Emphasis is given to Practical Geometry so that it can help in designing and drawing in handicraft and household works. Algebra is also taught in the same way which is helpful in simplifying arithmetic questions. Those equations of algebra are taught which help in solving handicraft problems.<br /><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><span style="margin-left: auto; margin-right: auto;"><a href="https://www.satyammathematics.com/" target="_blank"><img alt="Basic Education And Teaching Mathematics" border="0" data-original-height="1200" data-original-width="1600" height="478" src="https://1.bp.blogspot.com/-k7pbPLw0agU/XZipXGHC1lI/AAAAAAAAMhE/iwpV5JVsTKkYI5StfB1OAZkAnfeTTVUNwCLcBGAsYHQ/s640/Basic-Education-And-Teaching-Mathematics.jpg" title="Basic Education And Teaching Mathematics" width="640" /></a></span></td></tr><tr><td class="tr-caption" style="text-align: center;"><h4><span style="font-size: large;"><i><u><a href="https://www.satyammathematics.com/" target="_blank">Basic Education And Teaching Mathematics</a></u></i></span></h4></td></tr></tbody></table>In making mathematics courses in basic education, mathematics is often separated from its practical course. It is written directly in the syllabus, such as addition, rest, multiplication, division, decimal, unitary rule, etc. This often has the effect that when teaching teachers, the course is more difficult than problems related to daily life. Add. Therefore, the mathematics course should be associated with problems related to daily life.<br />There are many problems related to daily life in mathematics, some of them are as follows -<br /><h4 style="text-align: left;"><i><u><span style="font-size: large;">(1.) Industry Related -</span></u></i></h4>The shapes of triangles, quadrilaterals, squares and rectangles etc. can be made. When they weigh seeds and manure and cottonseed for the fields, at that time they can be told about weighing units like - kilogram, gram etc. While making beds and roads in fields and gardens, measuring their land, removing area etc. can be taught. By selling the produce produced in the field and garden, woven cloth can be made aware of their profit and loss and practical mathematics. In this regard, knowledge of their receipts, cash book and balance sheet will also be easy. They can also be taught a field book while constructing beds in the farm. They can also be made aware of speed, friction, etc. while weaving clothes. The knowledge of different shapes of geometry can be made while designing a woven garment. At the time of coloring, we get knowledge of colors. Knowledge of solid geometry, sphere, cube etc. can be easily given in making a model of clay. When they work with the earthen slopes, then their knowledge of counting will also become easy. Weighing, various measurements, etc. can be taught while making wooden and clay toys. They can be told to bring colors in different proportions in coloring. In this way, different types of mathematics can be taught on different types of industries.<br /><h4 style="text-align: left;"><b><i><u><span style="font-size: large;">(2.) Home and Family Related -</span></u></i></b></h4>Mathematics can be taught in many ways in the contexts related to food, drinking, building of houses, reading and writing, transactions. Percentage related questions can be made in relation to the income tax of the guardians of the children. Interest-related questions can be raised in the context of depositing, withdrawing and levying interest on money in post offices and banks.<br /><h4 style="text-align: left;"><b><i><u><span style="font-size: large;">(3.) Related to society -</span></u></i></b></h4>Interest, Profit and Loss, Partnership and other major rules of arithmetic can be easily explained to the children by running a co-operative store in the school. Children should also be accounted for the festivities in school. With this, they can easily learn things such as transactions, purchases and expenses. In the society, marriage, marriage, shraddh and many practical and social work, transactions, buying and selling, many types of mathematics in the context of children can be taught.<br /><h3 style="text-align: left;"><i><u><span style="font-size: large;">4. Equipment -</span></u></i></h3><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><span style="margin-left: auto; margin-right: auto;"><a href="https://www.satyammathematics.com/" target="_blank"><img alt="Basic Education And Teaching Mathematics" border="0" data-original-height="321" data-original-width="450" height="456" src="https://1.bp.blogspot.com/-_Y-2pLCnvyI/XZipvHpcINI/AAAAAAAAMhM/5nf6D6FDuIQNi5J3VvkpeviVPBhlDbvQgCLcBGAsYHQ/s640/Basic_Education_And_Teaching_Mathematics.jpg" title="Basic Education And Teaching Mathematics" width="640" /></a></span></td></tr><tr><td class="tr-caption" style="text-align: center;"><h4><span style="font-size: large;"><i><u><a href="https://www.satyammathematics.com/" target="_blank">Basic Education And Teaching Mathematics</a></u></i></span></h4></td></tr></tbody></table><div>Having the syllabus, it is also necessary to have the necessary equipment and materials for mathematics. With these tools and materials, the teaching of mathematics becomes simple and interesting. Apart from this, there are some such subtle things in mathematics teaching, which is impossible for some if not all students. In such a situation, if subtle things are clarified by showing equipment and painting, then the children understand it quickly. In addition to blackboard, point, cuticle, duster, geometrical sets, counting items such as chains and measuring instruments, drains of different colors of solid geometry, items of different heights and depths, models of various shapes such as spheres. ), Cube, Rectangular Solid, Prism and Cone etc. different types of coins, substances with different density, different types of weighing, grading, etc. Charts and drawings and diagrams of various kinds, should be decorated in a tastefully school. It is also a means of teaching mathematics to children. As far as possible, pictures should be made by hand. The cleanliness and arrangement of these devices should also be banned by teachers and children.</div><h3 style="text-align: left;"><b><i><u><span style="font-size: large;">5. Method -</span></u></i></b></h3>In basic education, the teaching method of Mathematics is not to give out the rules by direct rules, but should solve the problem that arises while learning; eg, a child spun 40 meters in one day and 35 meters on the other day. . Now it will need to know how many meters of yarn he spun on both days. This time is a good opportunity to teach the teacher the rules of addition. In this way, many problems will arise in relation to the craft and using them, knowledge of mathematics will be given easily. The teacher should also consider while teaching mathematics that children are very small in basic classes, so they should be taught in the Inductive Method because the Deductive Method requires a lot of logic and understanding.<br />By doing this, teaching of mathematics will be done with the help of real life related matters. Sometimes absurd and untrue examples appear in books like - a man is 14 years old and has 3 children. Now it is a matter of wondering if a 14 year old boy can have 3 children.<br />The In the same way, such questions are also asked, which answer 20.5 man. Is it possible to have 20.5 men? Sometimes such questions are also asked that if the price of a horse is 2 rupees, then the value of 8 horses is said. Can a horse be worth 2 rupees? Therefore, such questions should not be addressed to children which are artificial and untrue. It has a bad effect on children. They consider mathematics as unrelated to life and understand a strange and terrible subject. The teacher should ask the child to do the same questions which are numerical, descriptive, related to eating and drinking, wearing and wearing, playing and playing, etc. Along with this, materials related to mathematics such as counting tools, coins, geometric sets, shapes of solid geometry, etc. should also be used while teaching mathematics. Doing so will create a natural tendency among children. He will get juice in mathematics. They will start taking interest in mathematics. They will have the tendency to research - research and will be able to solve their problems on their own.<br />Sometimes teachers make a mistake, they threaten children when they learn mathematics and make them make mistakes and beat them and beat them. In addition, they impose subtle and unobtrusive principles in mathematics without considering the age and understanding of children. The result of this is that the children become indifferent to mathematics and run away from it. By rote they may pass the exam but are unable to take real use of mathematics in their lives. Therefore, teachers should beware of these mistakes. They should create such an atmosphere of love so that the children can feel free to resolve their doubts with the teacher and do not hesitate to ask anything to the teacher. Mathematics teacher should also keep in mind that as long as the interest of the children is in the subject, then mathematics should be taught because only the favorable situation and the work done at the right time is completely successful. At the time when the children get bored while studying any subject of mathematics and when they are not interested in reading it, the result will be the same as when the pot is filled and water is filled. Therefore, children should be taught as long as they remain interested in the subject.<br />The boys should have speed and accuracy in solving maths questions and there should not be any kind of mistake in mathematics related writing. This requires drill in math work. But the practice should be done in such a way that the child is not bored of doing it. The teacher should do this exercise through Play-way-Method. In practice, questions should be chosen in such a manner that children continue to take interest in them. The teacher should not insist on the short cut of a question, but rather it should be done in the order in which children think. Weak children should also take care of mathematics teacher. Bright and weak (Weak) boys should be taught as much as possible. Sometimes teachers sit too quickly to bring weak children with fast boys. By doing this, the foundation of weak child remains weak which hinders further progress. Children should not get angry on impure answers, but should try to get them correct answers.<br /><h3 style="text-align: left;"><b><i><u><span style="font-size: large;">6. Text-Book</span></u></i></b></h3>Some people believe that there is no need for a textbook in basic education. But this is his biggest mistake. It is mandatory to have books for basic education, but these books should be written on the principle of basic education. The questions given in the mathematics textbook should be related to life. The questions should be real, there is no glimpse of artificiality in them. The method of placing the questions should also be systematic so that the simple questions come first and then the most difficult. Oral and mental questions should also be included. In good books of mathematics, it is necessary to have pictures and shapes somewhere for confirmation.</div><img src="http://feeds.feedburner.com/~r/SatyamMathematics/~4/eKBETvhmL0k" height="1" width="1" alt=""/>satyam coaching centrehttp://www.blogger.com/profile/12788483628699913686noreply@blogger.com0https://www.satyammathematics.com/2019/10/basic-education-and-teaching-mathematics.htmltag:blogger.com,1999:blog-4893862652325568386.post-6226410525916329622019-10-02T07:53:00.000+05:302019-10-02T07:53:04.113+05:30Symbols in Mathematics<div dir="ltr" style="text-align: left;" trbidi="on"><h1 style="text-align: left;"><b><i><u>Symbols in Mathematics</u></i></b></h1><h2 style="text-align: left;"><b><i><u>1. Introduction to Symbols in Mathematics</u></i></b></h2><b><i>In this article, the importance and usefulness of symbols in mathematics is explained. Just as symbols have an important place in religion and institution in our lives and wherever they play their important role, symbols are also important in mathematics. Symbol plays his role like Sagar in Gagar despite appearing briefly. Mathematics cannot be imagined without symbols, so it is very important to understand which symbol will be used where. Symbols help to simplify mathematics and can be saved from being difficult. Using symbols saves our time and at the same time we can quickly and quickly understand mathematical operations by symbols and Thus others are able to explain. Thus the symbol is a wonderful creation of nature which enhances the beauty of mathematics and adds four moons to it. We must learn to use them properly.</i></b><br /><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><b style="margin-left: auto; margin-right: auto;"><i><a href="https://www.satyammathematics.com/" target="_blank"><img alt="Symbols in Mathematics" border="0" data-original-height="1069" data-original-width="1600" height="426" src="https://1.bp.blogspot.com/-QLYB3qElDg8/XZBTDevn49I/AAAAAAAAMc4/DJfVl7AD6i8nTcVHMqY6DT0FExodjCMDACLcBGAsYHQ/s640/Symbols-in-Mathematics.jpg" title="Symbols in Mathematics" width="640" /></a></i></b></td></tr><tr><td class="tr-caption" style="text-align: center;"><h4><span style="text-align: left;"><i><span style="font-size: large;"><u><a href="https://www.satyammathematics.com/" target="_blank">Symbols in Mathematics</a></u></span></i></span></h4></td></tr></tbody></table><b><i>If you like this article, then share and like it with your friends. If you have any problem or any suggestion then comment and tell. Read this article completely.</i></b><br /><h2 style="text-align: left;"><b><i><u>2.Symbols in Mathematics</u></i></b></h2><b><i>The importance of mathematics in human life is well known. Symbols are very important in mathematics. It will not be an exaggeration if it can be said that the journey of Mathematics from ancient times to ancient times cannot be understood without understanding the symbols associated with different branches. Not only mathematics, but also the heights of religion and culture, literature and art cannot be understood without understanding the symbols.</i></b><br /><b><i>Explanation of the word symbol is not easy and it is even more difficult to explain them completely. New meanings of symbols are coming and in such a situation it is a difficult task to give them full expression. How difficult this task will be in the context of mathematics can be gauged in such a way that this entire tradition developed during hundreds of years is considered to be based on symbols, that is, its field is also used in symbolic expression of what is being said in a broader sense. During the period many strings of meaning are visible.</i></b><br /><b><i>However, from time to time, various mathematicians have done the useful work of explaining the symbols of mathematics in simple language from time to time. The popularity of symbols is a proof of how much they are used in mathematics.</i></b><br /><b><i>Despite the multiplicity of symbols, they are difficult to interpret. It is often believed that signs and symbols are one, but they are not. While the symbol or sign expresses the orthodox symbol, the symbol is a visual sign of an invisible object with a scientific view. This world of symbols is not only enjoyable but also awe-inspiring. A meaning opens and the next moment another meaning comes out in the world of thought and contemplation.</i></b><br /><b><i>The symbol which is used in some other way in mathematics is sometimes used in some new sense in other subjects. In this way the scope of symbols not only increases but also gives it dignity.</i></b><br /><b><i>Note-If you want to know which symbols are in mathematics.please click below.</i></b><br /><b><i>Mathematics Symbols</i></b><br /><h3 style="text-align: left;"><b><i><u><span style="font-size: large;">3. Relation of Symbols</span></u></i></b></h3><b><i> The symbol is the object of mind and intellect, mind and intellect are the property of soul. The soul is eternal and eternal truth. The symbol is a symbol of that eternal truth. The truth is that the less you understand, the less.</i></b><br /><b><i>As far as mathematics is concerned, it is a mine of symbols. There is hardly any area of life that does not sound symbolic expressions. One scholar sees them in a limited sense and another in an unlimited sense. A chain is formed, in this way the whole subject of meanings begins to identify with the supernatural, articulating the infinite capabilities of the human mind. The world of symbols, despite being quite complex, is interesting and comprehensive so much that whether it is mathematics, philosophy, literature or art, science or other scriptures are all contained within its eternal limits.</i></b><br /><b><i>It is clear from the background of symbolism, continuity and philosophicality that writing on this subject is not an easy task. Writing on it is not an easy task. There is no dearth of works by these various scholars, but only a few heights of stratification have been reached.</i></b><br /><h3 style="text-align: left;"><b><i><u><span style="font-size: large;">4. Explanation -</span></u></i></b></h3><b><i> It is difficult to interpret the symbol in natural form. What we mean by the use of this word, in that sense there is no book available on this subject in the country or abroad. In English, a symbol is called a symbol such as signs, signs, signs and postures etc. The word 'sign' is in English for signs. But these synonyms for signs etc. will be found many but scientifically there is no other word in that language other than Symbol. But the symbol is neither a sign nor a symptom nor a symbol. If the symbol refers to the mark which is the appearance of an invisible, non-visible, visible object, then it may not be appropriate to say that according to grammar, the meaning of an impression is false.</i></b><br /><h3 style="text-align: left;"><b><i><u><span style="font-size: large;">5. Meaning according to different dictionary</span></u></i></b></h3><b><i>Meaning by English Dictionary Oxford Dictionary -</i></b><br /><b><i>Symbol is a person, an object, an event etc. that represent a more general quality or situation: white has always been a symbol of purity in Western cultures. Ex. Mandela became a symbol of the anti-apartheid struggle.</i></b><br /><b><i>Sign - A sign is number, letter etc. that has a fixed meaning, especially in science, mathematics and music, what is the chemical symbol for copper?</i></b><br /><b><i>A list of symbols used on the map is given below.</i></b><br /><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><a href="https://1.bp.blogspot.com/-hnge95P0TN0/XZBTo1RD6FI/AAAAAAAAMdA/h1DVtM4d2Acc79ZsXpAa4JRIvyS6tPKjwCLcBGAsYHQ/s1600/Symbols_in_Mathematics.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img alt="Symbols in Mathematics" border="0" data-original-height="662" data-original-width="1280" height="330" src="https://1.bp.blogspot.com/-hnge95P0TN0/XZBTo1RD6FI/AAAAAAAAMdA/h1DVtM4d2Acc79ZsXpAa4JRIvyS6tPKjwCLcBGAsYHQ/s640/Symbols_in_Mathematics.png" title="Symbols in Mathematics" width="640" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><h4><span style="text-align: left;"><span style="font-size: large;"><i><u>Symbols in Mathematics</u></i></span></span></h4></td></tr></tbody></table><b><i>According to the math dictionary -</i></b><br /><b><i>Symbol - A letter or mark of any sort representing quantities, relations or operations.</i></b><br /><b><i>Algebraic Symbols - symbols representing numbers and algebraic combinations and operations with these numbers.</i></b></div><img src="http://feeds.feedburner.com/~r/SatyamMathematics/~4/j9FNNPDp0LY" height="1" width="1" alt=""/>satyam coaching centrehttp://www.blogger.com/profile/12788483628699913686noreply@blogger.com0https://www.satyammathematics.com/2019/10/symbols-in-mathematics.htmltag:blogger.com,1999:blog-4893862652325568386.post-44737630545522703832019-09-29T08:29:00.000+05:302019-09-29T08:29:06.627+05:30Education And Training Of Mathematics Teacher<div dir="ltr" style="text-align: left;" trbidi="on"><h1 style="text-align: left;"><b><i><u>Education And Training Of Mathematics Teacher</u></i></b></h1><h2 style="text-align: left;"><b><i><u>1. Introduction to Education and Training of Mathematics Teacher -</u></i></b></h2><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><span style="margin-left: auto; margin-right: auto;"><a href="https://www.satyammathematics.com/" target="_blank"><img alt="Education And Training Of Mathematics Teacher" border="0" data-original-height="1065" data-original-width="1600" height="424" src="https://1.bp.blogspot.com/-Ee8qDvCDmaQ/XY9lc3fYwMI/AAAAAAAAMcQ/DF_yPccgOMgkUPFJ4LWi6nQMFpc6qVW5QCLcBGAsYHQ/s640/Education-And-Training-Of-Mathematics-Teacher%2B%25282%2529.jpg" title="Education And Training Of Mathematics Teacher" width="640" /></a></span></td></tr><tr><td class="tr-caption" style="text-align: center;"><h4><span style="text-align: left;"><i><u><span style="font-size: large;"><a href="https://www.satyammathematics.com/" target="_blank">Education And Training Of Mathematics Teacher</a></span></u></i></span></h4></td></tr></tbody></table><b><i>It has been said in this article that both the syllabus and the book are dead, they are given live by the teacher, so special attention should be paid to the teacher's teaching and training. The teacher should also have practical knowledge like how to treat relatives, if you do transactions in the market, then what things should be kept in mind, how should you treat your elders? So that it can impart practical knowledge to the students.</i></b><b><i>If you like this article, then share and like it with your friends. If you have any problem or have any suggestion, then comment and tell. Read the article fully.</i></b><br /><h2 style="text-align: left;"><b><i><u>2. Present Position</u></i></b></h2><b><i>The definitive statement regarding the current professional (academic) and academic status of mathematics teachers is a subject of research, but studies can only be presented to a limited extent on the basis of experiences and general observations. For the development of Mathematics education as a special subject in America, 'The Mathematics Association of America, Inc.' and 'Council of Teachers of Mathematics' from the past 5-6 decades, through regular commissions and committees, regular efforts to improve it are doing. Nothing like this is seen in India right now. Here some observations on the status of mathematics education are presented as follows -</i></b><br /><b><i>(1.) There is also a lack of knowledge and understanding of mathematics subject matter suffixes, relations operations, etc.</i></b><br /><b><i>(2.) Education in its broader form is 'social service', but at present it has become a profession. In mathematics education, professionalism has taken a negative form. It is rare to promote its institutional form. Money value has been acquired on it.</i></b><br /><b><i>(3.) The development of mathematics education in business is not bad, but the defeat of the standards of professionalism in it is worth considering. The general teacher and the mathematics teacher in particular have no knowledge of the professional values of the education profession.</i></b><br /><b><i>(4.) Mathematics teaching has become an individual practice. This leads to a clear defeat of collaboration and participation among teachers.</i></b><br /><b><i>(5.) Teachers do not see the penetration of mathematical skills, values and slag.</i></b><br /><b><i>(6.) Only superficial knowledge of mathematics is found by teachers to be meaningful. The magnitude and scope of the content of mathematics must increase at the level of knowledge, but the depth of the subject has decreased greatly. It can be said that the volume of mathematical knowledge in the teachers has definitely declined. This should be a matter of concern.</i></b><br /><b><i>(7.) The ignorance of teachers towards the methods, techniques, skills of teaching mathematics and lack of curiosity for their acquisition is obvious.</i></b><br /><b><i>(8.) He has no relation with the interest, aptitude, aptitude of the student. They are only interested in completing the formalities of completing the prescribed content.</i></b><br /><b><i>(9.) There is no relation in the teacher's work with teaching aptitude and teachers do not even try to understand the importance of mathematics.</i></b><br /><b><i>(10.) The teacher does not even want to know the difficulties and shortcomings of his learner. It is beyond imagination to be interested in removing them.</i></b><br /><b><i>(11.) Classroom teaching is completed on the traditional lecture system.</i></b><br /><b><i>(12.) Teachers are not interested in giving sufficient practice, maintenance work to the learners. Even if given these tasks as his routine job, the teacher is not able to take time to examine them, which makes him redundant.</i></b><br /><b><i>(13.) Lack of patience in teachers, lack of interest in understanding their students, lack of knowledge of the basic principles of the subject, lack of skill in teaching, etc. are the shortcomings of the teacher, which have made the mathematics subject difficult. There is a general feeling in the student towards this topic. This makes the subject, despite being the most important, not popular among the students.</i></b><br /><h3 style="text-align: left;"><b><i><u><span style="font-size: large;">3. Condition for Effective Teaching for Teachers</span></u></i></b></h3><b><i>For effective teaching, teachers of all disciplines, including mathematics, must have perfect mastery in the subject concerned. This is the first necessary condition for the success of instruction. A person who is well versed in subject knowledge finds effective ventures and tactics for his teaching. Then in relation to mathematics it is well known that its methods of study and teaching are the same. Thus, in mathematics, the perturbation in his methods of study is correlated. Garnet is a subject that trains a person himself in his methods of teaching. Hence, one can say that studying mathematics is self training in the methods of teaching mathematics. Along with having a complete grasp on the subject of mathematics, the teacher must also specialize in the use of instructional techniques. For successful instruction in mathematics, the teacher must have developed both balanced knowledge and skills in use of instruction techniques in a balanced way. Its importance is made clear in the statement that "We do not need teachers who have nothing to teach (Teachers who have nothing to teach) nor those who are just supplying knowledge and promoting skills (Mere purveyors of knowledge and pro motors of skill). Balanced development of subject knowledge and instruction techniques is an important point in mathematics teacher.</i></b><br /><h3 style="text-align: left;"><b><i><u><span style="font-size: large;">4. Trichotomy of knowledge -</span></u></i></b></h3><span id="goog_163517405"></span><br /><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><span style="margin-left: auto; margin-right: auto;"><a href="https://www.blogger.com/goog_163517404"><img alt="Education And Training Of Mathematics Teacher" border="0" data-original-height="1065" data-original-width="1600" height="424" src="https://1.bp.blogspot.com/-ktk6Q8nuT7Q/XY9l9HkcwoI/AAAAAAAAMcY/moAUEUeGr6ExKrPgk4Ew0mWj0oH-2-qfQCLcBGAsYHQ/s640/Education-And-Training-Of-Mathematics-Teacher.jpg" title="Education And Training Of Mathematics Teacher" width="640" /></a></span></td></tr><tr><td class="tr-caption" style="text-align: center;"><h4><span style="text-align: left;"><i><u><span style="font-size: large;"><a href="https://www.blogger.com/">Education And Training Of Mathematics Teacher</a></span></u></i></span></h4></td></tr></tbody></table><span id="goog_163517406"></span><b><i>Mathematics teacher is a confluence of three classes of general, professional and specialist. We are living in rapid changes. Rapidity of development and its implications on future changes, while on the one hand staggering the imaginations, on the other hand, encourages satisfaction on superficial information. Events are happening at such a rapid pace that it is difficult for a human to study them and organize them, so that the development process is not easy to understand. Therefore, only superficial information related to any stream of development and change is considered sufficient material for our satisfaction. It is necessary to underline here that the superficial measures of knowledge have increased, but its depths have reduced. Our present knowledge is shallow. Mathematics teacher has to take special care here.</i></b><b><i>The educational background of the mathematics teacher should be broad and broad based. Never feel contented with your subject knowledge. May he remain the evergreen Gyan-Pipasu. Mathematics teacher should be truly knowledgeable. His subject knowledge should be so broad and deep that he can understand human development and the development of modern culture. He was able to appreciate human progress and social values.</i></b><br /><b><i>Every mathematics teacher should have a professional aptitude. Here, the professional aptitude of teaching is the permanent state of mind of the person, which includes the key qualities as follows: - Intense interest in the selection of mathematics for study and service work, Properties of value of mathematics in cultural structure Ability, those fundamental rules, mechanical processes, generalizing procedures, possibilities of practical applications readiness in the interpretation of applications), they form a specific area of the study of mathematics and human endeavor.</i></b><br /><b><i>In addition to education for a cultural background for a mathematics teacher, professional preparation is also necessary. For this, the provisions for the development of the qualities which are fundamental in it should be emphasized prominently.</i></b><br /><b><i>(1.) Devotion to teaching as a profession.</i></b><br /><b><i>(2.) Consciousness towards duty and duty knowledge in his field of work and wife touches him for his subsistence.</i></b><br /><b><i>(3.) Enthusiasm to contribute to mathematics and mathematics education.</i></b><br /><b><i>(4.) Aptitude and proficiency in understanding the learners.</i></b><br /><b><i>(5.) Proficiency in the use of teaching materials, methods, techniques, skills.</i></b><br /><b><i>(6.) Anomaly in the use of modern information technology.</i></b><br /><b><i>(7.) Proficient in making mathematics attractive.</i></b><br /><b><i>(8.) Skill to provide stability to knowledge of mathematics.</i></b><br /><b><i>(9.) Aptitude in subject knowledge and maintenance of its learning.</i></b><br /><b><i>(10.) Realization of the contribution of Indian society and culture to the development of mathematics.</i></b><br /><b><i>(11.) The curiosity of Indian mathematics to relate to modern technology.</i></b><br /><b><i>(12.) Complete realization of the theory of mathematics in the context of modern philosophical ideologies of mathematics.</i></b><br /><b><i>(13.) Proficiency in finding and using various tricks to make mathematics education easy and attractive.</i></b><br /><b><i>(14.) The realization of the commercial importance of mathematics in the present era.</i></b><br /><b><i>(15.) Realization and skill in taking full advantage of the multi media approach in the instruction of mathematics.</i></b><br /><b><i>(16.) Maturity in core values of teaching-business.</i></b><br /><b><i>For the development of this professional knowledge, understanding and skills in mathematics teacher, the course should be designed in such a way that it can understand the importance of the subject in its social system. He was able to understand the functions and implications of mathematics in personal and social life and understand the interrelations of different professions and establish their relationship with mathematics education. In order to develop the insight of the teacher in the interpersonal, mental, social, emotional development sequence of the learner. The teacher should be able to have complete knowledge of the subject matter of mathematics and its teaching. He will be able to use all the tips in making teaching and instruction effective, as well as being trained in teaching methods, techniques and skills and making his classroom instruction effective and efficient through observation and practice. Could make.</i></b><br /><h4 style="text-align: left;"><b><i><u><span style="font-size: large;">5. Job of the Mathematics Teacher</span></u></i></b></h4><b><i>The analysis of the job of a mathematics teacher reveals two major aspects of its responsibilities - (i.) General teacher (ii.) Distinguished teacher of mathematics. The first duty of a mathematics teacher to discharge the required responsibilities from all teachers in the teaching profession. is. The main among these obligations and duties are as follows -</i></b><br /><b><i>Active collaboration and participation in the smooth functioning of the school, Harmonious and effective contribution to the development and maintenance of Mutual Understanding between the school and the community, Co-curricular purposes of sponsorships, sponsorships of any academic organization, cooperation in the conduct of any academic organization, guidance and consultation Participation in, maintenance of related records, immediate presentation of desired reports, participation in community activities.</i></b><br /><b><i>Three main aspects of the specific role of a mathematics teacher emerge - the teaching of the mathematics subject, the teaching of the unit and the teaching of the specialty unit. As far as teaching as a specific subject of mathematics is concerned, the characteristics required of a teacher are as follows -</i></b><br /><b><i>(1.) He should realize that teaching mathematics is a challenge.</i></b><br /><b><i>(2.) The teacher should have a good knowledge of mathematics.</i></b><br /><b><i>(3.) The concept of mathematics as a scripture, its development, its importance in other areas of knowledge, its clear role in cultural development is required in the mathematics teacher.</i></b><br /><b><i>(4.) As a major part of General Education, the teacher must realize its imperative.</i></b><br /><b><i>(5.) Development of general concepts of mathematics, linking generalizations with application, differentiation between main and secondary points, identification of major learning points and anticipation of student's difficulties, complete knowledge of the sites of their occurrence and their removal. The skills and techniques needed to give students to do, etc., requires mastery of mathematics teacher.</i></b><br /><b><i>The aspects of knowledge, perception, skills required by the teacher for the teaching of a unit are as follows - content - concepts, items of information, skills developed by students, effective relevant instruction techniques and skills , Psychological and logical sequence of content, objectives in the form of behavioral changes, presentation of various sub-units, gathering of teaching materials. And their efficient use, pre-formulation of practical teaching matrices, anticipation of Difficult Spot of the unit and tips for resolving them, proper for assimilation, development and maintenance of content Tips determination, evaluation process.</i></b><br /><b><i>In teaching of a sub-unit, first the teacher should have clear knowledge of its set objectives. He should be proficient in the creation of various instruction situations. The foreshadowing of the difficulties experienced by the students under the presentation and the information on the intuitive tips to overcome them is required in the teacher. In order to make your instruction effective and efficient, the following things should be kept in mind while employing instruction to the teacher -</i></b><br /><b><i>(1.) Activities and exercises that are capable of producing the prescribed perceptions and skills in an effective and efficient manner.</i></b><br /><b><i>(2.) Selection of effective materials, procedures to overcome the difficulties of the learners in the instruction-learning process.</i></b><br /><b><i>(3.) The fulfillment of the conditions required for the use of instruction materials and the anomaly in their use and to make them comfortable with the requirement of the class.</i></b><br /><b><i>(4.) Development of desired motivation for knowledge of new subject, stimulant selection required for continuous flow of learning process, clarification for interest maintenance and development work in learning process, discussion ( ), Proficiency in the presentation of examples and examples.</i></b><br /><b><i>(5.) Proficiency in assessment transfers, diagnosis and treatment.</i></b><br /><b><i>In addition, in the instruction of a sub-unit of secondary mathematics, the teacher should have smooth answers to the following questions -</i></b><br /><b><i>(1.) Prior learning of what experiences and understandings in the learner is necessary for learning the content.</i></b><br /><b><i>(2.) What behavioral change is expected in the learner after learning the content?</i></b><br /><b><i>(3.) What processes, processes and techniques are required for desired behavioral changes?</i></b><br /><b><i>(3.) What specific difficulties can the learner face in acquiring the desired perception and ability?</i></b><br /><b><i>(4.) Which tips can be used effectively to overcome these difficulties?</i></b><br /><b><i>(5.) What materials and processes are needed for the development and maintenance of interest, motivation and learning for effective instruction.</i></b><br /><h3 style="text-align: left;"><b><i><u><span style="font-size: large;">5. Education and Training of Mathematics Teacher -</span></u></i></b></h3><b><i>The major factors responsible for the effectiveness of education and training of mathematics teachers are as follows -</i></b><br /><b><i>(1.) Selection of professional candidates, selection of professional candidates, teacher educational process, possibilities of appropriate conditions for work in the job (possibilities of appropriate working condition in the job), effective and efficient continuous education And Provisions of Effective and Efficient Continuous Education and Training.</i></b><br /><b><i>(2.) Choosing education as a profession has been considered as the last option, but this is no longer the case. In the event of increasing unemployment and reduced employment opportunities, the importance of teaching profession has increased because it is an area in which the demand for teachers will increase as the population increases. Therefore, due to the expected accessibility of employment opportunities in this field, the youth wants to get secondary teacher training (B.Ed) as soon as they pass the graduate examination. With the formation of the National Council of Teacher Education - NCTE in the country, teacher education has definitely got a new direction in the whole country. Pre-examination has been made mandatory for admission to it. Universities select candidates on the basis of merit as a result of this examination for their respective colleges and their departments. In Rajasthan, this examination is done at the state level. Various universities conduct this examination in turn. This exam is called Pre Teacher Education Test. The university conducting the exam selects the trainees on the basis of merit for all the universities of the state as per the laid down rules. Currently the system being adopted in Rajasthan is going well. There may be some shortcomings in this, but by experience these shortcomings can be overcome gradually.</i></b><br /><b><i>(3.) In this system, as a future teacher of Mathematics and Science, the person receives teacher training for livelihood only. The young girls who actually have aptitude and aptitude in teaching and mathematics are very rare. The present test of teacher aptitude and aptitude is just a formality.In this, good marks are being gained by studying and coaching the available gaids. Only those candidates with natural interest in both business and mathematics should be selected for teacher training in mathematics. The selection of such characters is not easy. For this, records of students have to be prepared from the school level itself. In every classroom, examination records related to individual student will have to be prepared in the activities of tests, clubs, projects etc. The same work will have to be done at higher secondary, college and university level. It is only by studying and analyzing these records that the right selection of future teachers for mathematics and science subjects can be made.</i></b></div><img src="http://feeds.feedburner.com/~r/SatyamMathematics/~4/nHMQk9BrB4A" height="1" width="1" alt=""/>satyam coaching centrehttp://www.blogger.com/profile/12788483628699913686noreply@blogger.com0https://www.satyammathematics.com/2019/09/education-and-training-of-mathematics-teacher.htmltag:blogger.com,1999:blog-4893862652325568386.post-85271245725764460332019-09-28T14:56:00.000+05:302019-09-28T15:15:13.700+05:30Definitions of Mathematics <div dir="ltr" style="text-align: left;" trbidi="on"><h1 style="text-align: left;"><b><i><u>Definitions of Mathematics</u></i></b></h1><h2 style="text-align: left;"><i><u>1. Introduction to Definitions of Mathematics</u></i></h2><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><span style="margin-left: auto; margin-right: auto;"><a href="https://www.satyammathematics.com/definitions-of-mathematics" target="_blank"><img alt="Definitions of Mathematics " border="0" data-original-height="900" data-original-width="1600" height="360" src="https://1.bp.blogspot.com/--Nxn7jFk6fQ/XYYmzjB1PcI/AAAAAAAAMXg/zfVz7TDmnpcvxEwf1FHksy6ty6f4LnV4gCLcBGAsYHQ/s640/Definitions-of-Mathematics.jpg" title="Definitions of Mathematics " width="640" /></a></span></td></tr><tr><td class="tr-caption" style="text-align: center;"><h4><span style="font-size: large;"><i><u><a href="https://www.satyammathematics.com/definitions-of-mathematics" target="_blank">Definitions of Mathematics </a></u></i></span></h4></td></tr></tbody></table>The definitions given by various scholars are described in this article. It is very difficult to define mathematics in words because mathematics is ubiquitous and universal, but in order to understand us in practical terms, we think it necessary to give definition according to our personal opinion so that we can get basic information.Mathematics is endowed with both the properties of concrete and micro abstract. It pervades all subjects. It is both art and (science). Its boundaries are eternal and eternal. No mathematics or science can be imagined without mathematics. It would not be an exaggeration to call mathematics the parent and nutrient of all subjects. All subjects depend on mathematics for their completeness. Mathematics is the main tool for the development of the three sides of the personality, Physical, Intellectual, and Spiritual. If you want to know more about how our personality can be developed by mathematics, then read our article Importance of Mathematics part-2. Although mathematics cannot be confined within the limits of any definition, it is necessary to develop definitions, nature, study methods, basic elements and insights in the field for basic knowledge of mathematics.<br />If you like this article, then share and like it with your friends and if you have any problem or any suggestion then comment and tell. Read this article completely.<br /><h2 style="text-align: left;"><b><i><u>2. Definitions of Mathematics</u></i></b></h2>The simplest meaning of mathematics is reflected in 'computation by enumeration'. Mathematics has been called the science of length-magnitudes and numbers in the education dictionary. Thus, both Hindi and English words mean counting, measuring and computation. In fact, the emergence of mathematics is the inclusion of human curiosity. In the first stage of his mental development, questions must have arisen in human mind by looking at his environment and sky, hearing words, touch, etc. What, how many? Then there are the possible questions that arise at the second level of development, how much? Seeing a change, the question must have arisen from astonishment. This led to the development of spiritual subjects such as philosophy, logic, philosophy of religion, knowledge, etc. As far as the first level question is concerned, even the lower level beings experience it. 'Measurement' is experienced in mental examination. Animals and birds also have its basic natural strength. Due to this, birds come for migrating hundreds and thousands of kilometers away due to the change of seasons. But at this stage, humans have the specific intellectual power for high-level calculation, which while being natural, is also affected by the environment. At this stage in humans, skills are developed in complex to complex processes of experiences, exercises, training. At the ultimate spiritual level, religious, philosophical beliefs and higher mathematical processes are derived.<br /><div style="text-align: left;">Mathematics is everywhere. It is not possible to give its perfect definition. Mathematicians and scientists have given definitions according to what they experienced according to their personal nature. The concept of mathematics is being clarified by presenting its definitions under some points<br /><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><a href="https://1.bp.blogspot.com/-wuj1zZmGlpI/XYYnNRilXiI/AAAAAAAAMXo/A2E0Fdo5eq8981GUlFIomXtHe1f5-3SOwCLcBGAsYHQ/s1600/Definitions_of_Mathematics.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img alt="Definitions of Mathematics " border="0" data-original-height="640" data-original-width="1280" height="320" src="https://1.bp.blogspot.com/-wuj1zZmGlpI/XYYnNRilXiI/AAAAAAAAMXo/A2E0Fdo5eq8981GUlFIomXtHe1f5-3SOwCLcBGAsYHQ/s640/Definitions_of_Mathematics.png" title="Definitions of Mathematics " width="640" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><h4><span style="font-size: large;"><i><u>Definitions of Mathematics </u></i></span></h4></td></tr></tbody></table><h3 style="text-align: left;"><i><u><span style="font-size: large;"><b>3. Science of Magnitude and Numbers</b></span></u></i></h3></div> The fundamental element of mathematics is number. Science is a storehouse of direct experiences. The numbers give a sense of the magnitude of the physical world. Also, they represent the nature, shape and type of the object world as magnitude. This is not a goal in itself, but rather constructs basic materials for a purpose. They provide numerical information for any process of inquiry. This inquiry process appeals to what, how much, how much man's curiosities. This definition of mathematics is prevalent from the primitive stage of human civilization. Probably, the tribals used to choose the leadership of their group on the basis of their wealth. Livestock numerical magnitude was used for this. Thus, the initial use of mathematics was in calculating or counting.<br /><h3 style="text-align: left;"><b><i><u><span style="font-size: large;">4. Mathematics as the science of quantity and space -</span></u></i></b></h3>Like science, mathematics is also a systematic and systematic form of Empirical Experiences. In this also, there is a study of the interrelations of numerical facts related to the interval. In the analysis, election and regulation of these facts there is a natural use of Logical Reasoning which is used in problem-solving in a new situation. Mathematics has become a major tool of physical research due to its processing nature.<br />According to Barthlaut - "Mathematics is an indispensable instrument for all physical researches."<br />By thinking about this form of mathematics, it becomes clear that the means of expression for science subjects is mathematics. Establishment of work-causal relationship is based on mathematical logic to understand the phenomena occurring in the interval. That is why Kant went on to say - "Natural science is only science as long as it is mathematical (A natural science is a science only in so for as it is mathematical)." The ideas of comte also correspond to the views of Kant. According to Kamte - "Science education that does not begin with mathematics is necessarily fundamentally flawed (A scientific education which does not commence with mathematics is, of necessity, defective at its foundation)."<br /><h3 style="text-align: left;"><i><u><span style="font-size: large;">5. An important means of generalization</span></u></i></h3>Mathematics is the main tool for perception and generalization of objects based on specific experiences. This is a natural process of induction reasoning. That is why Henri Poincare says - "Mathematics is the giving of the same name to different things". According to the Harvord committee of 45 - "Mathematics can be defined as the science of abstract form. An essential requirement of the essence of structure in a physical system sense is the appreciation of coating in art and connotation in music." Is not less than. It is nothing less than astrology in economics as generalized by objects and events. Mathematics is specific objects and events. The study of the sequence displayed in the generalized format by abstract is - General Education in a Free Society (Mathematics may be defined as the science of abstracted from ...... the discernment of structure is essential no less to the appreciation of a painting or a symphony than to understand the behavior of a physical system, no less in economics than in astronomy. Mathematics studies order obstructed from the particular objects and phenomena which exhibit it, and in a generalized form - General Education in a Free Society). "<br /><h3 style="text-align: left;"><b><i><u><span style="font-size: large;">6. Applied Science for the Expression of Sciences</span></u></i></b></h3>Mathematics and mathematical methods are the only means for acquiring and presenting knowledge in Physical and Biological Sciences. The major role of mathematics for this is reflected in Roger Bacon's statement - "Mathematics is the gateway and key to the sciences. Since a man who is not ignorant of mathematics cannot get the knowledge of the sciences and the objects of the world, the whole knowledge of mathematics is neglected. Is worse for. Worse than that, such ignorant humans neither know this ignorance nor can they cure it. (Mathematics is the gate and key of the sciences ...... Neglect of mathematics work injury to all knowledge, since he who is ignorant of it cannot know the other sciences or the things of the world. And what is worse , men who are thus ignorant are unable to perceive their ignorance and so do not seek a remedy. ")<br />Sullivan (JWN Suliwan - Atlantic monthly, March, 1933) showed the importance of mathematics in physics in this way - "As far as physics is concerned, it has been proved that the nature of the principles that are discussed in this, we should Need knowledge of their mathematical structure rather than knowledge of it (it has become evident that, so far as the science of physics is concerned, we do not require to know the nature of the entities, we discuss, but only their mathematical structure) "JW Mellor) in Chemistry made his statement -" Physical and practical Valid Chemicals Uttrapekshit developments is almost impossible without the executive conscious mass of higher mathematics (It is Almost impossible to follow the latter developments of physical or general chemistry without working knowledge of higher mathematics). " It is underlined. The imperative of mathematics in biology is proved by Comte's statement that - "In mathematics we find the primordial source of conscience and see mathematics as the destination of biologists where they conduct research. (In mathematics we find the primitive source of rationality and to mathematics must be the biologists resort to means to carry on their researches). "Physical sciences include physics and chemistry in addition to astronomy. . It is well known that currently astrology itself is a major branch of mathematics. It has arithmetic, geometry, trichrometry, algebra. Thus mathematics is the power to provide expression and existence to physical and biology.<br /><h3 style="text-align: left;"><b><i><u><span style="font-size: large;">7. Mathematics as the method of progress of various subjects -</span></u></i></b></h3>The statement of Mathematics Introduction to Economics - Mcgraw Hill Book Co. Inc. 1936) by Evans (G. L. Evans) is an adequate explanation for this definition. It is clear that every scripture of study is satisfied in calling itself science or believing it. Political science, economics, military science, geography, history etc. It is said that scientific method has become the main method of study, which is based on mathematics itself. These subjects are clearly identified by natural and applied sciences. Theoretical sciences have been called from the point of view. Mathematics is a major force in the development of these subjects and in moving them towards completion. Evans, as we call it to be distinguished from the natural and applied sciences, is a process that comes late in the developmental order of the subject. Authentically it has been observed that some fields of knowledge are hardly ready for this, as its free will is an uniqueness in constructing definitions and concepts. It does not just identify the facts, but when we get this feeling for the concept and definition, then we join the chain of deductive reasoning. We are drawn to a characteristic method of construction and analysis. We call this method the mathematical method. It is not a question of whether mathematics is desirable in this subject or not. In fact, the adoption of a mathematical method is an essential condition for moving forward in the path of progress.<br />(The systematization which occurs in a theoretical science, as we properly call it in order to distinguish it from a natural or an applied science, is a process which is apt to came late in the development of a subject. Everyday some fields of knowledge are hardly ready from it, for it is tyfied by a free spirit of making hypotheses and definitions rather than a mere recognition of facts. But when we find this feeling for hypotheses and definition and, in addition become involved in chains of deductive reasoning, we are driven to a characteristic method of construction and analysis which may be call the mathematical method. It is not a question whether mathematics is desirable or not in such subject. We are in fact forced to adopt the mathematical method as a condition of further progress). "<br /><h3 style="text-align: left;"><b><i><u><span style="font-size: large;">8. Mathematics as the means to draw conclusion and judgment.</span></u></i></b></h3>It is clear that mathematics is a process of collection, classification and analysis of numerical facts. This entire action is performed to achieve a certain objective. Its purpose is basically to test the concept. After analysis, there are inference, retesting, Interpretation, conclusion and decision. Thus, mathematics is a means of concluding and deciding in its ultimate destiny. According to Benjamin Peirce 1809–1880, "Mathematics is the science that reaches the required conclusion."<br /><h3 style="text-align: left;"><b><i><u><span style="font-size: large;">9. Mathematics as the perception of generalization</span></u></i></b></h3>In the case of absolute, the subject remains in a state of confusion. There is such a complete state of generalization of mathematics in which a person finds himself unable to explain in normal language what subject he is talking about or what is being said is true. This is the ultimate state of feeling.According to Russell, "Mathematics is a subject in which it can never be said about which subject is being talked about or what is being said is true.</div><img src="http://feeds.feedburner.com/~r/SatyamMathematics/~4/pseWaAYddAM" height="1" width="1" alt=""/>satyam coaching centrehttp://www.blogger.com/profile/12788483628699913686noreply@blogger.com0https://www.satyammathematics.com/2019/09/definitions-of-mathematics.htmltag:blogger.com,1999:blog-4893862652325568386.post-86178205907770421092019-09-19T07:09:00.000+05:302019-09-19T07:09:38.880+05:30Importance of Mathematics<div dir="ltr" style="text-align: left;" trbidi="on"><h1 style="text-align: left;"><i><u>Importance of Mathematics -</u></i></h1><h2 style="text-align: left;"><i><u>Introduction-</u></i></h2>The importance of mathematics has been mentioned in this article. It has been elaborated that the field of mathematics is very wide and has made inroads in other subjects as well. The entry of Mathematics has enriched other subjects and broadened their scope. A very brief description was posted in its first part. But in this part, detailed information is being presented incorporating the previous part. Hope you will like it like the previous part. If you like the article, then share and like it with your friends and if you have any suggestion or any problem, then comment and tell. Read this article completely.<br /><h2 style="text-align: left;"><i><u>1. Importance of Mathematics</u></i></h2>Today's era is the era of science. All the physical and technological progress due to science should be given to mathematics. Along with the progress of mathematics, there has been progress in the field of science and the progress of science in future depends on mathematics itself. If we study the mathematics courses in the progressive countries of the world, we will see that the level of the study material of mathematics in the primary and secondary schools there is very progressive and the students get unprecedented help in learning science through the study of mathematics. Along with social progress, the levels of mathematics courses are also being improved and the educationists there are still working in this direction. In countries where the curriculum of mathematics is not progressive, physical progress has also been relatively less. The Kothari Commission has written on the importance of Science and Mathematics, "Science should be made an important subject. Therefore we recommend that Science and Mathematics should compulsorily teach all students in the first ten years of school teaching as a part of general education. Additionally, for students with higher than average qualifications, special courses in these subjects at secondary stage If the system. These programs can only be useful when science Patycharyaon be made latest re-organize, to communicate the re-power in teaching methodology and should be appropriate facilities for teaching the subject.<br />The commission has written mentioning the important place of mathematics in modern education -<br />The main characteristic of adopting scientific vision is to express things quantitatively. Hence, mathematics becomes more important in modern education. It has an important hand in the advancement of physics, as well as it is being used more and more in the development of biological sciences. The advent of automation science and cybernetics in this century has led to the birth of new scientific industrial revolution and it has become even more necessary to pay special attention to the study of mathematics. The appropriate basis of knowledge of this subject should be laid in schools.<br />Mathematics can be called the soul of science. Science without mathematics will prove incapable of maintaining its existence. Modern era, because it is scientific age, so the foundation of this era is based on mathematics. It is necessary to have a comprehensive knowledge of the important contribution of mathematics in meeting the needs of the technological age.<br />Today the principles of mathematics are being widely used in physics, chemistry, biology, botany, geology, astrology, geography, economics, psychology, logic, commerce, music and many important fields. With the use of mathematics, it is possible to have objectivity and practicality in the content of these areas and due to this, material and prosperity has developed in the society.<br /><h2 style="text-align: left;"><i><u>2. Personality Development -</u></i></h2><h3 style="text-align: left;"><i><u><span style="font-size: large;">(1.) Development of intelligence: - </span></u></i></h3>There is no other subject other than Mathematics which can keep the students active like Mathematics. To solve any problem of arithmetic, students have to do mental work. Which can develop creative and creative in students. Due to the study of arithmetic, reasoning, memory, concentration, thinking and thinking power etc. Nashik actions develop.<br /><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><a href="https://1.bp.blogspot.com/-RwB1Ft1xsdo/XX-xMboevfI/AAAAAAAAMUc/2bWRC2GYCXYiPcmIAnawdxanr-QqmxvFQCLcBGAsYHQ/s1600/Importance-of-Mathematics-part-2.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img alt="Importance of Mathematics" border="0" data-original-height="1067" data-original-width="1600" height="426" src="https://1.bp.blogspot.com/-RwB1Ft1xsdo/XX-xMboevfI/AAAAAAAAMUc/2bWRC2GYCXYiPcmIAnawdxanr-QqmxvFQCLcBGAsYHQ/s640/Importance-of-Mathematics-part-2.jpg" title="Importance of Mathematics" width="640" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><h4><span style="font-size: large;"><i><u>Importance of Mathematics</u></i></span></h4></td></tr></tbody></table><h2 style="text-align: left;"><b><i><u><span style="font-size: large;">(2.) Development of culture: - </span></u></i></b></h2>The study of arithmetic gives the students the knowledge of equality, regularity and orderliness which are the major parts of the culture. By culture we mean the good and welfare things which are given by their ancestors. They join. Apart from this, mathematics has contributed in removing poverty, ignorance, disease, illiteracy, superstition from the society.<br /><h3 style="text-align: left;"><i><u><span style="font-size: large;">(3.) Discipline: -</span></u></i></h3>By conducting mathematics studies to the students, mental powers like regularity, correctness, originality, orderliness, honesty, concentration, imagination, confidence, memory, quick understanding power are developed by which their brain is disciplined.<br /><h3 style="text-align: left;"><i><u><span style="font-size: large;">(4.) Development of sociality: - </span></u></i></h3>Man is a social animal and students also have to go ahead and become a part of society. Knowledge of social life mathematics is needed because in society also the need to keep transactions, business and accounts. Which is dependent on the knowledge of mathematics. Different inventions, needs, in moving different parts of society from one place to another and bringing different parts of society closer. To switch to support a major contribution to mathematics.<br /><h3 style="text-align: left;"><b><i><u><span style="font-size: large;">(5.) Development of scientific approach: -</span></u></i></b></h3>Knowledge of Mathematics is also necessary for students of Zoology and Botany. Students without knowledge of mathematics will have difficulty in studying these ideas. Knowledge of arithmetic is necessary to know the number of bones, nerves etc. of an organism, length of bones, mutual ratios of bones, weight of bones etc. While studying cells, it is necessary for students to have knowledge of square, circle, polygonal region etc. The study of geometry proves to be helpful in this context. Knowledge of percentage is desirable to find the amount of carbon ,hydrogen, nitrogen etc. in cells. To understand Mendel's theory, it is necessary to seek the help of mathematics.<br />Similarly, knowledge of basic principles of mathematics is also helpful in botany. Numerous mathematical functions are used in the study of flowers, leaves, roots etc. There is a need to establish mutual mathematical relationships in soil, germination, seeds, plant flowers, fruits etc. and these relationships are displaced by many experiments. In botany, suffixes like density, distribution, frequency, area etc. are also used. The graph is used in every field of botany which helps in understanding the relationship between the components of the situation.<br />Mathematics has made an unprecedented contribution in acquiring new knowledge in the areas of zoology and botany. Mathematics provides an important basis in new discoveries and research and helps in comparative study of findings.<br /><h3 style="text-align: left;"><i><u><span style="font-size: large;">6. Mathematics and Economics -</span></u></i></h3>Today's era is the era of economics and meaning holds an important place in the life of every human being. As technology progresses, the use of economics is increasing. It is possible to bring certainty in the laws of economics through mathematics. Now the situation has come that knowledge of mathematics has become necessary for the student of economics. Econometrics is an important branch of economics in which mathematics and statistics are used. There are many subjects in economics which cannot be a proper explanation without the use of mathematics. For example economic topics like utility, demand and supply, national income, pricing, family budget, index, foreign trade, economic planning, inflation, currency devaluation, foreign exchange rate, investment analysis, tax assessment, public debt, population etc. The use of mathematics is necessary for interpretation, explanation and accuracy. From the field of mathematics, the content of economics is presented by scientific method using percentage, average, interest, equation, formula determination, circular and various types of graphs etc. With the help of mathematics, the student can easily understand many things in the field of modern economics. Algebraic formulas are used extensively in the areas of pricing, demand and supply, currency, planning etc. National income, population, foreign trade, production, family budget etc. can be well explained by graphs and concepts can be explained by pictures. The construction of planning formats is possible with the help of mathematics. All the progressive countries of the world have made economic progress through planning and the last five-year plans in India can be explained only with the help of mathematics. Data is required in planning and their average and percentage are known for comparative study and evaluation. In the modern era, the prosperity of each country depends on more exports and every country tries to earn foreign exchange so that this currency can be used to get the latest technological goods.<br /><br />Acquiring more foreign currency is possible only when the balance of payments is in favor of the country. For this, exports have to be more than imports and all this information can be practical only when mathematics is used for it. Countries have to resort to devaluation of currency many times to favor payment balance. The function of the correct amount of this devaluation is impossible without mathematics. Therefore, it is necessary for economists in economic institutions to have a good knowledge of mathematics. Today every citizen is troubled by the steady increase in values. The effect of the decrease or increase in the amount of currency on the price level can be calculated with the help of mathematics. The life-cost index is used to determine dearness allowance etc. in which the principles and competencies of mathematics are used in abundance. In the modern era, an increase in population leads to an imbalance and an increase in poverty. Quantitative changes in the population by birth rate, death rate, survivor rate, etc. are known with the help of mathematics and their impact on employment and prices is assessed. Population experts of the world are recommending 'population mathematics' in schools.<br /><h3 style="text-align: left;"><i><u><span style="font-size: large;">7. Mathematics and Psychology</span></u></i></h3>Knowledge of mathematics has become necessary due to the use of measurement procedures in modern psychology. General knowledge of average, percentage, ratio, graph is very important for a student of psychology.However, experts in the field of psychology need to be well acquainted with mathematical thinking, as it is mandatory for them to use important procedures such as formulation, generalization, substitution. Knowledge of Mathematics is helpful for understanding important areas of psychology like development of child, learning of dynasty and environment, intelligence test, personality, measurement of interest and interest. In psychology, mathematics is used extensively in calculating tests, measurement, comparison, study of elements, authentication, diagnosis, treatment, etc. Relationships with any aspect of personality, speed of development, influence of environment, etc. are displayed with formulas and graphs. With the use of mathematics in every field of psychology, it has been possible to study the qualitative aspect in terms of quantity and numbers. The use of mathematics has been important in checking the veracity of the research conducted in the field of psychology. Without mathematics, psychology would remain only the script of definitions and narratives and its widespread use would not be possible. In today's era, psychology is being used in every field and with the help of mathematics, the form of the rules and conclusions of psychology is measured in terms of circumstances. In psychology, statistics is used extensively and in finding many conclusions, the principles and formulas of statistics are widely used. In psychological testing, the findings are made by using sufficient amount of mathematics.</div><img src="http://feeds.feedburner.com/~r/SatyamMathematics/~4/II0ksa1xXMI" height="1" width="1" alt=""/>satyam coaching centrehttp://www.blogger.com/profile/12788483628699913686noreply@blogger.com0https://www.satyammathematics.com/2019/09/importance-of-mathematics.htmltag:blogger.com,1999:blog-4893862652325568386.post-62274177286707043742019-09-15T08:22:00.000+05:302019-09-15T08:22:40.863+05:30Types of Triangle and Their Definition<div dir="ltr" style="text-align: left;" trbidi="on"><h1 style="text-align: left;"><b><i><u>Types of Triangle and Their Definition-</u></i></b></h1><h2 style="text-align: left;"><i><u>1.The figure formed by connecting three noncollinear points (the vertices) by line segments.</u></i></h2>(2.)The figure described in (1)together with the points in the same plane and interior to the figure. Six kinds of triangles are illustrated. As indicated in the above figures, an acute triangle is a triangle whose interior angles are all acute ;an obtuse triangle is a triangle that contains an obtuse interior angle ;a scalene triangle is a triangle is a triangle with two equal sides (the third side is called the base and the angle opposite it the vertex) ;a right triangle is a triangle one of whose angles is a right angle (the side opposite the right angle is called the hypotenuse and the other two sides the legs of the right triangle) ;an equilateral triangle is a triangle with all three sides equal (it must then also be equiangular, i. e., have its three interior angles equal). An oblique triangle is a triangle which contains no right angles. The altitude of a triangle is the perpendicular distance from a vertex to the opposite side, which has been designed as the base. The area of a triangle is one-half the product of base and the corresponding altitude. The area is equal to one-half the determinant whose first column consists of the abscissas of the vertices, the second of the ordinates (in the same order), and the third entirely of ones (this is positive if the points are taken around the triangle in counterclockwise order.)<br />Astronomical triangle - The spherical triangle on the celestial sphere which has for its vertices the nearer celestial pole, the zenith, and the celestial body under consideration.<br /><h2 style="text-align: left;"><i><u>2.Congruent triangles-</u></i></h2><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><a href="https://1.bp.blogspot.com/-Y58xU1KmwP0/XXaECV_FMwI/AAAAAAAAMQE/Zg9wwxVp6bAHHxOT1Pa0ki0POT8OfAaogCLcBGAs/s1600/Types-of-Triangle-and-Their-Definition.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img alt="Types of Triangle and Their Definition" border="0" data-original-height="1600" data-original-width="1600" height="640" src="https://1.bp.blogspot.com/-Y58xU1KmwP0/XXaECV_FMwI/AAAAAAAAMQE/Zg9wwxVp6bAHHxOT1Pa0ki0POT8OfAaogCLcBGAs/s640/Types-of-Triangle-and-Their-Definition.jpg" title="Types of Triangle and Their Definition" width="640" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><h4><span style="font-size: large;"><i><u>Types of Triangle and Their Definition</u></i></span></h4></td></tr></tbody></table>In Plane geometry, it is customary to say that two figures are congruent if one of them can be made to coincide with the other by a rigid motion in space (i.e., by translations and rotations in space). Thus it might be said that two figures are congruent if they "differ only length in location."Two line segments of equal length are congruent and two circles of equal radii are congruent. Each of the following is a necessary and sufficient condition for two triangles to be congruent:(i.) There is a one-to-one correspondence between the sides of the other for which corresponding sides are equal (ii.) there is a one-to-one correspondence between the sides of one triangle and the sides of the other for which two sides and the angle, determined by these sides are equal, respectively, to the corresponding sides of the other triangle and the angle determined by these sides (SAS) ;(iii) there is a one-, to - one correspondence between the angles of one triangle and the angles of the other for which two angles and the sides between the vertices of these angles are equal, respectively, to the corresponding angles of the other triangle and the side between the vertices of these angles (ASA). If we change the definition of congruence to allow only rigid motions in the plane, a different concept of congruence results. In solid geometry, two figures are congruent if one of them can be made to coincide with the other by a rigid motion in space. Sometimes such figures are said to be directly congruent and two figures for which one is directly congruent to the reflection of the other through a plane are oppositely congruent (then two figures are either directly or oppositely congruent if and only if one can be made to coincide with the other by a rigid motion in four-dimensional space). Often when giving axioms for a geometric system,congruence is taken as an undefined concept restricted by suitable axioms.<br /><h3 style="text-align: left;"><i><u><span style="font-size: large;"><br />3.Pascal's triangle -</span></u></i></h3>A triangular array of numbers composed of the coefficients in the expansion composed of the coefficients in the expansion of (x+y) ^n for n=0,1,2,3,etc.The "triangle" extends down indefinitely, the coefficients in the expansion of (x+y) ^n being in the (n+1)st row. As shown, the array is bordered by 1's and the sum of two adjacent numbers in one row is equal to the number in the next row between the two numbers. The array is symmetric about the vertical line through the "vertex"<br /> 1<br /> 1 1<br /> 1 2 1<br /> 1 3 3 1<br /> 1 4 6 4 1<br /> 1 5 10 10 5 1<br /><h3 style="text-align: left;"><i><u><span style="font-size: large;">4.Pedal Triangle -</span></u></i></h3>The triangle formed within a given triangle by joining the feet of the perpendiculars from any given point to the sides. The triangle DEF is the pedal triangle formed within the triangle ABC by the joining the feet of the altitude. The figure illustrates the fact that the altitudes of the given triangle bisect the angles of this pedal triangle.<br /><h3 style="text-align: left;"><i><u><span style="font-size: large;">5.Polar Triangle -</span></u></i></h3>Polar triangle of a spherical triangle. The a spherical triangle whose view is ertices are poles of the sides of the given triangle, the poles being the ones nearest to the vertices opposite the sides of which they are poles.<br /><h3 style="text-align: left;"><i><u><span style="font-size: large;">6.Solution of a Triangle -</span></u></i></h3>Finding the remaining angles and sides when sufficient of these have been given For a plane right triangle, it is sufficient to know any two sides, or to know one of the acute angles and one side. The unknown parts are found by use of trigonometric tables and the definitions of the trigonometric functions :if a, b, c represent the legs and hypotenuse, respectively, and A, B are the angles opposite sides a and b then a=b then a=b tan A =c sin A, b=c cosA, A =tan^-1(a/b),B=90-A. For an oblique plane triangle, it is sufficient to know all three sides and one angle (, except that when two sides and the angle opposite one of them is given there may be two solutions.<br />For a right spherical triangle, Napier's rules supply all the formulas needed. For formulas providing solutions of an oblique spherical triangle in cases when solutions of an oblique spherical triangle in cases when solutions exist.<br /><h3 style="text-align: left;"><b><i><u><span style="font-size: large;">7.Spherical Triangle -</span></u></i></b></h3>A spherical polygon with three sides ;a portion of a sphere bounded by three arcs of great circles. In the spherical triangle ABC, the sides of the triangle are a=angle BOC, b=angle AOC, and c=angle AOB. The angles of the triangle. </div><img src="http://feeds.feedburner.com/~r/SatyamMathematics/~4/EN62i7uvOz8" height="1" width="1" alt=""/>satyam coaching centrehttp://www.blogger.com/profile/12788483628699913686noreply@blogger.com0https://www.satyammathematics.com/2019/09/triangle-figure-formed-by-connecting.htmltag:blogger.com,1999:blog-4893862652325568386.post-15937871529355725692019-09-08T15:24:00.003+05:302019-09-14T21:58:47.648+05:30Satyam Mathematics <div dir="ltr" style="text-align: left;" trbidi="on"><h1 class="w3-center"><i><u>Satyam Mathematics</u></i></h1><h2 style="text-align: left;"><i><u>1.Mathematics-</u></i></h2><div><b><i>The logical study of shape,arrangement,quantity and many related concepts.Mathematics often is divided into three fields:algebra,analysis and geometry,However,no clear divisions can be made,since these branches have become thoroughly intermingled.Roughly,algebra involves numbers and their abstractions,analysis involves continuity and limits and geometry is concerned with space and related concepts.Tech. The postulational science in which necessary conclusion are drawn arc drawn from specified premises.</i></b></div><h2 style="text-align: left;"><b><i><u>2.Applied mathematics-</u></i></b></h2><div><b><i>A branch of mathematics concered with the study of the physical,biological and sociological worlds.It includes mechanics of rigid and deformable bodies (elasticity,plasticity,mechanics of fluids),theory of electricity and magnetism,relativity,theory of potential,thermodynamics,biomathematics and statistics broadly speaking a mathematical structure utilizing,in addition to the purely mathematical concepts of space and number,the notions of time and matter belongs to the domain of time and matter belongs to the domain of applied mathematics.In a restricted sense,the term refers to the use of mathematical principles as tools in the fields of physics,chemistry,engineering,biology and social studies.</i></b></div><h3 style="text-align: left;"><b><i><u><span style="font-size: large;">3.Mathematics of finance-</span></u></i></b></h3><div><b><i>The study of the mathematical practices in brokerage,banking and insurance.</i></b></div><h3 style="text-align: left;"><b><i><u><span style="font-size: large;">4.Pure Mathematics-</span></u></i></b></h3><div><b><i>The study and development of the principles of mathematics for their own sake and possible future usefulness,rather than for their immediate usefulness in other fields of science or knowledge.The study of mathematics independently of experience in other scholarly disciplines.Often the study of problems in applied mathematics leads to new developments in pure mathematics and theories developed as pure mathematics often find applications later.Thus no sharp line can be drawn between applied and pure mathematics.</i></b></div><div class="w3-content" style="max-width: 400px;"><div class="mySlides w3-container w3-red"><h1><b>Did You Know?</b></h1><h1><i>We plan to read self everytime</i></h1></div><img class="mySlides" src="https://1.bp.blogspot.com/-m5_OQhwwdTo/XRcf81BzdYI/AAAAAAAALI8/X1Ka_-iq-ykjbQKv6973hG8Y40U_9ttUgCLcBGAs/s640/satyam-quotes.jpg" style="width: 100%;" /> <br /><div class="mySlides w3-container w3-xlarge w3-white w3-card-4"><span class="w3-tag w3-yellow">Satyam!</span> Mathematics</div><img class="mySlides" src="https://1.bp.blogspot.com/-mus_pLW1H0k/XRcfXAPYqSI/AAAAAAAALI0/toscPBDLDPEQAn7Hx3w1DP9A61drc35_gCLcBGAs/s640/Satyam-Mathematics.jpg" style="width: 100%;" /> </div><script> var slideIndex = 0; carousel(); function carousel() { var i; var x = document.getElementsByClassName("mySlides"); for (i = 0; i < x.length; i++) { x[i].style.display = "none"; } slideIndex++; if (slideIndex > x.length) {slideIndex = 1} x[slideIndex-1].style.display = "block"; setTimeout(carousel, 2000); } </script> </div><img src="http://feeds.feedburner.com/~r/SatyamMathematics/~4/F6BD0zCeonE" height="1" width="1" alt=""/>satyam coaching centrehttp://www.blogger.com/profile/12788483628699913686noreply@blogger.com0https://www.satyammathematics.com/2019/09/satyam-mathematics.htmltag:blogger.com,1999:blog-4893862652325568386.post-75755678715603580632019-09-07T07:55:00.000+05:302019-09-07T07:55:03.697+05:30Diagnosis Examinations in Mathematics <div dir="ltr" style="text-align: left;" trbidi="on"><h1 style="text-align: left;"><i><u>Diagnosis Examinations in Mathematics </u></i></h1><h2 style="text-align: left;">1.<b><i><u>Diagnosis Examinations in Mathematics in Mathematics teaching -</u></i></b></h2>The term Diagnosis is used in Medical Science. Before treating the patient, their symptoms are studied and diagnosed and it is decided that what type of disease is there and how its treatment is possible? Diagnosis is necessary before treating the patient. If there were errors in diagnosis then it would be difficult to cure the patient. Diagnosis has great importance in medicine. In order to make a correct diagnosis, it is necessary to study the symptoms of the patient in detail. If inattentiveness was taken in the study of symptoms, the treatment would not be effective.<br /><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><a href="https://1.bp.blogspot.com/-o-aCoajN734/XXH5v3ecGvI/AAAAAAAAMM8/P1uLWqgYGMIyEOiz_b6EdEjlsZJ03qqLwCLcBGAs/s1600/Diagnosis_Examinations_in_Mathematics.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img alt="Diagnosis Examinations in Mathematics " border="0" data-original-height="1600" data-original-width="1067" height="640" src="https://1.bp.blogspot.com/-o-aCoajN734/XXH5v3ecGvI/AAAAAAAAMM8/P1uLWqgYGMIyEOiz_b6EdEjlsZJ03qqLwCLcBGAs/s640/Diagnosis_Examinations_in_Mathematics.jpg" title="Diagnosis Examinations in Mathematics " width="426" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><h4><span style="font-size: large;"><i><u>Diagnosis Examinations in Mathematics </u></i></span></h4></td></tr></tbody></table>Diagnosis and treatment in the classroom is also necessary for mathematics teachers. Most of the students are found to be weak in this subject and they do not understand many suffixes and principles clearly. If the teacher diagnoses the difficulties and weaknesses of the students, they can help them to learn the subject. Only after proper diagnosis can he adjust the teaching method as necessary.<br />It is necessary to consider here what are the reasons for the students being weak in mathematics and how can we be informed about these reasons? We know that physical, mental and social development of children is not equal in the classroom. In addition, some students are particularly exceptional in their physical and educational abilities. In such symptoms, they can also be excellent and can be inferior. It is the duty of a mathematics teacher that every student should take full advantage of teaching in the classroom. There are also students in the class who cannot make progress with classmates of their age and fall behind in this subject. Due to the students falling behind in the class, the teacher's work is interrupted and he experiences difficulties in making the mathematics subject an interesting subject for those students. Students' difficulties in mathematics can be diagnosed by clinical examinations. Clinical examinations in mathematics are also a kind of achievement tests, but the main purpose of clinical examinations is to diagnose the math problems of the students so that they can be treated. The student is not awarded marks in the clinical examination, but by looking at his answers, it is studied what kind of errors the student has made and what are the special things in these errors which are necessary for the teacher's knowledge. A special difference between the clinical examination and the achievement test is that the achievement test contains questions about the entire syllabus, but in the clinical examination different examinations are made for different sections of a sub-subject. For example- If we have to make a clinical examination about percentage in mathematics, then we will create a clinical examination by dividing the content of percentage into different sections and questions on suffixes, procedures, relations, calculations etc. related to each section. And study what kind of errors students make in these areas. O We will create questions for diagnosis by dividing the content of 'percent' into the following sections as per the requirement -<br />(1.) Meaning of percentage. Percent practical use in life.<br />(2.) Converting percentages into decimal fractions and ordinary fractions into percentages.<br />(3.) To convert percentages into ordinary fractions and ordinary fractions into percentages.<br />(4.) To find a certain percentage of a number.<br />(5.) Display of percentage by graph.<br />In Mathematics clinical examinations, students are also required to study calculation errors because most students make decimal calculations and unit related errors. If the calculation errors of the students are not treated then they will not be able to find the correct solution to the problems. The teacher should get detailed information about the difficulties and weaknesses of the students through clinical examinations and take necessary remedies before teaching the text of the advance lesson in class.<br />Due to students being weak in mathematics -<br />Students are often found to be weak in mathematics due to the following reasons, which is essential for the mathematics teacher -<br /><h2 style="text-align: left;"><b><i><u>2. Due to sharp or retarded student (Due to sharp or retarded student) -</u></i></b></h2>Students who are sharp or retarded fall behind in the classroom. Sharp students do not get the required encouragement in the classroom and keep their attention outside the classroom. The level of classroom teaching is not favorable to them and they start thinking that what they are being told comes to them or can be learned later. The result is that they fall behind. Similarly, students with low intelligence do not understand the teacher's things and they are not able to progress in the classroom with the teaching speed of the teacher. Such children also fall behind and they find mathematics a very difficult subject. As a result, students do not get the full benefit of classroom teaching.<br />In such a situation, it becomes the duty of the teacher of mathematics to use such teaching methods that meet the subject related needs of the children who are intelligent and intelligent. The teacher should also overcome the personal difficulties of the students in mathematics through personal efforts so that they continue to progress. The organization of the content presented in the class should also be such that the students with sharp intellect and with mental intelligence find the text content interesting and attractive.<br />3. Impact of students' domestic problems -<br />Sometimes domestic problems also present obstacles for students to study. There are many elements like fear, quarrels, sickness, illiterate family, poverty which keep the attention of the students. If the mathematics teacher is familiar with the students' circumstances, then he can coordinate with these obstructing elements while making the teaching plan. The teacher can solve many problems of the students by sympathy for students and loyalty to their work. It is very difficult to give a definite solution to any problem, because the solution to human problems depends only on the humanitarian point of view.<br /><h3 style="text-align: left;"><b><i><u><span style="font-size: large;">4. Effect of students' math background</span></u></i></b></h3>It has also been observed that students' mathematics background has an impact on their progress. Due to lack of clear knowledge of the suffixes and procedures of previous classes in mathematics, students have difficulties in understanding the new suffixes and processes of mathematics. Many students do not have clear knowledge of number related digits, localization of numbers, suffixes related to all four processes of numbers etc. and they make errors in calculations. They do not know well about many kinds of essential things in addition, rest, multiplication and division. Due to these deficiencies, they find mathematics to be a difficult subject in all further classes. Before starting a new lesson, a teacher of Mathematics can solve the problems of students by getting them through clinical examinations. Similarly, students make errors using the decimal system. In problems based on rupees, money, kilometers, centimeters, quintals, kilograms, grams, etc., they make errors due to unclear information about the corresponding suffixes of the decimal system. The teacher can know the errors of the students through clinical examinations and can prepare a teaching plan for their treatment. Use of computer is also beneficial to make the calculation successful.<br />Many types of mistakes are also made in mathematics. Students do not understand the terminology of mathematics, the language of the problem, the meaning of the definitions and make errors. They are not able to solve problems due to lack of knowledge of symbols, formulas, units etc.<br /><h3 style="text-align: left;"><b><i><u><span style="font-size: large;">5. Chronic absenteeism and physical deficiencies -</span></u></i></b></h3>Chronic absenteeism and physical deficiencies also present obstacles to learning mathematics and students remain weak in this subject. The mathematics teacher has special responsibilities in this context.</div><img src="http://feeds.feedburner.com/~r/SatyamMathematics/~4/i-HCSU55bWM" height="1" width="1" alt=""/>satyam coaching centrehttp://www.blogger.com/profile/12788483628699913686noreply@blogger.com0https://www.satyammathematics.com/2019/09/diagnosis-examinations-in-mathematics.htmltag:blogger.com,1999:blog-4893862652325568386.post-59871958967573560522019-09-06T07:53:00.000+05:302019-09-06T07:53:11.342+05:30Commercial Arithmetic <div dir="ltr" style="text-align: left;" trbidi="on"><h2 style="text-align: left;"><b><i><u><span style="font-size: large;">Commercial Arithmetic -</span></u></i></b></h2><h2 style="text-align: left;"><i><u>1.Shares and Dividends</u></i></h2>A company is established with the efforts of a few willing partners to run a large business. Directors are chosen for managing the company. The required capital is divided into small parts. These parts are called shares which are usually of 100 or 10 rupees. Any person can buy and sell shares as per his wish. The person who bought the shares is called a share holder or partner. Dividend or Dividend is divided among the partners in proportion to the capital invested.<br />Initially, some part is taken from each participant by not taking the entire money of its parts. The remaining portion of the share is demanded from them when required.<br />No partner can withdraw his parts from the company. He can sell his parts. If the company is in profit, then the market value of the share increases from the real value and the market value of the share decreases on loss. But the market value of the share does not affect the capital of the business. Suppose Sohan has a share of Rs 100 on which the company gives him 6% profit. Sohan will get a benefit of Rs 5 per year. Even if the value of the share in the market rises to Rs 115, the partner will only get Rs 6.<br /><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><a href="https://1.bp.blogspot.com/-HNjzSO1FslM/XWokDvwYRhI/AAAAAAAAMFg/tO71xje9YpMRTmIQii6qpC2lHSiSGr7bgCLcBGAs/s1600/Commercial-Arithmetic.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img alt="Commercial Arithmetic -" border="0" data-original-height="152" data-original-width="333" height="292" src="https://1.bp.blogspot.com/-HNjzSO1FslM/XWokDvwYRhI/AAAAAAAAMFg/tO71xje9YpMRTmIQii6qpC2lHSiSGr7bgCLcBGAs/s640/Commercial-Arithmetic.png" title="Commercial Arithmetic -" width="640" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><h4><span style="text-align: left;"><i><u><span style="font-size: large;">Commercial Arithmetic</span></u></i></span><span style="font-size: small; font-weight: 400; text-align: left;"> -</span></h4></td></tr></tbody></table>The company gives profit on the actual value of the share and not its market value.<br />The company pays dividends on the value of the share that has been paid. In the above example, if Sohan has paid only Rs 75, then the company will pay him (75x6) / Rs 100 ie Rs 4.50.<br /><h2 style="text-align: left;"><i><u>2. Banking -</u></i></h2><div style="text-align: left;"> Every country in the world has its own currency, with the help of which business runs. The currency of our country is India. The entities that buy and sell currency are called banks. In other words, a bank is an institution where people can deposit their savings and can get a loan from there under certain conditions.</div><h3 style="text-align: left;"><i><u><span style="font-size: large;">3. Taxation</span></u></i></h3>The government spends a lot of money to carry out some basic activities like maintaining law and order, providing fair justice, protecting the country, maintaining the status of currency, etc. Collective demands are also increasing with time. As a result of this, people are now expecting the government to play an important role in improving people's lives and providing more and more facilities to them. The new definition of public welfare state has now become that the difference between the general public and the upper class persons should be minimized. Today's citizens are demanding the government to implement various social measures like removing unemployment and providing best facilities for education, health etc. All these activities have placed a new responsibility on the government and as a result government expenditure is increasing. To meet this expense, the government has to make arrangements to raise funds from the residents of the country and in some situations (like tourists and travelers) non-residents. The money to be collected is obtained from various sources, of which there is an important source.<br /><h4 style="text-align: left;"><i><u><span style="font-size: large;">3 (1.) Taxation</span></u></i></h4>You must be familiar with the names of income tax, property tax, gift tax, sales tax etc. All these taxes are proposed, increased or reduced each year in the Central Government Budget or the State Governments Budget. The taxes levied by the Central Government include income tax, property tax, gift tax, Central Excise and Customs, Central Sales Tax, etc., while taxes levied by the State Governments, Agricultural State Tax, Entertainment Tax, State Excise and Sales Tax. Etc. come. Local bodies like Municipal Corporation, Municipalities, Cantonment Board, Zilla Parishad etc. are also imposed. Property taxes, professional taxes, octroi, education fees etc. come under the taxes brought by them. In other words, it is quite clear in which areas the central government has to impose taxes. As the central government receives a significant amount of tax as compared to the states and local bodies, the central government provides financial assistance to each state / union territory from its central pool to meet the expenditure on development. . The following are the symptoms of tax -<br />(1.) It is a mandatory contribution, although it can be paid at will.<br />(2.) It is a personal obligation.<br />(3.) It is a contribution towards a common good and there is no cost to get some additional facility.<br />(4.) It is imposed according to certain statutory requirements.<br /><h4 style="text-align: left;"><i><u><span style="font-size: large;">3 (2.) Income Tax</span></u></i></h4>It is a tax that is levied on the income of an individual or group of people. Every person (or group of people) whose annual income exceeds a specified limit, has to pay a part of their income to the government as income tax. At the beginning of every financial year, the government fixes the income tax rates.<br /><h4 style="text-align: left;"><i><u><span style="font-size: large;">4. Payment under installments -</span></u></i></h4>They often take payment in installments of money that banks give as loan. The insurance amount is also paid in installments.The insurance amount is also paid in installments. Sometimes merchants and shopkeepers also allow their customers to pay in installments. Some people buy houses on installments etc. Savings are also made in installments for the loan redressal fund.<br />To pay at equal time intervals under certain conditions is called payment in installments. The amount of money that is paid at one time interval is also called the installment amount or the installment in short.<br /><h4 style="text-align: left;"><i><u><span style="font-size: large;">5. Partnership</span></u></i></h4>Doing business with two or more persons is called a partnership and each person is called a partner. The money held by the partners is called capital. Finally, the profit or loss in the business is distributed to the partners in proportion to the amount of capital and the time it is engaged.<br />Types of Shares - There are two types of shares -<br />(1.) Simple sharing (2.) Complex sharing<br />(1.) Ordinary sharing - is one in which the partners invest their capital for the same time. In this, the profit or loss is divided according to the ratio of capital.<br />(2.) Complex sharing - is one in which partners invest their capital for different times. Therefore, the profit or loss made to each partner at the end of the year depends on both the capital and the time he / she applies.</div><img src="http://feeds.feedburner.com/~r/SatyamMathematics/~4/j49zs8kYI-4" height="1" width="1" alt=""/>satyam coaching centrehttp://www.blogger.com/profile/12788483628699913686noreply@blogger.com0https://www.satyammathematics.com/2019/09/commercial-arithmetic.htmltag:blogger.com,1999:blog-4893862652325568386.post-43772211120262631712019-08-31T07:34:00.000+05:302019-08-31T07:34:06.054+05:30Mathematics club<div dir="ltr" style="text-align: left;" trbidi="on">Mathematics club<br /><h2 style="text-align: left;"><i><u>1.Introduction -</u></i></h2>Mathematics is commonly referred to as a difficult subject. This situation is not new. From the primary level, such views of students are formed in relation to this subject. Perhaps similar views are of teachers and parents and guardians too. On the other hand, it is also the case that students are attracted to mathematics in large numbers. The main reason for this contradiction is that even though mathematics is considered difficult, students choose this subject because of its practical utility. Everyone understands the importance of mathematics in life. Still, its usefulness could not make it attractive. Mathematics is the scripture of symbols. It has primacy of subtle elements. Students easily assimilate the knowledge of the school world. But they have difficulty in understanding the subtle elements of mathematics. The second thing is that in mathematics, students get very less entertaining material. Therefore, to increase the interest of students in mathematics, it is necessary to include entertainment in it. With this, it is possible to reduce the difficulty caused by its subtlety. It is difficult to adequately incorporate entertainment in class-room instruction. Mathematical club is a fun and formal organization. Clubs are created in all regions of the world for leisure utilization and recreation. Therefore, to make the mathematics subject more interesting, a math club should be formed at the secondary level. The club itself develops and maintains interest in mathematics. Also, there is a meaningful platform for organizing the above mentioned activities because they cannot be organized under classroom teaching as per the requirement.<br /><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><a href="https://1.bp.blogspot.com/-xDuwjQYbiy8/XWi60P05ExI/AAAAAAAAMAA/8jSWB2eiBacxoHUaQ0OKMQttQ9KE0L-UgCLcBGAs/s1600/Mathematics-Club.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img alt="Mathematics club" border="0" data-original-height="194" data-original-width="259" height="479" src="https://1.bp.blogspot.com/-xDuwjQYbiy8/XWi60P05ExI/AAAAAAAAMAA/8jSWB2eiBacxoHUaQ0OKMQttQ9KE0L-UgCLcBGAs/s640/Mathematics-Club.jpg" title="Mathematics club" width="640" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><h4><span style="font-size: large;"><i><u>Mathematics club</u></i></span></h4></td></tr></tbody></table><h2><i><u>2.Club Activity-</u></i></h2>Actions such as games, games, puzzles, quiz, phecdotes are available for entertainment, but it is not possible to give sufficient time to these actions regularly in instruction. . These can be organized by Mathematics Club only. These events can help reduce the monotony of teaching mathematics.<br />All students like sports and sports. In particular, students up to the secondary level like games that contain elements of mystery, curiosity and wonder. Mathematical puzzles, coded questions and competitions all have these things. If these activities organized by the club refer to classroom teaching and help in solving problems, then students' interest in mathematics can be increased significantly.<br /><h3 style="text-align: left;"><span style="font-size: large;"><i><u>3. The usefulness of the club</u></i></span></h3>The Mathematics Club provides strength and stimulation to the study of mathematics. Its support is voluntary so it includes only those students who are really interested in mathematics and want to know the nature of the subject which is different from classroom work. Events in the Mathematics Club do not follow any formal hierarchical arrangement. In these, opportunities are given to those events which suit the wishes of its members. Secondary level students want to live together. They depend on each other in the backdrop of mental, social, family relationships, they want to hear their views and also want to hear the views of others. They enjoy the criticism of others and also want to listen to their criticism. Their differences with each other stimulate interest and stimulate discussion. The Mathematics Club provides an ideal platform in which free exchange of mathematical ideas can take place. It provides opportunities for clear critique of mathematical ideas. The Mathematics Club provides such an informal social environment as may not be possible in the regular classroom. It provides ample opportunities for free social interaction.<br /><h3 style="text-align: left;"><i><u><span style="font-size: large;">4. Organization -</span></u></i></h3>Mathematics club members should be formed by the students. The teacher's roles should be confined to the guide. They should help the students to run the club properly.<br />The school head became its patron. Its assistance should be voluntary but the member numbers should be limited so that the expectations of all the members can be satisfied. Its objectives should be clear. Active participation in each member is mandatory. The sponsor is a senior mathematics teacher who is proficient in running such organizations efficiently. Club meetings should be convened regularly as per the legislation. Its executive should have officials like Chairman, Vice President, Secretary, Co-Secretary, Treasurer. They should be elected by the members. Executive and general assembly meetings should be held by the members of the chairman itself. Executive and general assembly meetings should be held under the chairmanship of the Speaker. If the mental level of the members is almost equal, then their interest will remain in the programs of the club. For this, a legislation should be made first. It should be financed through school funds and membership fees. Voluntary organizations, related departments of State and Central Government and N.N. C. Er. Financial grants can be obtained from T.T.</div><img src="http://feeds.feedburner.com/~r/SatyamMathematics/~4/PEQJ85N89HY" height="1" width="1" alt=""/>satyam coaching centrehttp://www.blogger.com/profile/12788483628699913686noreply@blogger.com0https://www.satyammathematics.com/2019/08/mathematics-club.htmltag:blogger.com,1999:blog-4893862652325568386.post-5680297252138666082019-08-30T08:35:00.000+05:302019-08-30T08:35:00.096+05:30Heuristic Method in Mathematics<div dir="ltr" style="text-align: left;" trbidi="on"><h2 style="text-align: left;"><i><u>Heuristic Method in Mathematics</u></i></h2><h2 style="text-align: left;"><i><u>1.Bhumika (Introduction) -</u></i></h2>This method was discovered by Professor H. E. Armstrong. It was used to teach the subject of science, but due to its usefulness, it has also been used in mathematics. The word heuristic is a Greek word meaning "I search". In this method, students are active as investigators and they work themselves and get solutions for problems. This method is very important from an academic point of view because it produces scientific and mathematical perspective among the students. The child is an investigator. He is not a passive listener. He himself discovers the truth. He himself compiles the facts and finds the conclusion.<br /><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><span style="margin-left: auto; margin-right: auto;"><a href="https://www.satyammathematics.com/" target="_blank"><img alt="Heuristic Method in Mathematics" border="0" data-original-height="954" data-original-width="1300" height="468" src="https://1.bp.blogspot.com/-TWKqMUMalME/XWFkpV5teOI/AAAAAAAAL5c/rAd63Ha_lrccg5tlsb5IitupNK7fFt6UACLcBGAs/s640/Heuristic-Method-in-Mathematics.jpg" title="Heuristic Method in Mathematics" width="640" /></a></span></td></tr><tr><td class="tr-caption" style="text-align: center;"><h4><span style="font-size: large;"><i><u><a href="https://www.satyammathematics.com/" target="_blank">Heuristic Method in Mathematics</a></u></i></span></h4></td></tr></tbody></table>The student is the center of the process of this method. He searches through prior knowledge, observation, examination, thinking, argumentation etc. and tries to educate himself. In this method, the teacher presents problems in front of the students and the students themselves find solutions to them through their own efforts. These problems can also be presented to students through textbooks or other means. In this method, the teacher's job is to create a suitable environment for the students and make available their materials, instruments etc. which the students use to solve problems. The teacher's main job here is to provide guidance to the student so that they can discover new rules, solutions and relationships through their own efforts. It is necessary to keep in mind here that the age, ability and ability of students should also be taken into consideration in the search for rules related to the course material, otherwise this method will not prove profitable. The student is completely independent in problem solving.In the field of Mathematics, there are many sub-disciplines that can be discovered by the students related theories. For example, students can understand the text by knowing the following things themselves. Truthfulness, certainty, subtle observance, thinking power, self-learning are the ingredients of this method.<br />Percent - (1.) Percent is a fraction that contains every 100.<br />(2.) The use of percentages is helpful in comparative studies.<br />(3.) 100 in percentage is considered as base because 100 is a number which is neither too small nor too big.<br />Square root- (1.) Square root is related to square of geometry.<br />(2.) Square root is the measure of the side of a square. It is related to the number line.<br />(3.) The greater the square root, the greater will be the area of that square. The square root of the numbers can be found.<br />(4.) A square is a number that represents the area of a square.<br />Area - (1.) The amount of space that an object occupies is called its area.<br />(2.) Area of the rectangle = length x width<br />(3.) Area of the four walls of the room = 2 (L + W) x height<br />(4.) The floor and ceiling area of a room is same.<br />In this way, many such examples can be presented about which the students themselves, with the help of material and teacher, can understand the new definitions and principles. There are a number of sub-topics in mathematics textbooks about which the student himself can learn new things if he has the necessary hints and guidance on how to achieve them.<br />In this method, the teacher's job is to provide guidance and the students have to work hard on their own. The teacher presents the problem in front of the students and the students compile and study the material related to their efforts. The teacher is available for counseling and resolves the difficulties of the students and gives them necessary suggestions so that there is no obstruction in the progress of every student. The success of this method depends on the ability of the teacher to create the environment. In this method, the guidance and encouragement given by the teacher leads the students in the search for new knowledge. The prompts given by the teacher do not allow the students to move away from the right path. For example, the teacher presented the following problem to the students -<br />If a rectangle and a parallelogram lie between the same base and the same parallel lines, find the relation of their areas.<br />Here the teacher will indicate that if we find the area of the rectangle and the parallelogram, we will be able to find some.<br />After this, the students draw rectangles and parallelograms of various measurements given by the teacher in their books and find their area.<br /><h2 style="text-align: left;"><i><u>2.The teacher will solve the following difficulties of students at the individual or group level -</u></i></h2>(1.) Difficulty in finding the area of a parallelogram.<br />(2.) Difficulty in finding the area of a rectangle.<br />(3.) Difficulty in establishing interrelations in the areas of two triangles.<br />(4.) Any other difficulty related to this problem.<br /><h3 style="text-align: left;"><i><u><span style="font-size: large;">3. Benefits from the Heuristic method -</span></u></i></h3>(1.) There is an eagerness to know the truth among children and they make a habit of understanding the facts carefully. The child is an explorer himself.<br />(2.) Students accept the facts and evidence only after examining the arguments. This tendency proves useful to them in future high-level research. Get used to self-study.<br />(3.) Students develop the ability to criticize properly. Self-confidence develops.<br />(4.) Through this method, students develop confidence, self-reliance and scientific attitude. Develops the power to observe, test, compare, decide.<br />(5.) In this method, the teacher's work is very beneficial from the point of view of the development of the children and the students can take real benefit of the teacher's services. The accumulation of knowledge is based on self-motivation.<br />(6.) In this method, students themselves discover new knowledge and their knowledge is permanent and practical. There is no burden on memory.<br />(7.) In this method, there is no need to give home work to the children. After studying the problems himself, he finds the solution. The teacher and student come close.<br />(8.) The teacher gets opportunities to know the qualities and demerits of children and he can establish personal contact with them.<br />(9.) In this method the student can make maximum use of his experiences and abilities to gain new knowledge and increase his level of knowledge. Research is conducted for doing research.<br />(10.) In the process of learning, students can get correct information of many such things which are possible only by this method. The habit of hard work develops.<br /><h3 style="text-align: left;"><i><u><span style="font-size: large;">4. Limitations of the Heuristic method -</span></u></i></h3>(1.) In the initial stage, it is not possible for children to discover new knowledge. Their development is not of the level required by this method. Therefore, they cannot be expected to do research. This method will often fail in small classes. The task of teaching becomes very difficult.<br />(2.) Formal teaching by the teacher is necessary. The entire syllabus can be taught through this method. Only a few sub-topics in mathematics can be taught with this method. Lack of desired environment in the school.<br />(3.) Not all students in the class are of equal ability. Therefore, the use of this method is not possible for the existing classes. There is a lack of proper books.<br />(4.) In this method search is less and time is more waste. Current courses cannot be completed by this method within the stipulated time. Expecting high hope is totally inconsistent.<br />(5.) Many difficulties are presented by this method in front of the teacher. Collecting material for all students is not only difficult but impossible.<br />(6.) This method is useful only for such classes which have less number of students.<br />(7.) There are many esoteric aspects of knowledge and principles that students cannot understand without teaching. By relying on this method, the students will be able to learn only the thick things and remain ignorant of many subtle things.<br />(8.) This method is not practical in exam-centered education system.<br />(9.) This method is not possible for every teacher.<br /><h3 style="text-align: left;"><i><u><span style="font-size: large;">5. Suggestions to teachers -</span></u></i></h3>(1.) Do not use this method at primary level.<br />(2.) Use this method only for some selected sub-subjects when the student has qualified in mathematics.<br />(3.) When this method is used, give necessary and clear instructions to the whole class about the method.<br />(4.) There are sub-topics in geometry and algebra which need to be selected carefully.<br />(5.) After compiling the material, the diamond should plan to use this method.<br />In this method, the child is an investigator. He has to find the truth. The specialty of this method is to compile facts with the help of subtle inspection, thinking power and self-learning ability. Experimentation and problem solving are part of the analysis process. In this way research tendency and rational thinking develop.<br />Herbert Spencer's statement is notable in this context. He wrote, "Minimum statement should be made in front of the children. They should be motivated to find more and more."</div><img src="http://feeds.feedburner.com/~r/SatyamMathematics/~4/e9O0mbgjgXQ" height="1" width="1" alt=""/>satyam coaching centrehttp://www.blogger.com/profile/12788483628699913686noreply@blogger.com0https://www.satyammathematics.com/2019/08/heuristic-method-in-Mathematics.htmltag:blogger.com,1999:blog-4893862652325568386.post-43133969244611704282019-08-29T07:53:00.000+05:302019-08-29T07:53:36.618+05:30Exact Differential Equation<div dir="ltr" style="text-align: left;" trbidi="on"><h1 style="text-align: left;"><b><i><u><span style="font-family: "aparajita" , "sans-serif";"><span style="font-size: large;">Exact Differential Equation</span></span></u></i></b></h1><div class="MsoNormal"><span style="font-family: "aparajita" , "sans-serif";"><span style="font-size: large;">A differential equation of the form Mdx+Ndy=0<span style="mso-spacerun: yes;"> </span>………..(1)<o:p></o:p></span></span></div><div class="MsoNormal"><span style="font-family: "aparajita" , "sans-serif";"><span style="font-size: large;">Where M and N are functions of x and y or constants is said to be<span style="mso-spacerun: yes;"> </span>exact if the expression on the left hand side of (1) can be obtained directly by differentiating some function of x and y, If<span style="mso-spacerun: yes;"> </span>f(x,y) be such a function we must have d[f(x,y)]=Mdx+ndy<o:p></o:p></span></span></div><div class="MsoNormal"><span style="font-size: large;"><span style="font-family: "aparajita" , "sans-serif";">Or<span style="mso-spacerun: yes;"> </span>(</span><span style="font-family: "cambria math" , "serif"; mso-bidi-font-family: Aparajita;">𝛛</span><span style="font-family: "aparajita" , "sans-serif";">f/</span><span style="font-family: "cambria math" , "serif"; mso-bidi-font-family: Aparajita;">𝛛</span><span style="font-family: "aparajita" , "sans-serif";">x)dx+(</span><span style="font-family: "cambria math" , "serif"; mso-bidi-font-family: Aparajita;">𝛛</span><span style="font-family: "aparajita" , "sans-serif";">f/</span><span style="font-family: "cambria math" , "serif"; mso-bidi-font-family: Aparajita;">𝛛</span><span style="font-family: "aparajita" , "sans-serif";">y)dy=Mdx+Ndx<o:p></o:p></span></span></div><div class="MsoNormal"><span style="font-family: "aparajita" , "sans-serif";"><span style="font-size: large;">The necessary condition that the equation Mdx+Ndy=0<o:p></o:p></span></span></div><div class="MsoNormal"><span style="font-size: large;"><span style="font-family: "aparajita" , "sans-serif";">Be exact is that M=(</span><span style="font-family: "cambria math" , "serif"; mso-bidi-font-family: Aparajita;">𝛛</span><span style="font-family: "aparajita" , "sans-serif";">f/</span><span style="font-family: "cambria math" , "serif"; mso-bidi-font-family: Aparajita;">𝛛</span><span style="font-family: "aparajita" , "sans-serif";">x)<span style="mso-spacerun: yes;"> </span>and N=(</span><span style="font-family: "cambria math" , "serif"; mso-bidi-font-family: Aparajita;">𝛛</span><span style="font-family: "aparajita" , "sans-serif";">f/</span><span style="font-family: "cambria math" , "serif"; mso-bidi-font-family: Aparajita;">𝛛</span><span style="font-family: "aparajita" , "sans-serif";">y)<o:p></o:p></span></span></div><div class="MsoNormal"><span style="font-size: large;"><span style="font-family: "aparajita" , "sans-serif";">Again as (</span><span style="font-family: "cambria math" , "serif"; mso-bidi-font-family: Aparajita;">𝛛</span><span style="font-family: "aparajita" , "sans-serif";">M/</span><span style="font-family: "cambria math" , "serif"; mso-bidi-font-family: Aparajita;">𝛛</span><span style="font-family: "aparajita" , "sans-serif";">y)=(</span><span style="font-family: "cambria math" , "serif"; mso-bidi-font-family: Aparajita;">𝛛</span><sup><span style="font-family: "aparajita" , "sans-serif";">2</span></sup><span style="font-family: "aparajita" , "sans-serif";">f/</span><span style="font-family: "cambria math" , "serif"; mso-bidi-font-family: Aparajita;">𝛛</span><span style="font-family: "aparajita" , "sans-serif";">y</span><span style="font-family: "cambria math" , "serif"; mso-bidi-font-family: Aparajita;">𝛛</span><span style="font-family: "aparajita" , "sans-serif";">x)<span style="mso-spacerun: yes;"> </span>and (</span><span style="font-family: "cambria math" , "serif"; mso-bidi-font-family: Aparajita;">𝛛</span><span style="font-family: "aparajita" , "sans-serif";">N/</span><span style="font-family: "cambria math" , "serif"; mso-bidi-font-family: Aparajita;">𝛛</span><span style="font-family: "aparajita" , "sans-serif";">x)=(</span><span style="font-family: "cambria math" , "serif"; mso-bidi-font-family: Aparajita;">𝛛</span><sup><span style="font-family: "aparajita" , "sans-serif";">2</span></sup><span style="font-family: "aparajita" , "sans-serif";">f/</span><span style="font-family: "cambria math" , "serif"; mso-bidi-font-family: Aparajita;">𝛛</span><span style="font-family: "aparajita" , "sans-serif";">x</span><span style="font-family: "cambria math" , "serif"; mso-bidi-font-family: Aparajita;">𝛛</span><span style="font-family: "aparajita" , "sans-serif";">y)<o:p></o:p></span></span></div><div class="MsoNormal"><span style="font-family: "aparajita" , "sans-serif";"><span style="font-size: large;">The above condition may also be stated as <o:p></o:p></span></span></div><div class="MsoNormal"><span style="font-size: large;"><span style="font-family: "aparajita" , "sans-serif";">(</span><span style="font-family: "cambria math" , "serif"; mso-bidi-font-family: Aparajita;">𝛛</span><span style="font-family: "aparajita" , "sans-serif";">M/</span><span style="font-family: "cambria math" , "serif"; mso-bidi-font-family: Aparajita;">𝛛</span><span style="font-family: "aparajita" , "sans-serif";">y)=(</span><span style="font-family: "cambria math" , "serif"; mso-bidi-font-family: Aparajita;">𝛛</span><span style="font-family: "aparajita" , "sans-serif";">N/</span><span style="font-family: "cambria math" , "serif"; mso-bidi-font-family: Aparajita;">𝛛</span><span style="font-family: "aparajita" , "sans-serif";">x) assuming that (</span><span style="font-family: "cambria math" , "serif"; mso-bidi-font-family: Aparajita;">𝛛</span><sup><span style="font-family: "aparajita" , "sans-serif";">2</span></sup><span style="font-family: "aparajita" , "sans-serif";">f/</span><span style="font-family: "cambria math" , "serif"; mso-bidi-font-family: Aparajita;">𝛛</span><span style="font-family: "aparajita" , "sans-serif";">y</span><span style="font-family: "cambria math" , "serif"; mso-bidi-font-family: Aparajita;">𝛛</span><span style="font-family: "aparajita" , "sans-serif";">x)=(</span><span style="font-family: "cambria math" , "serif"; mso-bidi-font-family: Aparajita;">𝛛</span><sup><span style="font-family: "aparajita" , "sans-serif";">2</span></sup><span style="font-family: "aparajita" , "sans-serif";">f/</span><span style="font-family: "cambria math" , "serif"; mso-bidi-font-family: Aparajita;">𝛛</span><span style="font-family: "aparajita" , "sans-serif";">x</span><span style="font-family: "cambria math" , "serif"; mso-bidi-font-family: Aparajita;">𝛛</span><span style="font-family: "aparajita" , "sans-serif";">y)<o:p></o:p></span></span></div><div class="MsoNormal"><span style="font-size: large;"><span style="font-family: "aparajita" , "sans-serif";">The condition is sufficient i.e. if (</span><span style="font-family: "cambria math" , "serif"; mso-bidi-font-family: Aparajita;">𝛛</span><span style="font-family: "aparajita" , "sans-serif";">M/</span><span style="font-family: "cambria math" , "serif"; mso-bidi-font-family: Aparajita;">𝛛</span><span style="font-family: "aparajita" , "sans-serif";">y)=(</span><span style="font-family: "cambria math" , "serif"; mso-bidi-font-family: Aparajita;">𝛛</span><span style="font-family: "aparajita" , "sans-serif";">N/</span><span style="font-family: "cambria math" , "serif"; mso-bidi-font-family: Aparajita;">𝛛</span><span style="font-family: "aparajita" , "sans-serif";">x)<o:p></o:p></span></span></div><div class="MsoNormal"><span style="font-family: "aparajita" , "sans-serif";"><span style="font-size: large;">(1) must be an exact differential equation<o:p></o:p></span></span></div><div class="MsoNormal"><span style="font-size: large;"><span style="font-family: "aparajita" , "sans-serif";">If we put p=</span><span style="font-family: "cambria" , "serif"; mso-bidi-font-family: Aparajita;">ʃ</span><span style="font-family: "aparajita" , "sans-serif";">Mdx then (</span><span style="font-family: "cambria math" , "serif"; mso-bidi-font-family: Aparajita;">𝛛</span><span style="font-family: "aparajita" , "sans-serif";">P/</span><span style="font-family: "cambria math" , "serif"; mso-bidi-font-family: Aparajita;">𝛛</span><span style="font-family: "aparajita" , "sans-serif";">x)=M,so that (</span><span style="font-family: "cambria math" , "serif"; mso-bidi-font-family: Aparajita;">𝛛</span><sup><span style="font-family: "aparajita" , "sans-serif";">2</span></sup><span style="font-family: "aparajita" , "sans-serif";">P/</span><span style="font-family: "cambria math" , "serif"; mso-bidi-font-family: Aparajita;">𝛛</span><span style="font-family: "aparajita" , "sans-serif";">y</span><span style="font-family: "cambria math" , "serif"; mso-bidi-font-family: Aparajita;">𝛛</span><span style="font-family: "aparajita" , "sans-serif";">x)=(</span><span style="font-family: "cambria math" , "serif"; mso-bidi-font-family: Aparajita;">𝛛</span><span style="font-family: "aparajita" , "sans-serif";">M/</span><span style="font-family: "cambria math" , "serif"; mso-bidi-font-family: Aparajita;">𝛛</span><span style="font-family: "aparajita" , "sans-serif";">y)<o:p></o:p></span></span></div><div class="MsoNormal"><span style="font-size: large;"><span style="font-family: "aparajita" , "sans-serif";">But (</span><span style="font-family: "cambria math" , "serif"; mso-bidi-font-family: Aparajita;">𝛛</span><span style="font-family: "aparajita" , "sans-serif";">N/</span><span style="font-family: "cambria math" , "serif"; mso-bidi-font-family: Aparajita;">𝛛</span><span style="font-family: "aparajita" , "sans-serif";">x)=(</span><span style="font-family: "cambria math" , "serif"; mso-bidi-font-family: Aparajita;">𝛛</span><span style="font-family: "aparajita" , "sans-serif";">M/</span><span style="font-family: "cambria math" , "serif"; mso-bidi-font-family: Aparajita;">𝛛</span><span style="font-family: "aparajita" , "sans-serif";">y)=(</span><span style="font-family: "cambria math" , "serif"; mso-bidi-font-family: Aparajita;">𝛛</span><sup><span style="font-family: "aparajita" , "sans-serif";">2P</span></sup><span style="font-family: "aparajita" , "sans-serif";">P/</span><span style="font-family: "cambria math" , "serif"; mso-bidi-font-family: Aparajita;">𝛛</span><span style="font-family: "aparajita" , "sans-serif";">y</span><span style="font-family: "cambria math" , "serif"; mso-bidi-font-family: Aparajita;">𝛛</span><span style="font-family: "aparajita" , "sans-serif";">x)=(</span><span style="font-family: "cambria math" , "serif"; mso-bidi-font-family: Aparajita;">𝛛</span><sup><span style="font-family: "aparajita" , "sans-serif";">2</span></sup><span style="font-family: "aparajita" , "sans-serif";">P/</span><span style="font-family: "cambria math" , "serif"; mso-bidi-font-family: Aparajita;">𝛛</span><span style="font-family: "aparajita" , "sans-serif";">x</span><span style="font-family: "cambria math" , "serif"; mso-bidi-font-family: Aparajita;">𝛛</span><span style="font-family: "aparajita" , "sans-serif";">y) or (</span><span style="font-family: "cambria math" , "serif"; mso-bidi-font-family: Aparajita;">𝛛</span><span style="font-family: "aparajita" , "sans-serif";">N/</span><span style="font-family: "cambria math" , "serif"; mso-bidi-font-family: Aparajita;">𝛛</span><span style="font-family: "aparajita" , "sans-serif";">x)=(</span><span style="font-family: "cambria math" , "serif"; mso-bidi-font-family: Aparajita;">𝛛</span><span style="font-family: "aparajita" , "sans-serif";">/</span><span style="font-family: "cambria math" , "serif"; mso-bidi-font-family: Aparajita;">𝛛</span><span style="font-family: "aparajita" , "sans-serif";">x[</span><span style="font-family: "cambria math" , "serif"; mso-bidi-font-family: Aparajita;">𝛛</span><span style="font-family: "aparajita" , "sans-serif";">p/</span><span style="font-family: "cambria math" , "serif"; mso-bidi-font-family: Aparajita;">𝛛</span><span style="font-family: "aparajita" , "sans-serif";">y])<o:p></o:p></span></span></div><div class="MsoNormal"><span style="font-size: large;"><span style="font-family: "aparajita" , "sans-serif";">Integrating both sides with respect to x,we get N=(</span><span style="font-family: "cambria math" , "serif"; mso-bidi-font-family: Aparajita;">𝛛</span><span style="font-family: "aparajita" , "sans-serif";">P/</span><span style="font-family: "cambria math" , "serif"; mso-bidi-font-family: Aparajita;">𝛛</span><span style="font-family: "aparajita" , "sans-serif";">y)+</span><span style="font-family: "cambria math" , "serif"; mso-bidi-font-family: Aparajita;">𝞍</span><span style="font-family: "aparajita" , "sans-serif";">(y),where </span><span style="font-family: "cambria math" , "serif"; mso-bidi-font-family: Aparajita;">𝞍</span><span style="font-family: "aparajita" , "sans-serif";">(y) is function of y alone.<o:p></o:p></span></span></div><div class="MsoNormal"><span style="font-size: large;"><span style="font-family: "aparajita" , "sans-serif";">Mdx+Ndy=(</span><span style="font-family: "cambria math" , "serif"; mso-bidi-font-family: Aparajita;">𝛛</span><span style="font-family: "aparajita" , "sans-serif";">P/</span><span style="font-family: "cambria math" , "serif"; mso-bidi-font-family: Aparajita;">𝛛</span><span style="font-family: "aparajita" , "sans-serif";">x)dx+{(</span><span style="font-family: "cambria math" , "serif"; mso-bidi-font-family: Aparajita;">𝛛</span><span style="font-family: "aparajita" , "sans-serif";">P/</span><span style="font-family: "cambria math" , "serif"; mso-bidi-font-family: Aparajita;">𝛛</span><span style="font-family: "aparajita" , "sans-serif";">y)+</span><span style="font-family: "cambria math" , "serif"; mso-bidi-font-family: Aparajita;">𝞍</span><span style="font-family: "aparajita" , "sans-serif";">(y)}dy=(</span><span style="font-family: "cambria math" , "serif"; mso-bidi-font-family: Aparajita;">𝛛</span><span style="font-family: "aparajita" , "sans-serif";">P/</span><span style="font-family: "cambria math" , "serif"; mso-bidi-font-family: Aparajita;">𝛛</span><span style="font-family: "aparajita" , "sans-serif";">x)dx+(</span><span style="font-family: "cambria math" , "serif"; mso-bidi-font-family: Aparajita;">𝛛</span><span style="font-family: "aparajita" , "sans-serif";">P/</span><span style="font-family: "cambria math" , "serif"; mso-bidi-font-family: Aparajita;">𝛛</span><span style="font-family: "aparajita" , "sans-serif";">y)dy+</span><span style="font-family: "cambria math" , "serif"; mso-bidi-font-family: Aparajita;">𝞍</span><span style="font-family: "aparajita" , "sans-serif";">(y)dy<o:p></o:p></span></span></div><div class="MsoNormal"><span style="font-size: large;"><span style="font-family: "aparajita" , "sans-serif";"><span style="mso-spacerun: yes;"> </span>=dP+dF(y),wheredF(y)=</span><span style="font-family: "cambria math" , "serif"; mso-bidi-font-family: Aparajita;">𝞍</span><span style="font-family: "aparajita" , "sans-serif";">(y)dy=d[P+F(y)] which shows that Mdx+Ndy is an exact differential.The procedure suggests the following.Working rule for solving an exact differential equation-(a)Integrate M with respect to x regarding y as a constant.<o:p></o:p></span></span></div><div class="MsoNormal"><span style="font-family: "aparajita" , "sans-serif";"><span style="font-size: large;">(b) Then integrate N with respect to y and retain only those terms which have not been already obtained by integrating M,i.e.in (a) above.<o:p></o:p></span></span></div><div class="MsoNormal"><span style="font-family: "aparajita" , "sans-serif";"><span style="font-size: large;">(c) Add the two expressions obtained in (a) and (b) above and equate the result to an arbitrary constant.<o:p></o:p></span></span></div><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><a href="https://1.bp.blogspot.com/-RUmfEUzF7HE/XWZc1VOfP1I/AAAAAAAAL-o/ZNroZkRIkb0D27hd2NhTa8hsKAzVwjb1QCLcBGAs/s1600/exact-differential-equation.PNG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img alt="Exact Differential Equation" border="0" data-original-height="543" data-original-width="537" height="640" src="https://1.bp.blogspot.com/-RUmfEUzF7HE/XWZc1VOfP1I/AAAAAAAAL-o/ZNroZkRIkb0D27hd2NhTa8hsKAzVwjb1QCLcBGAs/s640/exact-differential-equation.PNG" title="Exact Differential Equation" width="632" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><h4><b style="font-size: medium; text-align: left;"><i><u><span style="font-family: "aparajita" , sans-serif;"><span style="font-size: large;">Exact Differential Equation</span></span></u></i></b></h4></td></tr></tbody></table><div class="MsoNormal"><span style="font-family: "aparajita" , "sans-serif";"><span style="font-size: large;"><br /></span></span></div><br /></div><img src="http://feeds.feedburner.com/~r/SatyamMathematics/~4/samOmsVDV8s" height="1" width="1" alt=""/>satyam coaching centrehttp://www.blogger.com/profile/12788483628699913686noreply@blogger.com0https://www.satyammathematics.com/2019/08/exact-differential-equation.htmltag:blogger.com,1999:blog-4893862652325568386.post-81067562044152433782019-08-24T08:11:00.000+05:302019-08-24T08:11:37.842+05:30Shri Krishna Janmashtami<div dir="ltr" style="text-align: left;" trbidi="on"><div dir="ltr" style="text-align: left;" trbidi="on"><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><span style="margin-left: auto; margin-right: auto;"><a href="https://www.satyammathematics.com/" target="_blank"><img alt="Shri Krishna Janmashtami" border="0" data-original-height="195" data-original-width="260" height="477" src="https://1.bp.blogspot.com/-QXgyVbV3gV0/XWCfD92qDAI/AAAAAAAAL4Q/XBjH-KbGTBQtSjOGXNzDCWngnAX5ll7ggCLcBGAs/s640/shri-krishna-janmashtami.jpg" title="Shri Krishna Janmashtami" width="640" /></a></span></td></tr><tr><td class="tr-caption" style="text-align: center;"><h4><span style="font-size: large;"><i><u><a href="https://www.satyammathematics.com/" target="_blank">Shri Krishna Janmashtami</a></u></i></span></h4><div class="separator" style="clear: both; text-align: center;"><span style="margin-left: 1em; margin-right: 1em;"><a href="https://www.satyammathematics.com/" target="_blank"><img alt="Shri Krishna Janmashtami" border="0" data-original-height="570" data-original-width="760" height="480" src="https://1.bp.blogspot.com/-Htce5tvfISE/XWChV0GBMrI/AAAAAAAAL4c/QZZX6NbkDRcvSOj98RD2m43rsQnvmxNkwCLcBGAs/s640/bhagavana-shiva.jpg" title="Shri Krishna Janmashtami" width="640" /></a></span></div><div><span style="font-size: large;"><i><u><a href="https://www.satyammathematics.com/" target="_blank"><br /></a></u></i></span></div></td></tr></tbody></table><br /></div><link href="https://www.w3schools.com/w3css/4/w3.css" rel="stylesheet"></link> <style> .mySlides {display:none;} </style> <body> <h2 class="w3-center">Indian Festival</h2><div class="w3-content" style="max-width: 400px;"> <div class="mySlides w3-container w3-red"> <h1><b>Did You Know?</b></h1><h1><i>We plan to celibrate Shri krishna Janmashtami</i></h1></div><img class="mySlides" src="https://1.bp.blogspot.com/-QXgyVbV3gV0/XWCfD92qDAI/AAAAAAAAL4Q/XBjH-KbGTBQtSjOGXNzDCWngnAX5ll7ggCLcBGAs/s640/shri-krishna-janmashtami.jpg" style="width: 100%;" /> <div class="mySlides w3-container w3-xlarge w3-white w3-card-4"> <span class="w3-tag w3-yellow">New!</span> Satyam Mathematics<br /> Mathematics<br /> </div><img class="mySlides" src="https://1.bp.blogspot.com/-Htce5tvfISE/XWChV0GBMrI/AAAAAAAAL4c/QZZX6NbkDRcvSOj98RD2m43rsQnvmxNkwCLcBGAs/s640/bhagavana-shiva.jpg" style="width: 100%;" /> </div><script> var slideIndex = 0; carousel(); function carousel() { var i; var x = document.getElementsByClassName("mySlides"); for (i = 0; i < x.length; i++) { x[i].style.display = "none"; } slideIndex++; if (slideIndex > x.length) {slideIndex = 1} x[slideIndex-1].style.display = "block"; setTimeout(carousel, 2000); } </script></body></div><img src="http://feeds.feedburner.com/~r/SatyamMathematics/~4/A7MsvjMm9Tc" height="1" width="1" alt=""/>satyam coaching centrehttp://www.blogger.com/profile/12788483628699913686noreply@blogger.com0https://www.satyammathematics.com/2019/08/shri-krishna-janmashtami.htmltag:blogger.com,1999:blog-4893862652325568386.post-46037709270143286312019-08-24T07:23:00.000+05:302019-08-24T07:23:34.028+05:30Laboratory Method in Mathematics<div dir="ltr" style="text-align: left;" trbidi="on"><h2 style="text-align: left;"><i><u>Laboratory Method in Mathematics</u></i></h2><h2 style="text-align: left;"><i><u>1.Bhumika (Introduction) -</u></i></h2>Laboratory method has proved extremely beneficial in the study of all branches of science. In order to improve and make the teaching of mathematics meaningful, scholars considered the laboratory method beneficial and found this method suitable for the teaching of mathematics. In this method, the children themselves check the truth of the facts, rules, principles, relations, etc. of mathematics with the help of instruments, instruments and other materials available in the mathematics laboratory and use them to find solutions to practical problems. With the help of this method, students' interest in mathematics is aroused and they themselves acquire direct knowledge with the help of tools. In this method, the principle of 'learning by action' is used. In this, only book knowledge is not considered useful.<br /><span style="font-size: large;"><i><b><u>The following instruments and equipment are required for the mathematics laboratory -</u></b></i></span><br />Model of geometry tools, spheres, cubes, squares, triangles, quadrilaterals etc. Model scales, scissors, survey tools, thermometers, barometers, levers, tablets, graph papers, slide rules, labels, calipers, calculating machines, sextant, clock, Computer, various means of measuring, charts of income tax etc., market rates, charts of bank rates, facts of population, etc. It is not necessary that the teacher should teach each sub-subject of Mathematics by laboratory method. There are many such sub-topics in mathematics in which students can understand and formulate different aspects in the laboratory themselves with the help of instruments. For example, in geometry, students can measure experimental information of various triangles, shapes of four sides, circles etc. in a student laboratory. The formulas can be determined by knowing the regions of different shapes in the laboratory. With the help of equipment in the laboratory, students get the right knowledge about the shape of objects, pictures etc. and their practical use is possible in life. Successful use of this method depends on the understanding of the teacher. The practical side of these sub-disciplines to the students by the work in the laboratory of the decimal system, measure of weight, percentage, average method of interest, time and distance, time and work, proportions, algebra formulas, practical work in geometry etc. Can be understood. In today's era, accounting is very important and it can be made a useful tool of study and comparison in the laboratory. Area of the playground, survey of school building, calculation of painting and painting cost etc. are the areas where students can compile facts themselves and calculate the required information. In the laboratory, weights, drawing, comparing, estimating, mathematical analysis of science facts, making models, finding practical solutions to theorems of geometry, understanding the mathematics side of new science discoveries, analyzing many formulas There are many activities like verifying the truth, which can be understood well in the laboratory. The ability to solve the problem can be developed with laboratory method.<br /><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><a href="https://1.bp.blogspot.com/-O0GFrHjewTI/XV_0nPzLnII/AAAAAAAAL34/6TYDkfqRiaQIDSJL3jaVShOONyueMZR6QCLcBGAs/s1600/Laboratory-Method-in-Mathematics.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img alt="Laboratory Method in Mathematics" border="0" data-original-height="184" data-original-width="274" height="429" src="https://1.bp.blogspot.com/-O0GFrHjewTI/XV_0nPzLnII/AAAAAAAAL34/6TYDkfqRiaQIDSJL3jaVShOONyueMZR6QCLcBGAs/s640/Laboratory-Method-in-Mathematics.jpg" title="Laboratory Method in Mathematics" width="640" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><h4><span style="font-size: large;"><i><u>Laboratory Method in Mathematics</u></i></span></h4></td></tr></tbody></table>In this method, mathematics can be related to the functional of other subjects. A useful connection can be made by laboratory method with subjects like Physics, Chemistry, Biology, Geography, Economics etc. Mathematics can be introduced as a practical subject at school level through this method. For this, it is necessary that the teacher continuously compile the necessary facts from different fields of science and social life and use them in the formulation of problems so that the students have the right facts to find practical solutions in the laboratory. Making the laboratory method successful depends on the teacher's own ability and understanding. It is not necessary that all work is done in the laboratory itself. As per the requirement, students can be taken to any related place and they can be used. For example - finding the height of a mountain top, finding the speed of the rockets left by the students, finding the width of the river without crossing it, making track tracks in the playground etc. Practical knowledge of the theoretical aspect will be gained.<br /><h2 style="text-align: left;"><i><u>2. The success of this method depends on the following things (The success of this method depends on the following) -</u></i></h2>(1.) Experiments in different areas of mathematics should be determined at the beginning of the session.<br />(2.) The teaching of sub-disciplines and experiments related to them should be harmonized.<br />(3.) The required number of instruments required for each experiment should be available and there should be a predetermined framework for writing the facts of each experiment.<br />(4.) Proper guidance is available in the laboratory by the teacher to the students.<br />(5.) The formulas etc. prescribed in the laboratory should be used to solve problems.<br />(6.) The laboratory method should develop the necessary awareness of the practical side of mathematics among the students.<br />(7.) Mathematical aspect of various subjects of science should be given important place in the laboratory.<br />(8.) The students should be carried out outside the laboratory to other expedient sites.<br />(9.) Subtle ideas of mathematics can only be taught by the teacher in class.<br />(10.) By this method, students can get knowledge of many sub-disciplines of mathematics even outside the prescribed limits and get opportunities to think about different aspects of the related content.<br />4. Examples of mathematical efforts -<br /> (1.) Experiments related to Dashmik coins.<br />(2.) Experiments based on measurement units.<br />(3.) Experiments based on weighing units.<br />(4.) Percentage based on commodity prices in the market and experiments related to profit and loss. Compilation of real facts is necessary to make such experiments successful.<br />(5.) Average related experiments in which students use the given facts to study their central tendency. Here, students can study all the three central tendencies, namely, Mean, Median, Moderate.<br />(6.) Students can find out the related rules by finding the squares of different numbers - such that if the number is in the place of 5 units, then the number obtained in its square will be 25. Similarly, tables of square root, cube root etc. of numbers can be prepared. The teacher can ask the students to create tables in which numbers whose square root and cube root are not known can be found in absolute numbers. These arrays can be displayed in the laboratory. Experiments related to area and volume can also be done for squares and cubes respectively.<br />(7.) Preparation of tables of interest rates of capital and loans deposited by banks and governments and study of the conditions of depositing capital with greater profit.<br />(8.) Preparation of the model of the room and the experiments related to their floor, ceiling, boundary areas.<br />(9.) Use of time, distance, work etc.<br />(10.) Drawing pictures of different triangles, finding their area and studying their relationships. Model of triangles.<br />(11.) To study and model four-sided areas. To find their area.<br />(12.) To prepare models of circles and spheres and to find their area and volume.<br />(13.) Drawing of figures and understanding the facts displayed in them.<br />(14.) To display algebra formulas by signs and diagrams.<br />(15.) To make practical use of many tools of geometry in the conditions of life and to study the areas related to them.<br />(16.) To manufacture cylindrical objects, measure them and find the area and entire area of their pages.<br />(17.) Using the laws of set theory in geometry and displaying figures with signs. Displaying the functions of set principles, etc. through pictures.<br />(18.) Using statistics formulas by collecting data.<br />(19.) Solving problems by linear programming.<br />(20.) Drawing and displaying pictures of various geometry practitioners accurately.<br />(21.) Compilation of various special problems of mathematics and displaying their solutions by charts etc.</div><img src="http://feeds.feedburner.com/~r/SatyamMathematics/~4/nDVgtuVvtsM" height="1" width="1" alt=""/>satyam coaching centrehttp://www.blogger.com/profile/12788483628699913686noreply@blogger.com0https://www.satyammathematics.com/2019/08/laboratory-method-in-mathematics.htmltag:blogger.com,1999:blog-4893862652325568386.post-66932078548208061132019-08-23T08:10:00.000+05:302019-08-23T08:10:02.731+05:30Problem Solving Method in Mathematics<div dir="ltr" style="text-align: left;" trbidi="on"><h1 style="text-align: left;"><i><u>Problem solving method in Mathematics</u></i></h1><h2 style="text-align: left;"><i><u>1.Bhumika (Introduction) -</u></i></h2>The problem solving method is to develop the ability of children to solve a problem by taking arguments and decisions.<br />A problematic situation represents the area of a structureless living space. In this method the facts lead to the objective.<br />Levine defined the place of life - "The person and his environment, as he sees, experiences and understands."<br />Everyone has a defined view of the environment around them - this indicates their area of life. When the field of life is composed, it is familiar and understandable. If it is composed, it is confusing. It is necessary to create such a field. Our behavior depends in large part on the cognitive structure of the site of life. In such a situation, he does not know which positions can be helpful in problem solving. Problem resolution is possible when the site of life takes shape. When we face a difficult obstacle or a non-composed area comes in front of us, then the problem arises. When we become aware of cognitive design, then it is called problem solving.<br />The father of problem solving method is a great mathematician and scientist like Herbert, DV, Tolman, Einstein etc.<br /><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><span style="margin-left: auto; margin-right: auto;"><a href="https://www.satyammathematics.com/" target="_blank"><img alt="Problem Solving Method in Mathematics" border="0" data-original-height="681" data-original-width="1023" height="426" src="https://1.bp.blogspot.com/-aii3YHqoPzI/XVtwjKg_I6I/AAAAAAAAL1g/mCxEUp1ElWw5hjKtgpGTDC0l8GRx6soigCLcBGAs/s640/Problem-solving-Method-in-mathematics.jpg" title="Problem Solving Method in Mathematics" width="640" /></a></span></td></tr><tr><td class="tr-caption" style="text-align: center;"><h4><span style="font-size: large;"><i><u><a href="https://www.satyammathematics.com/" target="_blank">Problem Solving Method in Mathematics</a></u></i></span></h4></td></tr></tbody></table>The first step of the problem resolution process is 'need to solve the problem'. After this, the person defines the problem and tries to understand the problem. Thereafter, he collects material for problem solving and examines its suitability and solves the problem.<br />If the solution is not suitable, then defining the problem again repeats the various steps of the problem resolution.<br />It is a widely accepted and popular method of teaching mathematics. In mathematics teaching, the teacher presents the problems to the students in the classroom and the students learn the solutions to the problems with the help of the learned rules, principles, concepts and suffixes. If the teacher presents the problems related to the students' lives to solve in the classroom, then the enthusiasm and readiness of the students to find the solution will arise and the pace of learning increases. There should be innovation in every problem. This motivates the students to find the solution.<br />A skilled teacher compiles real facts himself and creates problems keeping in mind the students' abilities. Students study the given situation in the problem and analyze the facts and with the help of formulas, rules, principles, theorems, etc., find out the solution of the problem. Successful solving of each problem provides new experiences to the students and develops solutions.<br />If the problem is live and is related to the needs and interests of the students, then the students will have the ability to solve the problem automatically and will explore and determine the solution and find out the solution by evaluating the solution. In the problem solving method, the following academics emphasized as follows -<br />Requirement: John DV<br />Interest: Thorndike<br />Achulata: Bugleski<br />Mathematics textbooks compile traditional, stereotyped and imaginary problems. These problems do not generate any enthusiasm in the students to solve them.<br /><h2 style="text-align: left;"><i><u>2. Rule of submission of problem</u></i></h2>(1.) The social situation inherent in the problem should be such that according to the interest and understanding of the students.<br />(2.) The problem should be related to the life of the child. Children should be familiar with the facts of the problem.<br />(3.) The language of the problem should be simple, comprehensible and meaningful. Problems filled with unnecessarily long and meaningless rhetoric make the mathematics subject difficult and frightening.<br />(4.) What to find in the problem? This should be clearly visible to the students. Often such problems are also available in the textbooks, even after repeated reading, it is not known what is in the problem. How much? how? Why? Have to know.<br />(5.) The problems should be based on the formulas, theorems, concepts, theories etc. learned by the students.<br />(6.) To make problems simple, clear, abstract and small size, clear picture, meaningful table, signs should be given.<br />(7.) After understanding the problem, it is necessary to have a foreknowledge of the method of solving them.<br />(8.) If teachers create problems on their own based on the environment, local conditions and interests of the students and present themselves in the classroom, then the mathematics subject will be interesting.<br />(9.) If the problem is long, then it should be divided into two or three parts so that the children do not have any unexpected confusion.<br />(10.) Expected answers to problems should be rational so that students can evaluate them on their own. If 200 years old man, 1 quintal boy in the north, 45 hours a day, the number of some boys 91/2, car speed 1000 km M If there are hours, the irrelevance of the answers forces them to re-examine.<br />(11.) In class, the problem should be presented by writing on the blackboard and it is beneficial to indicate by colored chalk.If shapes, pictures, maps, tables, graphs, etc. are included with the problem then it will help to understand the problem.<br />(12.) If problems are presented in the classroom through computers, facts published in films, world news, pictures published in magazines, etc., it will help to make the teaching real.<br />(13.) It is also considered a good method to give children a numerical format by knowing their problems in the classroom.<br />(14.) Teaching the real events, facts, details, themes of life in mathematics teaching by making them subjects is a part of modern learning.<br />(15.) Patience is essential in problem assessment and resolution.<br />(16.) It is the duty of a mathematics teacher to motivate students to identify themselves and find solutions.<br /><h3 style="text-align: left;"><i><u><span style="font-size: large;">3. Examples</span></u></i></h3><h3 style="text-align: left;"><span style="font-weight: normal;">(1.) Find each student which is the shortest route from school to their home. (By geometry shape)</span></h3><h3 style="text-align: left;">(2.) If the family income is reduced by 10%, then what changes in household expenses will be necessary? (Children will get information about their homes)</h3>(3.) How will you find the number of fish in the village pond?<br />(4.) How to find the height of the high tower built in the village?<br />(5.) If the number of students in the school increases by 50%, then what changes will have to be made in the current classroom system?<br />(6.) How do you know the width of a river without crossing it?<br />(7.) What are the possibilities required for one-way traffic to the streets of your city?<br /><h3 style="text-align: left;"><i><u><span style="font-size: large;">4. Contemplation and problem solving -</span></u></i></h3>There is not much difference between thinking and problem solving. According to John Dewey, contemplation is the solution to the problem. The specialty of a human being is his reasoning power. Reasoning power should be encouraged in the classroom. If students try to solve problems by creating thinking power and reasoning base, then their sequence of development will be dynamic. The development of work-related consciousness and ability to deal with problems is an important part of mathematics studies. In the class, teachers should present the magic class and magic circle and explain it in the blank spaces. All these are excellent examples of reinforcement of the thinking process. Inspirational problem is motivational in itself. Moving towards solving in a scientific manner is an important part of the problem solving method. The application of core competencies, high thinking, based on inference based on trust content, ability to collect paid content, analyze problem with patience, etc. are important components of problem solving method.<br />Mechanical behavior proves useful in problem solving. Motion and fixed responses are important parts of mechanical behavior. The tests have proved the greatness of the problem solving method. Curiosity and acumen give impetus to problem solving. The more lively and relevant the problem is, the more it will inspire the students to find a solution. Processes such as analysis, estimation, compression, analysis and synthesis provide certainty in the solution.<br />This method is based on logic and is democratic. Learning, consciousness, awareness, awareness, motivation, ability to test, rationality, acumen, scientificness, curiosity etc. are important aspects of this method. Our whole life is a conscious journey to find solutions to problems. Mathematics teaching provides the best training for this method. High level thinking is an integral component of this method.<br /><h3 style="text-align: left;"><i><u><span style="font-size: large;">5. Problem solving term -</span></u></i></h3>(1.) Understanding the facts given in the problem and their relation.<br />Understanding the facts and their relation in the problem) -<br />After presenting the problem, it is necessary for the teacher to give the class enough time so that each student can study the problem thoroughly. With this, each student will get information about what is given in the problem and what to find.<br />(2.) Problem analysis<br />After presenting the problem in the class, the problem should be analyzed by the question-answer method and with the help of the students, it should be clear that what is the correlation between the facts given in the problem? In this post, students will be able to understand which facts are unnecessary and which are necessary. In this way, the student will get into the habit of analyzing the problem which is necessary to solve the problem successfully. Students who will get into the habit of analyzing the problem which is essential to solve the problem successfully. Students who do not develop the ability to analyze the problem cannot solve the problem with the most confidence.<br />(3.) Finding a potential solution -<br /> After analysis, the student will be able to understand well that which mathematical rules, formulas, principles etc. are necessary to get the solution which is to be found. Here, the student will be able to decide which particular method is required to be used to achieve a known solution and if there is an alternative method, he will also consider it.<br />(4.) Making the correct calculation to get the solution (<br />Calculating the correct to get the solution) -<br />It has been observed that students, despite knowing the method of solving, are unable to get the correct answer to the problem. They make very simple errors in calculation. Students must have the ability to calculate accurately and quickly.The teacher can practice calculating separately so that students have no difficulty in calculating. It is observed that most of the students make errors while multiplying and dividing the decimal.<br />(5.) To find a solution to the problem and re-examine (<br />Find out the problem and check it again) -<br />After finding a solution to the problem, each student should re-examine the answer so that errors in the calculation or method may be corrected in the solution. It is necessary for the students to have the habit of re-examining the answer as it is not possible to find errors without it. The student should also think about the reasonableness of the answer received.<br />6. Properties of Problem Solving Method<br />(1.) Through the problem we can give correct information about the circumstances related to life. In this way, we can present the social importance of mathematics in the classroom.<br />(2.) The student develops the ability to analyze the problem and can differentiate the essential facts. Sometimes incomplete facts are given in the problem and it is not possible to find a solution. Its information depends on the correct analysis of the problem.<br />(3.) Self-confidence and self-reliance develops in children.<br />(4.) Using the problem-solving method, children get into the habit of battling with the problem, which is necessary for success in life.<br />(5.) In this method, children get used to proper thinking and proper use of logic.<br />(6.) is helpful in the study of higher mathematics.</div><img src="http://feeds.feedburner.com/~r/SatyamMathematics/~4/PDMxuMl8_xM" height="1" width="1" alt=""/>satyam coaching centrehttp://www.blogger.com/profile/12788483628699913686noreply@blogger.com0https://www.satyammathematics.com/2019/08/problem-solving-method-in-mathematics.htmltag:blogger.com,1999:blog-4893862652325568386.post-18984867386631335152019-08-20T07:51:00.000+05:302019-08-20T07:51:18.306+05:30Deductive Method in Mathematics<div dir="ltr" style="text-align: left;" trbidi="on"><h2 style="text-align: left;"><span style="font-size: large;"><i><u>Deductive Method in Mathematics</u></i></span></h2><h2 style="text-align: left;">1.<i><u>Introduction-</u></i></h2>When using this method we move from general to specific and from subtle to macro. In this method, knowledge is presented in the form of formulas, rules, relations, conclusions etc. in front of the students and the students memorize them. Students use these to find solutions to problems. Incorporation logic is used in this method and students learn the truth by practicing rules or formulas.<br />Every human is mortal.<br />Socrates is human.<br />So Socrates is mortal.<br />The incorporation method complements the arrival method. This method is not useful in itself, because by this method students cannot directly examine the rules or formulas, nor can they learn the method of finding them. While using this method, teachers tell the students the formulas and rules of the mathematics content which the students use to solve the questions. This method is mainly used in algebra, trichotomy and geometry. Many formulas and relations are used in these subjects and it is not possible to examine each and every sutra. The teacher informs the students of the sources of these subjects for practice.<br />Teachers in algebra, geometry and trigonometry normally talk mechanically in the classroom.<br />In this method, the students memorize the formulas by memorizing them because they are directly told the formulas. Formulas are not represented by the normalization method.<br />In this method, it is not possible for students to develop reasoning and deep thinking. If the formulas are not remembered in the examination, they cannot solve the question. Even fundamental development of mathematics is not possible with this method. The great mathematicians of the world gave birth to new thinking in mathematics only from the process of arrival. Development of originality by incorporation method is not possible. The incorporation method is not useful for gifted students because rote formulas make it difficult for such students to understand the theoretical aspect. By emphasizing rote, students do not understand the subtle concepts underlying mathematical processes.<br /><div class="separator" style="clear: both; text-align: center;"></div><br /><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><span style="margin-left: auto; margin-right: auto;"><a href="https://www.satyammathematics.com/" target="_blank"><img alt="Deductive Method in Mathematics" border="0" data-original-height="257" data-original-width="196" height="640" src="https://1.bp.blogspot.com/-E9uDm1ptHXs/XVAaLqlNClI/AAAAAAAALvA/N_DqmWWWQqAVbQIakh_AEhyG2MyE_YrsACLcBGAs/s640/Deductive-Method-in-Mathematics.jpg" title="Deductive Method in Mathematics" width="488" /></a></span></td></tr><tr><td class="tr-caption" style="text-align: center;"><h4><i><u><a href="https://www.satyammathematics.com/" target="_blank">Deductive Method in Mathematics</a></u></i></h4></td></tr></tbody></table><br />The deductive method is a special type of reasoning method. This method has special use in the field of mathematics because many facts, formulas, rules, etc. of this subject have been derived from deductive method. The person uses the deductive style of thinking when he tries to extract new relations and rules with the help of predetermined facts and hypotheses. In mathematics, geometry, algebra, trichrometry, etc. are areas where we use this method more and more. In this method, the help of basic elements, postulates and self-beliefs are taken. The incorporation method is used to learn mathematics in higher classes because the arrival method is only useful for small classes.<br /><h2 style="text-align: left;">2.<i><u> Qualities of Deductive Method-</u></i></h2>(1.) In this method, the student does not have to search every formula, method, rule or conclusion. This method is short as well as practical. By this method it is possible to gain more knowledge in less time.<br />(2.) The area of utility of formulas known by this method is very wide.<br />(3.) In this method, the students and teachers have to work less because the information related to the posts related to finding each sutra or rule is not necessary. Many subtle principles can be told to students in a short time.<br />(4.) This method is very good for solving new problems in different areas of life, because only the knowledge of formulas or methods is necessary to get a solution.<br />(5.) As the formula or rules are already known, there is a special facility in solving problems.<br />(6.) This method proves useful even when it is not possible to establish any relationship with the life of the text.<br /><h3 style="text-align: left;">3. <i><u>Limitations-</u></i></h3>(1.) The knowledge acquired by this method is not permanent because the method of finding the learned formulas or rules is not taught by it. The students are only told the subtle principles which the students forget. Many students do not understand the difference in formulas even after studying.<br />(2.) This method is not useful for small classes because in this method the student is not useful because in this method students do not learn based on their own experiences. It is very difficult for them to understand the formulas, subtle thoughts and actions. Many students do not understand the difference between the different formulas because there is no provision for finding the formulas by experiment in this method.<br />(3.) In this method, rote gets more emphasis and students do not get opportunities to reason and explore.<br />(4.) This method is not psychological because the principle of 'from subtle to gross' is contrary to the principles of psychology.<br />(5.) The success of this method depends on experimenting with the arrival method.<br />(6.) The knowledge learned by this method is not useful because a person cannot take proper advantage of it due to the excess of knowledge. This method is used mostly in the modern education system and we see directly that most of the students initiated from our universities</div><img src="http://feeds.feedburner.com/~r/SatyamMathematics/~4/5Cw9CGKWlig" height="1" width="1" alt=""/>satyam coaching centrehttp://www.blogger.com/profile/12788483628699913686noreply@blogger.com0https://www.satyammathematics.com/2019/08/deductive-method-in-mathematics.htmltag:blogger.com,1999:blog-4893862652325568386.post-73123577640850266962019-08-11T07:45:00.000+05:302019-08-11T07:45:32.813+05:30Inductive Method in Mathematics<div dir="ltr" style="text-align: left;" trbidi="on"><h1 style="text-align: left;"><i><u>Inductive Method in Mathematics-</u></i> </h1><div style="text-align: left;"></div><h2 style="text-align: left;">1.<i><u>Introduction-</u></i></h2><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><a href="https://1.bp.blogspot.com/-TyPD88RRN3k/XU7HgcL-sbI/AAAAAAAALts/cPDUecZEDgsAP6tX5_S1b3Fei-eUn6QyACLcBGAs/s1600/Inductive-Method-in-Mathematics.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img alt="Inductive Method in Mathematics" border="0" data-original-height="190" data-original-width="266" height="457" src="https://1.bp.blogspot.com/-TyPD88RRN3k/XU7HgcL-sbI/AAAAAAAALts/cPDUecZEDgsAP6tX5_S1b3Fei-eUn6QyACLcBGAs/s640/Inductive-Method-in-Mathematics.jpg" title="Inductive Method in Mathematics" width="640" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><h4><i><u>Inductive Method in Mathematics</u></i></h4></td></tr></tbody></table><div><i><u><br /></u></i></div><div>Advent is a special process in our brain that leads us to a general truth or principle by observing specific things. In this process, sensation, articulation, logic, judgment and generalization are necessary. Inspection of specific items is possible through sensation and articulation. The reasoning on inspection comes to a decision. In the arrival method, from the specific to the general. This is a familiar thinking style that we usually use in life. Students can experience reality using this method and establish rationality in general inferences.The student makes a variety of experiments representing the facts and proposes general principles. This is a generalization.</div><br />While using this method, the teacher presents some specific examples in front of the students and based on the broad facts of these examples, the students argue and arrive at a particular rule or principle. It leads to direct evidence. In this, students use their experience and intelligence while setting rules. This method is called the common method.<br />This method is particularly helpful for teaching new lessons. In this, different examples should be presented to the child so that he can generalize easily. The rules that are set should be examined. Thus, the arrival method consists of the following four stages -<br />(1.) Specific example<br />(2.) inspection<br />(3.) Generalization<br />(4.) test<br />The method of arrival is used when used in a science laboratory. Students experiment while studying many macro facts and determine the general rule. Arrival in modern mathematics is an important learning process. About the importance of this method, Professor J. N. Kapoor has written -<br />"The creation process of mathematics is the science of the arrival process. Arrival begins with an inspection. We arrive at a possible conclusion through inspection because it is an estimate."<br />Through the advent logic, specific rules or principles are presented by specific examples, but arrival logic is a process and not a theory in itself. The mathematician Blaise Pascal (1623–1662) of France first gave the idea of mathematical arrival.<br /><h2 style="text-align: left;">2. <i><u>Qualities of Inductive Method-</u></i></h2>(1.) Knowledge by arrival method is important from the point of view of the child's education and development, because the child gets to practice the procedures of regularization, normalization, formulation etc. based on the inspection of specific examples.<br />(2.) The knowledge gained by this method is permanent and useful because it is based on the student's own observation, testing, understanding and intelligence.<br />(3.) By studying this method, students do not feel tired and feel patience and happiness till they reach a definite result.<br />(4.) This method motivates the children to act on their own and develops their decision making ability, which increases their sense of confidence.<br />(5.) By this method new rules of mathematics, new relationships, new conclusions, new theories, etc. can be known.<br />(6.) This method is particularly useful for small classes, because 'the theory from the gross to the subtle', is a psychological and practical theory. This develops confidence, competence, independent thinking and vision in the students.<br />(7.) In this method, the interest of children in mathematics remains and the eagerness to learn new knowledge increases.<br />(8.) Students are familiar with the basic principles of finding rules, formulas and relationships.<br /><h3 style="text-align: left;">3.<i><u> Limitations-</u></i></h3>(1.) The reliability of the rules or results obtained by it depends on the number of instances. The more instances a rule or result is based on, the more its credibility increases.<br />(2.) The rules obtained by this method are pure only to some extent.<br />(3.) This method cannot be used in higher classes because there are many sub-topics which are not possible from the initial facts.<br />(4.) In order to use this method, the teacher has to work hard and prepare and also take more time. Gathering appropriate content for direct examples is not a simple task.<br />(5.) Successful use of this method is possible only for experienced teachers.<br />(6.) Only the rule can be detected by this method. The ability to solve problems is not possible by this method.<br />The advent of the theory of mathematical advent is attributed to the French mathematician Blaise Pascal (1623–1662). The mathematician Françanco Morolics (1494–1575.E) of Italy applied this principle. Mathematical advent is reflected in the writings of Indian mathematician Bhaskaracharya II (1114–1185). The statement of the famous mathematician Laplace has been considered as a fruitful tool for the most important discovery in the field of 'analysis and natural philosophy', which is called Advent. G. Piano (1858–1932 AD) undertook the responsibility of expressing the statements of mathematical theorems by logical notation. He is credited with quoting the doctrine of matrimony. His piano postures are notable examples of Advent in this regard.</div><img src="http://feeds.feedburner.com/~r/SatyamMathematics/~4/6LaOzCiMUTs" height="1" width="1" alt=""/>satyam coaching centrehttp://www.blogger.com/profile/12788483628699913686noreply@blogger.com0https://www.satyammathematics.com/2019/08/inductive-method-in-mathematics.htmltag:blogger.com,1999:blog-4893862652325568386.post-2409507151539259562019-08-10T07:28:00.000+05:302019-08-10T07:28:42.635+05:30Synthetic Method in mathematics<div dir="ltr" style="text-align: left;" trbidi="on"><h2 style="text-align: left;"><i><u>Synthetic Method in mathematics</u></i></h2><h2 style="text-align: left;">1.<i><u>Introduction-</u></i></h2><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><span style="margin-left: auto; margin-right: auto;"><a href="https://www.satyammathematics.com/" target="_blank"><img alt="Synthetic Method in mathematics" border="0" data-original-height="683" data-original-width="1024" height="426" src="https://1.bp.blogspot.com/-_2Ayx5l3kRg/XUZCAf5VhFI/AAAAAAAALoc/Xl6q_okN_pQ9SmjChk3cbPz4xWAiGL5OgCLcBGAs/s640/Synthetic-Method-in-mathematics.jpg" title="Synthetic Method in mathematics" width="640" /></a></span></td></tr><tr><td class="tr-caption" style="text-align: center;"><h4><i><u><a href="https://www.satyammathematics.com/" target="_blank">Synthetic Method in Mathematics</a></u></i></h4></td></tr></tbody></table><div><i><u><br /></u></i></div>This method is opposite and complementary to the analytical method. The derivative of the proviso or the solution to a problem is presented by the analytical method. Most textbooks are written by the synthesis method. In this method, they move from known to unknown and arrive at conclusions based on inference. In the practice of geometry, based on the facts known by this method, one obtains an unknown conclusion.Based on estimation, it is proven by composing it in practice. The reason for the composition is not given in this method.<br />A = B (known) and B = S (known) so A = S<br />In this method, unknown facts or relationships are detected with the help of known things. In the analytical method, the process reverses. By this method, the solution of the problem or the proof and conclusion of the conclusion which is already known can be presented in a sequential manner. But unknown findings can not be known.Why is it necessary to explain why special types of compositions are required to prove the various theories in geometry books? Since they help in proving sages, they are considered suitable. Students have to cram them and once forgotten they are not possible to reconstruct by logic.<br /><h2 style="text-align: left;">2. <i><u>Features of Synthetic Method -</u></i></h2>(1.) This method is simple, subtle and systematic. This is a useful method to present any mathematical solution in an organized way. This is the reason this method is used in textbooks.<br />(2.) The solution presented by this method is easily understood by the students because every term of the solution or the present presented by this method is based on known truths and principles. The student only has to memorize a particular composition or verse from which to find conclusions or sub-findings.<br />(3.) It is necessary to use the analytical method after the analytical method. This method is complementary to the analytical method.<br />(4.) The principle of 'moving from known to unknown' is psychological and convenient for students. The teacher's work has been simplified by this method.<br />(5.) This method is simpler than the analytical method and the method of solving or concluding does not occupy much space.<br /><h3 style="text-align: left;">3. <i><u>Limitations-</u></i></h3>(1) No solution or problem can be solved by synthesis method. Analysis is required for the solution.<br />(2.) Synthetic method can only prove but cannot explain because by this method it cannot be known why a composition has been made or why a post has been added or subtracted or a particular reason has been selected. is.<br />(3.) This method cannot develop the reasoning power, decision power and thinking power of the students.Students remain inactive and they have to rotate many positions. If students forget something once, then it cannot be created again.<br /><table border="1"> <tbody><tr> <th>No.</th> <th>Social Media</th> <th>Url</th> </tr><tr> <td>1.</td> <td><a href="https://www.facebook.com/satyamcochingcentre">Facebook</a></td> <td><a href="https://www.facebook.com/satyamcochingcentre">click here</a></td> </tr><tr> <td>2.</td> <td><a href="https://www.youtube.com/channel/UCIhWUzFYTFwPsKEHHd7LKGQ?view_as=subscriber">you tube</a></td> <td><a href="https://www.youtube.com/channel/UCIhWUzFYTFwPsKEHHd7LKGQ?view_as=subscriber">click here</a></td> </tr><tr> <td>3.</td> <td><a href="https://twitter.com/satyamcentre">Twitter</a></td> <td><a href="https://twitter.com/satyamcentre">click here</a></td></tr><tr> <td>4.</td> <td><a href="https://www.instagram.com/satyamcentre">Instagram</a></td> <td><a href="https://www.instagram.com/satyamcentre">click here</a></td> </tr></tbody></table>(4.) The knowledge gained by this method is not discovered by the boys themselves. That's why he is not permanent Children depend on the teacher to understand everything without any help. The child cannot learn much material through his own efforts. It is a dull and inanimate method.<br /><h3 style="text-align: left;">3<i><u>.Suggestions to Teachers-</u></i></h3>(1) Both methods should be used when reading different sub-topics of mathematics. Especially in proving the means of geometry or solving problems it is necessary to first analyze the various aspects of the problem or problem so that students can understand why a composition or a term is used and how we should make these conclusions Useful in getting<br />(2.) After analysis, material should be presented by synthesis method.<br />(3.) Keep in mind why? and how? The answers to the questions should be clear to the children through analytical method, which does not encourage the tendency to rote.<br />(4) It is a bitter truth that by applying analytical method it may take more time to explain to the teacher but it should not be considered a waste of time, but considered a useful requirement.<br />(5.) As far as possible, students should be given opportunities to find their own solution or to create sub-form so that their expected development is possible.<br />(6.) Such questions should be given place in examinations which test originality.<br />(7.) Textbooks are mostly written on synthetic methods. Therefore, teachers of mathematics are expected to overcome this deficiency by their own efforts. It is necessary to think in detail about the analytical side while preparing the lesson.</div><img src="http://feeds.feedburner.com/~r/SatyamMathematics/~4/g5OwcgnlQzg" height="1" width="1" alt=""/>satyam coaching centrehttp://www.blogger.com/profile/12788483628699913686noreply@blogger.com0https://www.satyammathematics.com/2019/08/synthetic-method-in-mathematics.htmltag:blogger.com,1999:blog-4893862652325568386.post-21284459604720992832019-08-03T07:25:00.000+05:302019-08-03T07:25:03.006+05:30Analytic Method in Mathematics<div dir="ltr" style="text-align: left;" trbidi="on"><h1 style="text-align: left;"><i><u>Analytic Method in Mathematics</u></i></h1><h2 style="text-align: left;">1. <i><u>Introduction -</u></i></h2>This method has proved to be more useful especially in geometry. We use this method in the analysis of mathematical problems, but in geometry it has special significance in the teaching of theorems. By analyzing the complex side of any problem with the help of this method it is known how the solution can be obtained and what conditions are necessary for it. The dissection of the various aspects of the problem is considered as an analysis.<br /><table border="1"> <tbody><tr> <th>No.</th> <th>Social Media</th> <th>Url</th> </tr><tr> <td>1.</td> <td><a href="https://www.facebook.com/satyamcochingcentre">Facebook</a></td> <td><a href="https://www.facebook.com/satyamcochingcentre">click here</a></td> </tr><tr> <td>2.</td> <td><a href="https://www.youtube.com/channel/UCIhWUzFYTFwPsKEHHd7LKGQ?view_as=subscriber">you tube</a></td> <td><a href="https://www.youtube.com/channel/UCIhWUzFYTFwPsKEHHd7LKGQ?view_as=subscriber">click here</a></td> </tr><tr> <td>3.</td> <td><a href="https://twitter.com/satyamcentre">Twitter</a></td> <td><a href="https://twitter.com/satyamcentre">click here</a></td></tr><tr> <td>4.</td> <td><a href="https://www.instagram.com/satyamcentre">Instagram</a></td> <td><a href="https://www.instagram.com/satyamcentre">click here</a></td> </tr></tbody></table>In this method, complex problems are divided into many common problems and their solutions are known to facilitate the solution of the whole complex problem.<br />According to this method, we move on from the unknown to the known and the conclusions given to the facts. The discovery of the origin of any accomplishment or the composition of a definite method is not possible and understandable through the synthesis method. Why is any accomplishment or problem being proven or resolved by any particular method or why a particular composition is necessary?Answer to these questions is possible only through analytical method. Analytical method is not used in any of the mathematical textbooks that have been written.<br />If we know that 'A' is true and it is to prove that 'B' is also true, according to analytical method, we will say that 'B' can be true when 'A' is true and 'B' and ' A 'mutual equals' Only by analyzing, students can know what things we should know and how to use them to solve any achievement.It is necessary to adopt analytical method of thinking.<br />Whenever we find a solution to a complex problem in life, through analytical method, only trying to find solutions by analyzing various aspects of the problem. This method develops ability to explore students and strengthens the sense of self-reliance. Students get explanation of each aspect of Genesis and they themselves create new generation.<br /><h2 style="text-align: left;">2.<i><u>Example (example)</u></i> -</h2><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><span style="margin-left: auto; margin-right: auto;"><a href="https://www.satyammathematics.com/" target="_blank"><img alt="Analytic method in mathematics" border="0" data-original-height="526" data-original-width="593" height="566" src="https://1.bp.blogspot.com/-dtj-xWn3W44/XUO3cPa5OYI/AAAAAAAALmE/3kCEaqW5VBQXgm6AeKfho42MDMueTDplACLcBGAs/s640/Analytic%2B-method-in-mathematics.PNG" title="Analytic method in mathematics" width="640" /></a></span></td></tr><tr><td class="tr-caption" style="text-align: center;"><h4><i><u><a href="https://www.satyammathematics.com/" target="_blank">Analytic method in mathematics</a></u></i></h4><div class="separator" style="clear: both; text-align: center;"><a href="https://www.satyammathematics.com/" target="_blank"><img alt="Analytic method in mathematics" border="0" data-original-height="773" data-original-width="1280" height="386" src="https://1.bp.blogspot.com/--5cynS80foU/XUO36wu5ByI/AAAAAAAALmM/iOs4H5hyfxk1-9UJ5okTSrEZPnHQm9BKgCLcBGAs/s640/Parallelogram-area.png" title="Analytic method in mathematics" width="640" />Analytic Method in Mathematics</a></div><div><i><u><a href="https://www.satyammathematics.com/" target="_blank"><br /></a></u></i></div></td></tr></tbody></table><br /><h3 style="text-align: left;">3.<i><u> Features of analytical method -</u></i></h3>(1.) Why was there any composition made to prove any accomplishment or to solve a solution? This is reflected only when we adopt analytical method of contemplation. The discovery of the origin of any accomplishment and the creation of the decisive is understandable by the analytical method.<br />(2) By this method, the student himself can find the solution or the composition of a new problem or solution. In this method, the solution is not necessary to stop.<br />(3) This method establishes the ability to explore the student and the sense of self-reliance.<br />(4) By this method, rationality, thinking power and decision power develops in children and there is an increase in ability to analyze problems.<br />(5) Knowledge gained by it is permanent and encourages the tendency of searching in children. The child remains curious for the new knowledge.<br />(6) The presents of the instruments given in textbooks are not confidential to the children.<br />(7.) In this method lies the ability to clarify and it is used to understand and solve many problems of life.<br /><h3 style="text-align: left;">4.<i><u>Limitations -</u></i></h3>(1.) This method takes more time to find solutions, because reasoning process is longer. Students have to go to the root of the problem.<br />(2.) Students get fewer informations and the amount of learning is less compared to the synthesis method.<br />(3.) This method is more useful for small children, because the level of reasoning does not have the required strength in younger age.<br />(4) Each teacher can not use this method successfully.<br />(5) The course can not be terminated in the prescribed time using the method.In the theories of geometry, 'given' and 'proven to', the situation is not as much available in many situations of life.</div><img src="http://feeds.feedburner.com/~r/SatyamMathematics/~4/GsK6a8wZ4Ec" height="1" width="1" alt=""/>satyam coaching centrehttp://www.blogger.com/profile/12788483628699913686noreply@blogger.com0https://www.satyammathematics.com/2019/08/analytic-method-in-mathematics.htmltag:blogger.com,1999:blog-4893862652325568386.post-75674458568784430592019-08-02T07:45:00.001+05:302019-08-02T07:45:13.625+05:30Importance of Teaching Methods in Mathematics <div dir="ltr" style="text-align: left;" trbidi="on"><h2 style="text-align: left;"><i><u>Importance of Teaching Methods in Mathematics </u></i></h2><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><a href="https://1.bp.blogspot.com/-S__Q0NKzi6U/XUOcLSjqSyI/AAAAAAAALl4/SA_NhaQhL-AvOueAXOIaq48urOU1x4sqwCLcBGAs/s1600/Importance-of-Mathematics.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img alt="Importance of Teaching Methods in Mathematics " border="0" data-original-height="333" data-original-width="500" height="426" src="https://1.bp.blogspot.com/-S__Q0NKzi6U/XUOcLSjqSyI/AAAAAAAALl4/SA_NhaQhL-AvOueAXOIaq48urOU1x4sqwCLcBGAs/s640/Importance-of-Mathematics.jpg" title="Importance of Teaching Methods in Mathematics " width="640" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><h4><i><u>Importance of Teaching Methods in Mathematics </u></i></h4></td></tr></tbody></table><div><i><u><br /></u></i></div><h2 style="text-align: left;">1.<i><u>Importance of Teaching Method</u></i></h2>In the last few years, our education institutions focus on classroom teaching methods. In its report, the Secondary Education Commission has highlighted the importance and use of dynamic teaching methods in detail. About the effective teaching methods in the past decade, many workshops, refresher courses, summer institutes etc. have been organized at our national level and awareness is also visible somewhere in this context.But in most of our educational institutions and especially in educational institutions in rural areas, all these things have no special effect. This is also true for mathematics teaching. Classes of mathematics are still equally monotonous and lifeless, as it was earlier. In the field of mathematics, successful teaching has been done in very small numbers and there is a great lack of innovative means. A general mathematical teacher is not often ready to adopt new methods.To achieve the objectives of education it is very necessary that students should be interested in studying in class. Special efforts have to be made to make mathematical topics interesting in the classroom. The success of the teacher depends on the effective teaching method. It has been observed that many diligent mathematics teachers do not get success in the absence of appropriate teaching method in the classroom. For the teacher of mathematics, knowledge of different methods of mathematics is necessary otherwise He will fail to achieve the objectives in the classroom.<br />The choice of teaching method of mathematics depends on the need for content, students' ability, teaching objectives, etc. The teaching of mathematics should be selected carefully by teaching method. Due to inappropriate teaching methods, students find a difficult subject and students begin to fear the subject. Using effective method, students take an interest in mathematics and do not intimidate them in class. Psychology is considered an important basis in different teaching methods.Decisions about teaching methods should be made only in the context of content and objectives. No definite method can be rendered for the teaching of any sub-subject. The best method is to learn the subject matter from the subject and understand the contents of the subject as well. Effective use of teaching by experience and contemplation is possible.<br /><h2 style="text-align: left;">2.<i><u> Limitations of Traditional Teaching Method -</u></i></h2>Students progress at very slow pace in traditional teaching methods of mathematics and discussions among students and teachers are ambiguous and uncertain. The teacher sometimes does not make the internal structure of mathematics as a source of inspiration.<br />(1.) The students have to follow the instruction of teacher and textbook and students are bound to resolve the problem only on the basis of the procedures mentioned.<br />(2.) Rule-example-practice is used.<br />(3.) The student has to reconsider the principles and procedures without thinking and without checking the rationality. Students solve the questions with the help of log sources without understanding the meaning of log. Remembers the theories of theorems without understanding.<br />(4) The emphasis is on the teaching of 'mathematical mechanics'. Calculations are considered mathematics, whereas calculation skills are merely means.<br />(5) The development of new ideas, logic, creativity, art, etc. is not developed by the language of mathematics.Conventional teaching methods are personal features.<br /><table border="1"><tbody><tr><th>No.</th><th>Social Media</th><th>Url</th></tr><tr><td>1.</td><td><a href="https://www.facebook.com/satyamcochingcentre">Facebook</a></td><td><a href="https://www.facebook.com/satyamcochingcentre">click here</a></td></tr><tr><td>2.</td><td><a href="https://www.youtube.com/channel/UCIhWUzFYTFwPsKEHHd7LKGQ?view_as=subscriber">you tube</a></td><td><a href="https://www.youtube.com/channel/UCIhWUzFYTFwPsKEHHd7LKGQ?view_as=subscriber">click here</a></td></tr><tr><td>3.</td><td><a href="https://twitter.com/satyamcentre">Twitter</a></td><td><a href="https://twitter.com/satyamcentre">click here</a></td></tr><tr><td>4.</td><td><a href="https://www.instagram.com/satyamcentre">Instagram</a></td><td><a href="https://www.instagram.com/satyamcentre">click here</a></td></tr></tbody></table>(6.) Creative thinking is not encouraged in the students.<br />(7) Today's requirements have been considered secondary and more time is spent in teaching the skills of initial calculations. We do not use many of these skills in our life. Do not use multi-digit numbers in life. The skills currently being taught for calculations of multi-digit numbers are not enough.They require computers. Use of computer should be compulsory.<br />(8.) The current teaching methods of mathematics are suitable for tomorrow but it is inappropriate in relation to today's needs.<br />(9.) Why and how is given a secondary position in mathematics.<br />(10.) The focus on the development of the ability to solve problems in students is reduced.<br />(11.) Due to these methods students have been approached for the formation of formalities, mechanism and old age towards mathematics. Important processes such as abstraction, structure, mathematical model construction etc. are not given place in teaching methods. Most teachers do not consider these as essential parts of mathematics.<br />(12.) The history of mathematics has not been the basis for inspiration, whereas the biographies of mathematicians are important for students to create excitement and awareness for mathematics.<br />(13.) Mathematics is not presented in the form of science, mathematics as art, mathematics as language and mathematics as a tool.<br />(14.) The teaching of mathematics remains subject-centered while it should be aim-centered.<br />(15) Competition in the examinations of this subject is evaluated primarily. Trends and creative thinking about mathematics is not evaluated.</div><img src="http://feeds.feedburner.com/~r/SatyamMathematics/~4/NymA6AejZ5s" height="1" width="1" alt=""/>satyam coaching centrehttp://www.blogger.com/profile/12788483628699913686noreply@blogger.com0https://www.satyammathematics.com/2019/08/importance-of-teaching-method-in-mathematics.htmltag:blogger.com,1999:blog-4893862652325568386.post-76742528888205725082019-08-01T07:37:00.000+05:302019-08-01T07:37:14.612+05:30General Principles of Teaching arithmetic<div dir="ltr" style="text-align: left;" trbidi="on"><h1><i><u>General Principles of Teaching Arithmetic</u></i></h1><div><h2 style="text-align: left;"><i><u>1.Relation to life</u></i></h2></div><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><a href="https://1.bp.blogspot.com/-tMqXce-k9wI/XUGmkZslQtI/AAAAAAAALlQ/YN27JINpuMcS2wllWr5acjDChDFBxaBkQCLcBGAs/s1600/General-Principles-of-Teaching-arithmetic.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img alt="General Principles of Teaching arithmetic" border="0" data-original-height="189" data-original-width="267" height="453" src="https://1.bp.blogspot.com/-tMqXce-k9wI/XUGmkZslQtI/AAAAAAAALlQ/YN27JINpuMcS2wllWr5acjDChDFBxaBkQCLcBGAs/s640/General-Principles-of-Teaching-arithmetic.jpg" title="General Principles of Teaching arithmetic" width="640" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><h4><i><u>General Principles of Teaching arithmetic</u></i></h4></td></tr></tbody></table><div><i><u><br /></u></i></div>The subject matter of this subject should be related to the facts and circumstances of life, otherwise this topic will become a monumental subject for the students. Most of the students in our schools find this subject very difficult and dull and they also get less marks in examinations. In fact arithmetic is a time-consuming and interesting subject, but due to inaccurate teaching methods, the interest of students is not developed in this subject.By making the basis of students' experience, forethought and interests in arithmetic, the subject becomes interesting and students are motivated to solve the questions. Stuart Mill has said - "Numbers are not intangible. All numbers are the number of objects." If we ask a student of a small class that what would be the answer to the addition of 5 and 7, then it would be difficult to add them. If we ask, "What will be the 5 oranges and 7 oranges?" Student can answer this easily.The processes of joint, rest, multiplication, part, etc can be done simply by establishing a relation of the physical objects and numbers, because the child can relate to processes with the understanding of less or more here.<br />A special advantage is to associate arithmetic text with the real facts of life, that the arithmetic knowledge of students becomes socialized.When we solve the problems of arithmetic, we can tell them the actual distance between the two familiar places, the actual rate of interest in the post offices, the movement of hourly kilometers of the postmaster, the price of the bicycle, the market price of Philips radio, the average weight of students of class X , Area of the farm near the school, the area of the four walls of the school, the volume of water lane in the school garden, the actual post office of the school The distance, the average weight of a melon, annual increase in the Indian population, mortality in India, the birth rate etc. India's National Income, assist in the development of correct mathematical approaches by spending information on the per capita on education, the cost of computer, the average monthly expenditure on keeping a car, expenditure on food in the average household etc.<br /><h2 style="text-align: left;">2. <i><u>Equation of Ideas -</u></i></h2>Counting is only one side of the arithmetic. A clear understanding of the arithmetic suffixes is also important.There are several suffixes in each sub topic in arithmetic whose information is not possible without using them in the calculation process. Students who do not have practical knowledge of these relations, do not start further lessons.<br />In addition to the explanations of the suffixes, the students should be given proper practice to use them. There are many sub-topics in decimal system, percentages, averages, ratios etc. in arithmetic whose clarity about the prefixes is compulsory and Sufficient practice is also required for their practical use. For example, when we teach a sub-topic of interest, the student must have a clear understanding of the following suffixes -<br />(1.) Interest is calculated on the principal.<br />(2.) Interest increases along with time period.<br />(3.) Interest is a type of rent used for capital.<br />(4.) Interest = Px R xT%<br />Similarly a clear knowledge of the following suffixes related to profit and loss is necessary -<br />(i) Profit or loss is at purchasing value.<br />(ii) Every business is used to profit.<br />(iii) In order to avail the profit, the sale price will be higher than the purchase price.<br />(iv) The expenses incurred in the business are added to the cost price.<br />(v) The higher the difference in sales and purchase price. The greater the difference between purchasing and selling-value, the greater the loss.<br />To clarify the suffixes, the principle of 'macro to micro' should be worked out.Where necessary, chart, picture model etc. should also be used. Whatever problems are presented, they should be related to the lives of the students and should be the basis for contemplation of forethought.<br /><h3 style="text-align: left;">3. <i><u>Mental calculation -</u></i></h3>While solving problems of arithmetic, students should practice mental arithmetic. After understanding the principles, the kind of meditation that the student does in the mind, for his application, is called mental work.While calculating, many things should be done in case of non-paper and pencil. With mental mathematics, students can think about the possible solutions and calculations related to the problem and make a decision about possible solutions.<br />The following benefits are derived from mental calculation-<br />(1.) The level of contemplation can be improved in the students.<br />(2.) Preferences, procedures and facts can be understood very quickly at the mental level.<br />(3) The expected findings can be quickly detected.<br />(4) The power to remember the subject matter increases.<br />(5.) Answers can be quickly detected.<br />Students who think about the uses of the principles of mathematics, suffixes, processes etc., at the mental level, knowledge of their subject is of good quality and And they have the convenience of learning new lessons. Along with verbal work in the classroom, adequate practice of mental math should be done. While solving the problem, the teacher can motivate mental contemplation in the right direction by question-answer about the suffixes. Before using written work, the practice of thinking in students is useful.<br /><h3 style="text-align: left;">4. <i><u>Scientific way of posing problems -</u></i></h3>In arithmetic, problems related to life should be created. Students do not have the joy of solving conventional problems because the facts given in them do not have any connection with their life. If the facts are correct and interesting, then the students will know the findings eagerly. Non-scientific and traditional problems have arisen most of the hindrances in arithmetic learning.The arithmetic teacher should be aware of the activities of the society so that the problems can be compiled by compiling the necessary facts and making scientific problems. When solving problems, students get information about the usefulness of arithmetic content and create an attitude about society. The problem solving method is more appropriate to teach arithmetic. The problems available in books are mostly filled with errors and errors.The following points should be taken into account in building problems:<br />(i) The language of the problem should be simple and clear.<br />(ii) The problem should not be unnecessarily long.<br />(iii) The facts given in the problem are clear and correct.<br />(iv) 'what to know' in the problem? Must be clear.<br />(v) If necessary, the problem can be written in different parts, so that the students can understand them well. Make Algebra the basis<br />(vi) Where possible, images, tables, etc. along with the problem can also be given to facilitate understanding the given facts.<br />(vii) The problem is suitable for the level of the children.<br />(viii) Integrated teaching of arithmetic and geometry should be done.<br /><h3 style="text-align: left;">5.<i><u> Individual variations in the classroom -</u></i></h3>All students in the class are not of equal merit. Some students are educated and others are savvy. It is necessary to co-ordinate the ability of the students and the level of teaching. A skilled teacher attempts to fulfill all the needs of the students in the classroom.Keeping in mind the personal differences of students, unit-schemes and lesson plans should be created. How many problems can be solved in a period. It can be decided by the teacher keeping in mind the ability of the students of their class. While teaching in class, it can be estimated by question-answer method that students are understanding the subject matter or not.Whenever a new lesson is taught, efforts should be made to clarify all related suffixes by several methods. Writing problems on the board by presenting the problem in the classroom can attract the attention of students to various aspects of the problem. Some students should read the problem before the whole class so that the language and facts can be explained. Every student should become clear that 'what is given'? And what to know? ''After this, discuss the method of solving the students with the teacher and verbally explain which method is appropriate in solving this problem and why other methods are not suitable. Provide teachers the correct direction to the mental reflection of the students. By doing so, he can elevate his thinking and reasoning level. Students in the class should be free to get rid of the problem of independence problem, so that they can examine themselves regarding the suitability of the related method.On such occasions, the teacher can assist students in finding solutions by giving personal attention. The greater use of Shyampatti is very helpful in attracting the attention of the orbit. The collective difficulties of calculation can be explained with the help of students on blackboard. If these things are kept in mind, after completing the teaching work, students can be reconciled with the personal differences.In the teaching work, skilled students can also get help as needed to overcome the difficulties of the weak students. Practice is required in class and at home for the clarity of the principles taught by students.<br />In the classroom, if efforts are made to clarify the precepts, concepts, principles, processes, calculations related to calculations, then there will be a reduction in the amount of individual variations in the students,Gradation will be achieved in the level of achievement in class and classroom will become classical.<br /><h3 style="text-align: left;">6. <i><u>Practice and written work -</u></i></h3>Practice work is essential for understanding the theories and processes of arithmetic. The program of practice is based on systematic and pre-planning. It is also necessary to be interesting to practice work. If students understand the new principles properly in the classroom then the practice becomes attractive to them.Practice work fulfills the important objectives of mathematics education. There are many such actions in mathematics that it is necessary to do repeatedly. Practices work through purity and speed in actions.<br />Practice work must be constantly checked. This will make the expected improvement in students' errors. They will not be able to improve them until the students are aware of the errors made by them.Practical work should be related to the materials taught in the classroom. Training is required for students to do written, correct, pure, clean and systematic work.</div><img src="http://feeds.feedburner.com/~r/SatyamMathematics/~4/LM-hQ7uD1ZI" height="1" width="1" alt=""/>satyam coaching centrehttp://www.blogger.com/profile/12788483628699913686noreply@blogger.com0https://www.satyammathematics.com/2019/08/general-principles-of-teaching-arithmetic.htmltag:blogger.com,1999:blog-4893862652325568386.post-75113968447370956332019-07-31T07:47:00.000+05:302019-07-31T14:46:50.328+05:30perpendicular bisector, perpendicular lines and planes <div dir="ltr" style="text-align: left;" trbidi="on"><h1 style="text-align: left;"><i><u><span style="font-size: x-large;">perpendicular bisector, perpendicular lines and planes </span></u></i></h1><h2 style="text-align: left;">1.<i><u>Perpendicular bisector-</u></i></h2><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><a href="https://1.bp.blogspot.com/-hP_jNgCaog8/XUFb_bH5haI/AAAAAAAALkw/08n8AmX2LG8GfVY9ERnOWWdiyfcgJaIIgCLcBGAs/s1600/perpendicular_bisector_perpendicular_lines_and_planes.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img alt="perpendicular bisector, perpendicular lines and planes " border="0" data-original-height="802" data-original-width="982" height="522" src="https://1.bp.blogspot.com/-hP_jNgCaog8/XUFb_bH5haI/AAAAAAAALkw/08n8AmX2LG8GfVY9ERnOWWdiyfcgJaIIgCLcBGAs/s640/perpendicular_bisector_perpendicular_lines_and_planes.jpg" title="perpendicular bisector, perpendicular lines and planes " width="640" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><h4><i><u>perpendicular bisector, perpendicular lines and planes </u></i></h4></td></tr></tbody></table><div><i><u><br /></u></i></div>For a line segment in a plane, the line perpendicular to the segment at this midpoint, for a line segment in space, the plane perpendicular to the segment at its midpoint. In either case, the perpendicular bisector is the set of all points equidistant from the end points of the segment.<br /><h2 style="text-align: left;">2.<i><u>Perpendicular lines and planes -</u></i></h2><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><a href="https://1.bp.blogspot.com/-wLcWALc_IOw/XUFcUe8ghHI/AAAAAAAALk4/akkldPCM-hI80T19YrJ7mAwpNznhOjclQCLcBGAs/s1600/perpendicular-bisector-perpendicular-lines-and-planes.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img alt="perpendicular bisector, perpendicular lines and planes " border="0" data-original-height="593" data-original-width="1024" height="370" src="https://1.bp.blogspot.com/-wLcWALc_IOw/XUFcUe8ghHI/AAAAAAAALk4/akkldPCM-hI80T19YrJ7mAwpNznhOjclQCLcBGAs/s640/perpendicular-bisector-perpendicular-lines-and-planes.jpg" title="perpendicular bisector, perpendicular lines and planes " width="640" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><h4><i><u>perpendicular bisector, perpendicular lines and planes </u></i></h4></td></tr></tbody></table><div><i><u><br /></u></i></div>Two straight lines which intersect so as to form a pair of equal adjacent angles are perpendicular (each line is said to be perpendicular to the other). The condition (in analytic geometry) that two lines be perpendicular is :(1) In a plane, that the slope of one of the lines be the negative reciprocal of that of the other, or that one be horizontal and the other vertical, (2.)In space, that the sum of the products of the corresponding direction numbers (or direction cosines) of the two lines be zero (two lines in space are perpendicular if there exist interesting perpendicular lines, each of which is parallel to one of the given lines). A common perpendicular to two or more lines is a line which is perpendicular to each of them. In a plane, the only lines that can have a common perpendicular are parallel lines and they have any number. In space, any two lines have any number of common perpendiculars (only one of which interests both lines, unless the lines are parallel). A line perpendicular to a plane is a line which is perpendicular to every line through its intersection with the plane. It is sufficient that it be perpendicular to two nonparallel lines in the plane. The condition (in analytic geometry) that a line be perpendicular to a plane is that its direction numbers be proportional to those of the normal to the plane, or, what amounts to the same thing, that its direction numbers be proportional to the coefficient of the corresponding variables in the equation of the plane. The foot of the perpendicular to a line (or plane) is the point of intersection of the perpendicular with the line (or plane). Two perpendicular planes are two planes such that a line in one, which is perpendicular to their line of intersection, is perpendicular to the other, i. e., planes forming a right dihedral angle. The condition (in analytic geometry) that two planes be perpendicular is that their normals be perpendicular, or that the sum of the product of the coefficients of like variables in their two equations be zero.<br /><br /></div><img src="http://feeds.feedburner.com/~r/SatyamMathematics/~4/pZIa5-x3k-4" height="1" width="1" alt=""/>satyam coaching centrehttp://www.blogger.com/profile/12788483628699913686noreply@blogger.com0https://www.satyammathematics.com/2019/07/perpendicular-bisector-perpendicular-lines-and-planes.htmltag:blogger.com,1999:blog-4893862652325568386.post-68656291962239695932019-07-30T07:46:00.000+05:302019-07-31T19:49:11.786+05:30Some Mathematics Definitions <div dir="ltr" style="text-align: left;" trbidi="on"><h1 style="text-align: left;"><span style="font-size: x-large;"><u><i> Some Mathematics Definitions</i></u></span></h1><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><a href="https://1.bp.blogspot.com/-WV0Mtl0O2pE/XUFfPue19fI/AAAAAAAALlE/jbounKppUgQwIBSUisUJfJMc8WTjtfEwQCLcBGAs/s1600/Some-Mathematics-Definitions.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img alt="Some Mathematics Definitions " border="0" data-original-height="195" data-original-width="260" height="477" src="https://1.bp.blogspot.com/-WV0Mtl0O2pE/XUFfPue19fI/AAAAAAAALlE/jbounKppUgQwIBSUisUJfJMc8WTjtfEwQCLcBGAs/s640/Some-Mathematics-Definitions.jpg" title="Some Mathematics Definitions " width="640" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><h4><i><u>Some Mathematics Definitions </u></i></h4></td></tr></tbody></table><div><span style="font-size: x-large;"><u><i><br /></i></u></span></div><h2 style="text-align: left;"><i><u>Angle-</u></i></h2>1.A geometric angle (or simply angle) is a set of points consisting of a point P and two rays extending from P(sometimes it is required that the rays do not lie along the same straight line). The point P is the vertex and the rays arc the sides (or rays) of the angle. Two geometric angles arc equal if and only if they are congruent. When the two rays of an angle do not extend along the same line in opposite directions from the vertex, the set of points between the rays is the interior of the angle. The exterior of an angle is the set of all points in the plane that are not in the union of the angle and its interior. A directed angle, then a radian measure of the angle for which one is designated as the initial side and the other as the terminal side. There are two commonly used signed measures of directed angles. If a circle is drawn with unit radius and center at the vertex of a directed angle, then a radian measure of the angle is the length of an arc that extends counterclockwise along the circle from the initial side to the terminal side of the angle or the negative of the length of an arc that extends clockwise along the circle from the initial side to the terminal side. The arc may wrap around the circle any number of times. For example if an angle has radian measure half of pi. Degree measure of an angle is defined so that 360 corresponds to radian measure of 2pi. A rotation angle consists of a directed angle and a signed measure of the angle. The angle is a positive or a negative angle according as the measure is positive or negative. Equal rotation angles are rotation angles that have the same measure. Usually angle means rotation angle. A rotation angle can be thought of as being a directed angle together with a description of how the angle is formed by rotating a ray from an initial position (on the terminal side).<br /><h2 style="text-align: left;">2.<i><u>Acute angle </u></i>-</h2>An angle numerically smaller than a right angle (usually a positive angle less than a right angle).<br /><h3 style="text-align: left;">3.<i><u>Addition of angles -</u></i></h3>The angle determined by a rotation from the initial side through one angle, followed by a rotation beginning with the terminal side of this angle, through the angle, algebraically, the ordinary algebraic addition of the same kind of measures of the angles (e. g. degree plus degrees or radians plus radians).<br /><h3 style="text-align: left;">4.<i><u>Adjacent angles </u></i>-</h3>Two angles having a common side and common vertex and lying on opposite sides of their common side.<br /><h3 style="text-align: left;">5.<i><u>Angles of depression </u></i>-</h3>The angle between the horizontal plane and the oblique lower than (beneath) the line of his eye.<br /><h3 style="text-align: left;">6.<i><u>Angle of elevation -</u></i></h3>The angle between the horizontal plane and the oblique line from the observer's eye to a given point above his eye.<br /><h3 style="text-align: left;">7.<i><u>Angle of friction </u></i>-</h3>If two bodies are in contact and one of these is at rest or in motion without acceleration, relative to the other, then the external forces acting on A are balanced by a normal reaction force N perpendicular to the plane of contact and a force of friction F in the plane of contact. When A is on the verge of moving, the acute angle is the angle of friction.<br />8.Angle of inclination of a line -<br />The positive angle, less than 180, measured from the positive x-axis to the given line.<br /><h4 style="text-align: left;">9.<i><u>Angle of Intersection -</u></i></h4>The angle of intersection of two lines in a plane is defined thus:The angle from line L1, say to line L2 is the Smallest positive angle that has L1 as initial side and L2 as terminal side, angle between lines L1 and L2 is the least positive angle between the two lines (the angle between two parallel lines is defined to be of measure 0).The angle between two lines in space (whether or not they intersect) is the angle between two intersecting lines which are parallel respectively to the two given lines. The cosine of this angle is equal to the sum of the products in pairs of the corresponding direction cosines of the lines. The angle two intersecting curves is the angle between the the tangents to the curves at their point of intersection. The angle between a line and a plane is the smaller (acute) angle which the line makes with its projection in the plane. The angle between two planes is the dihedral angle which they from, this is equal to the angle between the the normals to the planes. When the equation of the planes are in normal form, the cosine of the angle between the planes is equal to the sum of the products of the corresponding coefficients (coefficients of the same variables) in their equations.<br /><h4 style="text-align: left;">10.<i><u>Angle of a polygon </u></i>-</h4>An interior angle of a polygon is an angle whose vertex is a vertex of the polygon that meet at this vertex and whose measure is equal to the smallest positive measure that describes a rotation from one side through the interior of the polygon to the other side. An exterior angle is an angle whose vertex is a vertex of the polygon, whose sides contain one side (of the polygon) with an endpoint at this vertex and the other such side of the polygon extended through the vertex and whose measure is equal to the least positive measure that describes a rotation from one side of the angle to the other through the exterior of the polygon. At each vertex of a polygon, there is one interior angle and there are two exterior angles. These definitions suffice for any polygon for which no side contains points of more than two other sides (in other cases the must be ordered in some way so that the angles between them can be defined uniquely).<br /><h4 style="text-align: left;">11.<i><u>Angle of reflection </u></i>-</h4>The change of direction which, e. g., a ray of light, radiant heat, or sound, experiences when it strikes upon a surface and is thrown back into the same medium from which it same. Reflection follows two laws (1.)the reflected and incident rays are in a plane normal to the surface (2.)the angle of incidence is equal to the angle of reflection (the angle of incidence is the angle the incident ray makes with the normal at the point of incidence, the angle of reflection is the angle which the reflected ray makes with this normal.<br /><h4 style="text-align: left;">12.<i><u>Quadrantal angles </u></i>-</h4>The angles 0,90,180,270 all angles having the Same terminal sides as any one of these.<br /><h4 style="text-align: left;">13.<i><u>Reflex angle </u></i>-</h4>An angle greater than a straight angle and less than two straight angles, an angle between 180 and 360.<br /><h4 style="text-align: left;">14.<i><u>Related angle -</u></i></h4>The acute angle (angle in the first quadrant) for which the trigonometric functions have the same absolute values as for a given angle in another quadrant with reference to which the acute angle is called the related angle, 30 is the related angle of 150 and of 210.<br /><h4 style="text-align: left;">15.<i><u>Right angle -</u></i></h4>Half of a straight angle, an angle of 90.<br /><h4 style="text-align: left;">16.<i><u>Solid angle -</u></i></h4>A surface formed by rays with a common origin, the vertex of the solid angle and passing through a closed curve (a polyhedral angle is a special type of solid measure of the solid angle for which the curve is a polygon). A measure of the solid angle at P subtended by a surface S is equal to the area A of the portion of the surface of a sphere of unit radius with center at P, which is cut by a conical surface with vertex at P and the perimeter of S as a generatrix. The unit solid angle is the steradian. The total solid angle about a point is equal to 720 steradian.<br /><h4 style="text-align: left;">17.<i><u>Spherical angle</u></i> -</h4>The figure formed at the intersection of two great circles on a sphere, the difference in direction of the arcs of two great circles at their point of intersection.<br /><h4 style="text-align: left;">18.<i><u>Straight angle </u></i>-</h4>An angle whose sides lie on the same straight line but extend in opposite direction from the vertex, an angle of 180.<br /><h4 style="text-align: left;">19.<i><u>Supplementary angles -</u></i></h4>Two angles whose sum is 180, two angles whose sum is a straight angle. The angles are supplements of each other.<br /><table border="1"><tbody><tr><th>No.</th><th>Social Media</th></tr><tr><td>1.</td><td><a href="https://www.facebook.com/satyamcochingcentre">Facebook</a></td></tr><tr><td>2.</td><td><a href="https://www.youtube.com/channel/UCIhWUzFYTFwPsKEHHd7LKGQ?view_as=subscriber">you tube</a></td></tr><tr><td>3.</td><td><a href="https://twitter.com/satyamcentre">Twitter</a></td></tr><tr><td>4.</td><td><a href="https://www.instagram.com/satyamcentre">Instagram</a></td></tr></tbody></table><h4 style="text-align: left;">20.<i><u>Tetrahedral angle </u></i>-</h4>A polyhedral angle having four faces.<br /><h4 style="text-align: left;">21.<i><u>Trihedral angle-</u></i></h4>A polyhedral angle having three faces.<br /><h4 style="text-align: left;">22.<i><u>Trisection of an angle -</u></i></h4>The problem of trisecting any angle with straightedge and compasses, alone. Any angle can be trisected, however, in several ways, for instance, by the use of a protractor, the limcon of pascal the conchoid of Nicodemes or the trisectrix of Maclaurin.<br /><h4 style="text-align: left;">23.<i><u>Vertex angle-</u></i></h4>The angle opposite the base of a triangle.<br />24.Vertical angles - Two angles such that each side of one is a prolongation through vertex, of a side of the other.<br /><h4 style="text-align: left;">25.<i><u>Zero angle -</u></i></h4>The figure formed by two rays drawn from the same point in same direction (so as to coincide), an angle whose measure in degree is 0.<br /><div><br /></div></div><img src="http://feeds.feedburner.com/~r/SatyamMathematics/~4/iRjFDEyQtrQ" height="1" width="1" alt=""/>satyam coaching centrehttp://www.blogger.com/profile/12788483628699913686noreply@blogger.com0https://www.satyammathematics.com/2019/07/some-mathematics-definitions.htmltag:blogger.com,1999:blog-4893862652325568386.post-85216556786642770702019-07-29T07:45:00.000+05:302019-08-02T21:09:37.976+05:30Teaching of Arithmetic <div dir="ltr" style="text-align: left;" trbidi="on"><h1 style="text-align: left;"><b><i><u><span style="font-size: x-large;">Teaching of Arithmetic - </span></u></i></b></h1><h2 style="text-align: left;">1.<i><u>Introduction</u></i>-</h2>In his early days, when humans were under trees in trees, there was no need for arithmetic. Apart from food and safety, it was not necessary. His particular focus was limited to the then-leisure facilities.When the human group started to build, the number of needs began to grow and it needed to keep accounting with the development of civilization. He started counting his things and lost them when he lost them.Shaniya Shaniya, he started using the language of the number and listening to the mouth of others also understood it. In the beginning, the number of objects is calculated from different symbols or objects.<br /><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><span style="margin-left: auto; margin-right: auto;"><a href="https://www.satyammathematics.com/" target="_blank"><img alt="Teaching of Arithmetic " border="0" data-original-height="1067" data-original-width="1600" height="426" src="https://1.bp.blogspot.com/-HtZ0pCyAqiQ/XURYw0qbaZI/AAAAAAAALn0/T7jEiGxik2c-8GVXdgRAyuMIC1ivmqbmACLcBGAs/s640/Teaching-of-Arithmetic.jpg" title="Teaching of Arithmetic " width="640" /></a></span></td></tr><tr><td class="tr-caption" style="text-align: center;"><h4><i><u><a href="https://www.satyammathematics.com/" target="_blank">Teaching of Arithmetic </a></u></i></h4></td></tr></tbody></table><br />In fact, the need for knowledge of arithmetic is born when dealing with objects. To achieve the necessary tools, clothes, food etc., it became necessary for him to assess the value of the items and compare them with the values of other things.Along with the development of civilization, man developed arithmetic to solve his problems and gave the number system a scientific form. In our present life, our work can not be done without arithmetic. The suffixes of numbers and arithmetic are used in every field of life.<br />As our life and business are getting complicated, the use of arithmetic is increasing as well.Today, we employ many concepts and processes of arithmetic in every field of life.Number system is an important base of these and the characteristics of numbers have given birth to algebra and geometry. The set theory is based on the characteristics of numbers. In order to develop this number system of human has had to be persistent efforts for centuries and efforts are still being made to refine it today.<br />Life was not complex at the beginning of civilization. But with the development of business and life, humans had to create new arithmetic suffixes. The decimal system is unprecedented in this century. Before its discovery, the units of transactions, measure-weights, etc. were different and their basis of calculation was not even the same.But the decimal system has simplified hard calculations by assessing the calculation of different units as a basis. The invention of zero is the unique gift of the human brain. If we did not have knowledge of zero then today the nature of calculation processes would be very unscientific and possibly the amount of our progress would be very low.Newer measures are being taken to calculate, and with the help of computer hard calculations can be done very quickly.<br />So far, arithmetic has been considered as the subject of a calculation. But the simplicity of calculation processes is going to reduce the importance of this recognition.<br />In fact, arithmetic is related to calculation-side processes. Scientific studies of numbers are also an important part of arithmetic. Today the area of arithmetic has become very broad. It has been used in different areas. A typical form of arithmetic has been developed in these areas.<br />(1.) Family arithmetic (2.) Agricultural arithmetic (3.) Insurance arithmetic (4.) Bank arithmetic (5.) Production arithmetic (6.) Population arithmetic (7.) Business arithmetic (8.) Consumption arithmetic (9 .) Tax arithmetic (10.) Fatal arithmetic (11.) Computer arithmetic (12.) Sports arithmetic) (13.) Examination arithmetic<br /><h2 style="text-align: left;">2.<i><u>Meaning of Arithmetic :-</u></i></h2>Arithmetic is derived from the Greek word meaning 'science of numbers' and 'art of calculation'. Arithmetic involves the scientific study of the relation of numbers and the efficiency of the calculation. Mathematics teachers should emphasize on both sides of arithmetic. By emphasizing on one side, the second aspect of arithmetic becomes subtle.Knowledge of points and art of calculation - both parties are important. It is difficult to acquire skills in calculating without the scientific knowledge of numbers and knowledge of numbers is extremely important when calculating. Both are related to each other.One of the strong arguments in favor of teaching arithmetic is that it has significant use in daily life. To make arithmetic and its written symbols meaningful, use of everyday items should be used. In this way, students will understand the meaning of the numbers and symbols of the numbers by linking to the real objects.<br /><h2 style="text-align: left;"><u><i>3.Arithmetic is intended to teach the following things in primary classes-</i></u></h2>(1.) Ability to count quickly.<br />(2.) Ability to add, subtract, multiply and divide the small and large numbers written and verbal, and the ability to make problems based on them.<br />(3.) Knowledge of Variants<br />(4.) Knowledge of coins and their numerical value.<br />(5.) Ability to buy and sell goods. Ability to calculate value and calculate related to them. Ability to calculate with computer help<br />(6.) Ability to use arrays of sub-topics related to arithmetic courses.<br />(7) Knowledge of simple measurements, divisions and related processes related to them.<br />(8.) Knowledge of units measuring length and distance and ability to perform related calculations.<br />(9.) Ability to bring the principles of arithmetic to work in solving the problems of life.<br />(10.) Integrated teaching of arithmetic and geometry.<br /><h2 style="text-align: left;"><i><u>4 Objectives of Teaching of Arithmetic -</u></i></h2>(1) Knowing the number of languages, number-suffixes and number-symbols of children and the ability to use them successfully in life.<br />(2.) Creating the ability to think clearly about number, time and place in children.<br />(3) Use of mathematical ideas and the ability to reason in children.<br />(4) Creating the ability to properly understand arithmetic related statements in children and analyze them and find the right conclusions.<br />(5) Creating the ability to solve arithmetic practical problems in children. Creating the ability to use the computer.<br />(6.) Creating the ability to quantify the quantity, number, distance, and weight in the children.<br />(7.) Creating the ability to use the basic principles of arithmetic in children. Develop the ability to understand the numbers through the number line and geometric shapes.<br />(8.) Ability to calculate children quickly and accurately.<br />(9) Developing ideas, reasoning and decision-power in the children.<br />(10.) Adopting habit of cleanliness, purity and regular work in children.<br />(11.) The number of children - making the basis for the study of algebra and geometry of knowledge. Know the characteristics of the number line.<br /><h3 style="text-align: left;"><i><u>5.Develope the Following Qualities in Children -</u></i></h3>(1.) Time restriction.<br />(2) Save per month by adjusting expenses and earnings. Budgeting expenses and income Putting the habit of spending less.<br />(3.) To purchase and sell market prices through the benefit of goods.<br />(4.) To deposit money by opening savings accounts in post offices or banks.<br />(5.) While doing business, study the components that have an impact on business.<br />(6.) Attempts to understand the reasons for the increase and fall in the value of items.<br />(7.) To study the current economy and to try to understand its complexity in terms of theories of arithmetic.<br />(9.) To study current tax systems and calculate tax.<br />(10) Yoga in the development of the country by understanding the economic policies of the nation.<br />(11.) Finding the correct numerical approximation.<br />(12.) Painting numbers by geometric shapes.<br /><div><br /></div></div><img src="http://feeds.feedburner.com/~r/SatyamMathematics/~4/a50gccBSoV8" height="1" width="1" alt=""/>satyam coaching centrehttp://www.blogger.com/profile/12788483628699913686noreply@blogger.com0https://www.satyammathematics.com/2019/07/teaching-of-arithmetic.html