The Infinity Mathematics

A list of Regular and Irregular Verbs-[English Verbs]

2025-05-15T08:32:00.002+05:45

A list of irregular verbs.

V¹ V² V³V⁴ V⁵

Pay paid paid paying pays

Say said said saying says

Write wrote written writing writes

Do did done doing does

Make made made making makes

Take took taken taking takes

Go went gone going goes

Tear tore torn tearing tears

Teach taught taught teaching teaches

Come came come coming comes

Spend spent s pent spending spends

Listen listen listent listening listens

Throw threw thrown throwing throws

Win won won winning wins

Lose lost lost losing loses

Laugh laught laught laughing laughs

Cry cried cried crying cries

Fry fried fried frying fries

Dry dried dried drying dries

Show showed shown showing shows

Run ran run running runs

Dig dag dug digging digs

Send sent sent sending sends

Come came come coming comes

Read read read reading reads

Carry carried carried carrying carries

V¹ V² V³V⁴ V⁵

Fly flew flown flying flies

Drive drove driven driving drives

Drink drank drunk drinking drinks

Make made made making makes

Overtake ovetook overtaken overtaking overtakes

Take took taken taking takes

Write wrote written writing writes

Get got got getting gets

Tell told told telling tells

Sell sold sold selling sells

Say said said saying says

Buy bought bought buying buys

Sell sold sold selling sells

Bring brought brought bringing brings

See saw seen seeing sees

Send sent sent sending sends

Write wrote written writing writes

Speak spoke spoken speaking speaks

Steal stole stolen stealing steals

Win won won winning wins

Cut cut cut cutting cuts

Put put put putting puts

Read read read reading reads

Do did done doing does

Come came come coming comes

Build built built building builds

Blow blew blown blowing blows

Rise rose risen rising rises

V¹ V² V³V⁴ V⁵

Ride rode ridden riding rides

Drive drove driven driving drives

Sing sang sung singing sings

Spend spent spent spending spends

Teach taught taught teaching teaches

Fall fell fallen falling falls

Feel felt felt feeling feels

Sink sank sunk sinking sinks

Bend bent bent bending bends

Beat beat beaten beating beats

Bite bit bitten biting bites

Hear heard heard hearing hears

Wear wore worn wearing wears

Feed fed fed feeding feeds

Overcome overcame overcome overcoming overcomes

Grow grew grown growing grows

Catch caught caught catching catches

Shoot shot shot shooting shots

Try tried tried trying tries

Forget forgot forgetton forgetting forgets

Hold held held holding holds

Give gave given giving gives

Lend lent lent lending lends

Sing sang sung singing sings

Lay laid laid laying lays

Draw drew drawn drawing draws

See saw seen seeing sees

Deny denied denied denying denies

V¹ V² V³V⁴ V⁵

Deal dealt dealt dealing deals

Ring rang rung ringing rings

Wake woke waken waking wakes

Fly flew flown flying flies

Sit sat sat sitting sits

Stand stood stood standing stands

Identify identified identified identifying identifies

Verify verified verified verifying verifies

Purify purified purified purifying purifies

Meet met met meeting meets

Burn burnt burnt burning burns

Hit hit hit hitting hits

Heat heated heated heating heats

Sleep slept slept sleeping sleeps

Drink drank drunk drinking drinks

Have had had having has

Be was/were been being is/ am/ are

Try tried tried trying tries

Delay delayed delayed delaying delays

Smell smelt smelt smelling smells

Sigh sought sought sighing sighs

Speak spoke spoken speaking speaks

break broke broken breaking breaks

deal dealt dealt dealing deals

Shake shook shaken shaking shakes

Feed fed fed feeding feeds

Shoot shot shot shooting shoots

meet met met meeting meets

sing sang sung singing sings

buy bought bought buying buys

bring brought brought bringing brings

rise rose risen rising rises

put put put putting puts

get got got getting gets

Let led led letting lets

A list of regular verbs:

V¹ V² V³V⁴ V⁵

Clean cleaned cleaned cleaning cleans

Collect collected collected collecting collects

Paint painted painted painting paints

Move moved moved moving moves

Kill killed killed killing kills

Climb climbed climbed climbing climbs

Shout shouted shouted shouting shouts

Wash washed washed washing washes

Destroy destroyed destroyed destroying destroys

Stare stared stared staring stares

State stated stated stating states

Desire desired desired desiring desires

Test tested tested testing tests

Construct constructed constructed constructing constructs

Look looked looked looking looks

Phone phoned phoned phoning phones

Disturb disturbed disturbed disturbing disturbs

V¹ V² V³V⁴ V⁵

Smile smiled smiled smiling smiles

Correct corrected corrected correcting corrects

Cook cooked cooked cooking cooks

Remember remembered remembered remembering remembers

Design designed designed designing designs

Pump pumped pumped pumping pumps

Fire fired fired firing fires

Hire hired hired hiring hires

Terminate terminated terminated terminating terminates

Click clicked clicked clicking clicks

Satire satired satired satiring satires

Focus focused focused focusing focuses

Emphasize emphasized emphasized emphasizing emphasizes

Treat treated treated treating treats

Ask asked asked asking asks

Report reported reported reporting reports

Happen happened happened happening happens

Belive believed believed believing believes

Achieve achieved achieved achieving achieves

Pass passed passed passing passes

Wonder wondered wondered wondering wonders

Wander wandered wandered wandering wanders

V¹ V² V³V⁴ V⁵

Advise advised advised advising advises

Inspire inspired inspired inspiring inspires

Encourage encouraged encouraged encouraging encourages

Show showed showed showing shows

Refer referred referred referring refers

Return returned returned returning returns

Check checked checked checking checks

Share shared shared sharing shares

Follow followed followed following follows

Watch watched watched watching watches

***The End***

USE OF ICT IN CLASSROOM: TEACHERS AND STUDENTS PERCEPTION ON ICT TOOLS (SEMINAR PAPER)

2022-06-26T13:43:00.001+05:45

Use of ICT in Classroom: Teachers and Students Perception on ICT Tools

(A Seminar Paper)

Submitted To:

Central Department of Education

Department of Foundations of Education

For the Partial Fulfillment of Contemporary Educational Issues (Ed. 541), M. Ed. 4^th Semester

Submitted By:

Name: .........

Roll No: ......,

Symbol No.: ........

Room No: ...........

Major: ICTE Educations

Date: 18 Feb, 2022

Abstract

Information and Communication Technology (ICT) plays various roles to make mathematics teaching-learning activities more meaningful. Technology has seen a recent widespread integration into daily life, where access to vast amounts of information is now available. The ICT integrated teaching forcefully underpinning in our education system as a pedagogical intervention. The teachers and students are trying to habituate with incorporating their teaching learning activities.

This is a study on “Use of ICT in Classroom: Teachers and Students Perception on ICT Tools” The objective of the study was to investigate the teacher’s perception of the ICT tools used in classroom teaching and to explore students’ perceptions of ICT use in the learning. In order to achieve these goals, teachers and students access ICT in classroom teaching and learning at the Master's level. The major tools used for the study were observation and interviews of mathematics teachers and r students as the sample of the study. I used the qualitative research design. It contains method that I employed while collecting data, such as document analysis, interview, questionnaire and observation. The data were organized, grouped, analyzed, and interpreted according to the objectives of the study.

The study concluded that the teachers and students have a positive opinion of perceptions of ICT tools. The result of the study showed that the highly preferred tools have laptop/ desktop computers, multimedia projectors, cell phones, and software tools like the internet, email, office program, and related apps like Moodle. Promote both the teachers and learners to more interactive, communicative, and self-learning. I also found that it facilitated to create more collaborative and cooperative learning. The e-library, Moodle, and electric whiteboard were also preferred for promoting the self-learning and self-paced leaning.

Keywords: ICT tools, Access, Teaching and Learning, E-Learning, collaborative learning

List of Abbreviations

ICT: Information Communication and Technology

MOE: Ministry of Educations

GON: Government of Nepal

SSDP: School Sector Development Programs

TPD: Teacher Professional Development

NCED: National Center for Educational Development

TU: Tribhuvan University

HSEB: Higher Secondary Examination Board

ISP: Internet Subscriber Protocol

NGO: Non-Government Organization

OLPC: One Laptop per Child

DEO: Department of Education

UNESCO: United Nations Educational, Scientific and Cultural Organization

Table of Contents

Introduction. 1

1.1 Background of the study. 1

1.2 Objectives. 2

Methodology. 3

2.1 Document Analysis. 3

2.2 Interview with Teacher and Student. 3

2.3 Observation. 3

2.4 Data Analysis. 4

Literature Review.. 5

3.1 Policy and provisions. 5

3.2 Students Perception of ICT Tools in learning. 6

Findings &Discussion. 8

4.1 Status of ICT tools Teacher Perception in Classroom.. 8

4.1.1 Improper training. 9

4.2 Students Perception of ICT Tools at Home. 10

4.2.1 Access to ICT Tools at Home. 11

Conclusion. 13

References. 14

Appendices. 15

Appendix- A: Teacher’s Interview Guideline. 15

Appendix- B: Student’s Interview Guideline. 16

Use of ICT in Classroom: Teachers and Students Perception on ICT Tools

Introduction

1.1 Background of the study

Creative and innovative applications of information and communication technologies (ICT) have long seen as important potential tools to enable teaching and learning reform processes improving both access to education, and the quality of that education. Several scholars suggest that ICT tool was be an important part of education for the next generation.

The new technologies have the potential to up keep education across the curriculum and deliver opportunities for efficient student‐teacher communication in ways not possible before. ICT tools in education have the potential to transform teaching. Communications refers to the means of transferring knowledge from one person to another person or one place to another or so on. In other words, exchanging information views and felling has known as communication. All the development and discoveries are true today because of the growing trend of ICT (Dhital, 2018).

The traditional instruction style in Nepal is advocated not only by teachers but also by parents. Thus, Nepalese education is strongly influence by content and by examination driven practices, with little or no attention paid to encourage students to use their knowledge and skills to solve practical problems, or to try to access their own, already acquired knowledge and construct new ideas. Traditional methods of teaching and learning are still dominant in Nepal, so professional development in more modern pedagogical practice is an area deserving close attention. As it is taught distribute knowledge and skill to their students who in turn memorize facts, definitions, and algorithms, but who have little or no practice in thinking for themselves (MOE, 2013).

There is an increasing number of computers and other technology in our everyday life. Many students and teachers have using these technologies for better knowing and new way of learning. The ICT affects every aspect of our life like teaching, learning, reporting, communicating, and so on. However, educational systems around technologies (ICTs) teach students the knowledge and skills they need in the 21st century (UNESCO, 2002). It is the most emerging phenomenon for school and college education. It has created a new discourse of pedagogical transformation in education (UNESCO, 2014). The world is under increasing pressure to use the new information and communication

The discussion cleared that the pressure of ICT intervention is inevitable in higher education classrooms to meet the societal needs and transformation of society in Nepal. Now, higher education institutions are trying to establish the ICT as an instructional tool for learning. Due to this scenario, this study has explored the teacher's and students' perceptions of using ICT tools in the classroom. What are perception of the ICT tools that teacher and students prefer for learning? Therefore, this is the curiosity why many students like ICT use in education. Does it enhance the quality of ICT education? What are the student's and teachers perception to use ICT tools in learning, teaching-learning activities of ICT Classes, Application of ICT tools, ICT lab, internet facilities, and education system of ICT in education? Therefore, many researchers have concluded that students are more interested in ICT. Therefore these profiles mentioned above help to measure the use of ICT tools in classroom: teachers and students perception in the context of Nepal.

1.2 Objectives

The main objective of this study was to find out the “Use of ICT in Classroom: Teacher’s and Student’s Perception on ICT Tools” The specific objectives of this study were as follows:

I. To find out teachers’ perception of the ICT tools used in classroom teaching.

II. To explore students’ perceptions of ICT use in learning.

Methodology

The required methods of this study were interviews, observation, and document analysis. To conduct this “Use of ICT in Classroom: A Teacher and Student Perception on ICT Tools is a qualitative research design. This design deals with the procedure of the qualitative research, which was carried out to achieve the response to the problem.

2.1 Document Analysis

To collect, require data this study was different document analyses likewise, ICT Master Plan (2013-2017), School Sector Development Programs (2016-2023), and ICT National Policies-2015 and articles, etc.

2.2 Interview with Teacher and Student

I had selected on master's degree (University Campus, Kirtipur) of Kathmandu District purposively. I have taken two teachers and two students’ interview participation for qualitative data collection. The researcher granted permission from the Head of the Department and Subject teachers to conduct an experiment. For collecting information and data with related topics, the interview was being conduct for teacher and student based on interview manual. The teachers and students I selected for the study were ICT teaching and learning at the Master's level. The first fall, I went to this campus and then meet the department of the head (gatekeeper). I requested seminar paper research. Then, I meet the teacher and students and arranged the leisure time for an interview. Then I have approval from the teacher and student. First, fall one teacher interview about my proposal objectives (See Appendix-A). Then I took the students interview about my related objectives question (See Appendix-B).at the end of this interview hearty thanks for help.

2.3 Observation

As a data, gathering device direct observation makes an important contribution to descriptive research. The purpose of the classroom observation was to provide supplemental data for the study. This study was participant observation where the researcher was participating in the classroom. For my research, I have observed the student activity classroom and some important data collection. This observation is to observe teachers’ actual use of ICT in the classroom.

2.4 Data Analysis

The information and data collected from various sources and means were analyzed meaningfully by the qualitative method. As well as the time of study conclusion will be produced based on interviews, observation, and document analysis by using the descriptive method. This study received data collected. Then, data were grouped based on the objectives. In this section was a discussion about different topics and sub-topics. Then, according to the fundamental discussion were data arrangement. I have analyzed the data linked with many kinds of literature. Data were grouped based on the objectives. In this section was a discussion about different topics and sub-topics. Descriptive and interpretive analyses were used to analyze the data.

Literature Review

3.1 Policy and provisions

(ICT Master Plan(2013-2017)) has mainly focused on Integrating ICT in all aspects of education. Using ICT in education to increase access to quality education rural in areas. To give emphasis on the use of ICT to increase the efficiency and effectiveness of the management system in education. The development of ICT infrastructures, human resources, digital content, and system enhancement in education. To reduce the digital divide. This master plan should be ICT for all students, meaning that the policy would act as an enabler to reduce the digital gap. To promote educational access and equity for all regardless of age, gender, ethnicity, disability, or location. The role and function of ICT in education as a teaching and learning encourage digital learning materials. Use ICT in education to increase access to quality education in rural areas.

According (to ICT National Policies, 2015) has an Expansion of access to the Internet in all schools and the development of skilled human resources special ICT programmed for students, teachers, and schools. To support Administration, pedagogy, and learning with a view to improving the quality of education and training at all levels and enhancing access to education. A nationwide E-school and E-education as well as lifelong learning launched to promote e- learning. The technical school will be the foundation for human resource and skill development in ICT. The development of intellectual property in ICT. Greater emphasis on ICT in school education with policy provision of expansion of access of the internet to all schools, coordination, and collaboration with national and international institutions to develop skilled human resources for continuous, relevant, and quality education, promotion of Industry-Academia Collaboration (IAC), and formulation and implementation of special IT programs focusing students, teachers, and Collage to develop competent human resources.

(Moila, 2006) Did research on “the use of educational technology in teaching and learning: An investigation of a South African college.” The investigation followed a mixed-method approach that was more evaluated and was a case study. The study consists of 25 students and 5-ICT teachers from An investigation of a South African college College. The findings concluded that the computer technology was not used in ICT tools teaching and learning, there are no plans for the use of educational technology tools in ICT teaching and learning, inadequate educator training on the use of educational technologies in teaching and learning, and lack of relevant educational technology tools for rural Campus.

Educational institutions are also influenced by this technology and most of these have tried to adopt it. The teachers and students are no exceptions to using these tools. This tool helps to transform the teachers and students into a technocratic society (Mbangwana, 2008)

3.2 Students Perception of ICT Tools in learning

According to (School Sector Development Program(2016-2023)) Improving teacher capacity resources for teachers in the teaching and learning process. Interactive materials and classes; videos, online/offline modules/ kits for teaching ICT enable teaching and learning environment: ICT lab in 100 Collage. Provide ICT infrastructure and teaching-learning materials. Provide ICT teaching-learning materials to strengthen teaching interactive approaches. Curriculum Development Center has posted these materials in its web site but lagging behind in reaching needy school, teachers and students. Similarly, NCED has initiated ICT teacher training through Teacher Professional Development(TPD) Programs as an ample effort at the resource center level but it lacks teacher preparation programs, where the majority of teachers are prepared, organized by the Higher Secondary Board (HSEB) and Universities, specifical faculty of education, Tribhuvan University(TU).

Prepare ICT teaching and learning materials initially for ICT. Improve classroom delivery, increase access to learning materials, and effectiveness and efficiency of educational government and management system. Provide ICT infrastructure and teaching-learning materials. MOE has implemented some of the programs related to ICT in education. They are one laptop per child (OLPC) pilot project in selected 26 Collage of six districts; Lab modal (computer sharing mechanism) projects in some Collage and internet connectivity to District Educations Offices (DEOs) and schools (through matching funds to college) and computer labs with an internet connection from local Internet Subscriber Protocol (ISPs). Department of Education (DOE), with the involvement of some NGOs, has developed interactive digital learning materials for the students at the University Level.

(Lam & Lawrences, 2002) Stated that the technology not only gives learners the opportunity to control student's own learning process but also provides them with ready access to a vast amount of information over which the teacher has no control.

(Keong, Horain, & Daniel, 2005) Dose a researcher on “a study on the use of ICT in teaching in Malaysia. This research deployed a survey method to investigate the use of ICT and barriers to integrating ICT into teaching. The survey was carried out during the ICT tools in-service course conducted by the state education department. The finding concluded that the use of ICT in teaching could make the teaching process more effective as well as enhance the student’s capabilities in understanding basic concepts. Nevertheless, implementing its use in teaching is not without problems as numerous barriers may arise.

Findings &Discussion

This study focused on the teacher's and students perceptions of using ICT tools in the classroom. The results of this study were presented in this section according to the objectives

4.1 Status of ICT tools Teacher Perception in Classroom

Access to computers, ICT software, and ICT teaching and learning has increased globally in the past few decades, but in many places like Nepal, technology is rarely integrated substantially, or even at all, into everyday teaching. One reason for this is the here to for Lack of appropriate professional development for the application of technologies and tools in a classroom situation. In these issues, one teacher says, “I mostly used PowerPoint presentation to present my lessons. Similarly, I also use Google to search for materials and presents. In the same way, I explore the internet to find out sample materials for reading and sample research to make my students be familiar with current international trends in research.”

The teacher had a supportive perception of the use of ICT tools in the classroom in terms of the perception of teaching, developing the teaching materials, creating innovative teaching, and evaluations of student’s outcomes. It is because the ICT is helpful in the perception of classroom teaching. The learning software still needed to be improved because the digital era demanded rapid change in learning.

I am totally agreed with this statement at Collage Level not only in teaching ICT. The teacher does not provide sufficient time for ICT teaching and learning. However, college administration and ICT teacher collaboration at college. In this situation the ICT education field, in particular, more teachers should be interested in getting professional development training in the use of advanced technology. The initiative described in this paper was designed to encourage teachers to do this, though it was not very successful in this aspect.

Perception of teacher ICT tools teaching and learning at teacher training, infrastructure, and human skilled development resource for integrating ICT for teaching and learning were not sufficient in the Nepali context. A teacher says “in our college at one ICT (computer, laptop, multimedia, social media, software, and projector) lab which where students can easily access teaching and learning notes, assignment and project work.”

After this interview, I concluded that students get more effective ICT teaching and learning, and student ICT concept help student dream. The student collaboration learning feels good uses of ICT.

I agree in this situation student and teacher perception of ICT tools in teaching and learning. The college also maintains an ICT lab and teacher training. the expense of student performance on the national examination Increased knowledge about and skill in using technology combined with positive results in using it with students could help teachers to be more disposed toward incorporating it in their instructional practice. The issue for those delivering professional development to teachers concerns whether the new skills and knowledge are given an active role in teachers’ classes after the training is completed.

4.1.1 Improper training

For the successful and effective ICT tools used, teacher training is of most important ICT will be very useful for teacher and student. One of the preliminary steps in implementing any ICT-based educational approach is teacher perception, unless the teacher is fully comfortable with a new approach to teaching, providing students with computers. That is why training related to the specific subject with appropriate use must be essential for teachers. A teacher says “we are not sufficiently trained how to use ICT tools in (laptop/computer, multimedia projector, mobile phone, Software tools: internet, email, Microsoft word, excels, PowerPoint, Moodle.)Teaching and learning.”

After this interview, I concluded that the master trainer at the teacher training centers are does not have highly trained ICT human resources in the ministry. The teacher will also play a vital role in the colleagues and ICT for college administration and information management. So that knowledge is necessary to teach the ICT subjects.

From this, it can be seen that the training is not centered upon teaching the particular subject. The training that the ICT teacher need is not given yet. National Center for Educational Development (NCED) has been provided to the teacher through national radio and FM; compute science has been taught as an optional subject in school (grades 9 to 12), and Bachelor’s and Master’s levels are run by different colleges under various universities; various training institutes conduct technical education and vocational training courses in computer and ICT.

Supporting their lecturer and demonstration of materials. Showing photos, video, and materials through it. Investigate new things and help to compete in the global market. Help to increase the global competition. Help to create more collaborative and cooperative learning. Promote both the teachers and learners more interactive and communicative. Promote self-learning and self-paced learning.

4.2 Students Perception of ICT Tools at Home

In this 21^st digital era, the use of ICT in real classrooms to tech was most challenging in the Nepali context. Advancements in learning opportunities tend to be held back by the ICT capabilities of the lowest common denominator, namely the students with the least access to ICT. With ICT, access increases among students. The use of ICT tools in the classroom has long been a topic for consideration by ICT educators. One student says, “In our college 27 computers but it is not proper work and internet connectivity in computer.”

After this interview, I concluded that government-provided internet connectivity access to the local and College level. But, more effective ICT teaching and learning government provides internet connectivity in classroom learning.

But, ICT Master Plan (2013-2017) has emphasized the Expansion of access of the Internet to all schools; Coordination, and collaboration with national and international institutions to develop skilled human resources for continuous, relevant, and quality education. SSDP (2016-2023) to Promotion of Industry-Academia Collaboration (IAC); and Formulation and implementation of special IT programmer focusing on students, teachers, and schools in order to develop competent human resources.

In this regard, internet connectivity is available in ICT Lab, and policies about all college available internet connectivity are limited only to documents. The tool immediately was used on cell phones in the android version. It was the cheapest way to implement it. I also found that it facilitated to create more collaborative and cooperative learning. The e-library, Moodle, and electric whiteboard were also preferred for promoting self-learning and self-paced learning. In this situation government not to be able to regulate and coordinate on campus and government.

I do not agree with this problem but universities in developing countries should adopt e-learning technologies to improve teaching and learning processes. Pedagogical, technical and cost issues should be taken into account for each specific technology when integrating ICTs in teaching and learning practices as challenges.

In this digital era, ICT teaching and learning real-world problems one country and country coordination in online different ICT software uses to solve the educational problem. A student says, “In our teacher only uses Microsoft power-point and projector in ICT teaching and learning and it is using limited access to a computer.”

After this interview, I concluded that using ICT tools greatly increased students, motivation and engagement in learning. Students positively to the use of ICT tools: they engaged well with lessons and learning was very good.

In this regarded ICT National Polices (2015) has ICT skilled human resource development management, Increasing access to education, Integration of ICT in all aspects of education, Expansion of access of the Internet to all schools Coordination and collaboration with national and international institutions to develop skilled human resources for continuous, relevant and quality education. SSDP (2016-2023) To Promotion of Industry-Academia Collaboration, Formulation, and implementation of special IT programmers focusing on students, teachers, and schools to develop competent human resources. Development of ICT infrastructure in education.

ICT is a dynamic, easy-to-use tool as well as an interactive ICT for learning ICT tools in a unique style in which students have engaged in demonstrations, construction, and exploration that are not available through paper-pencil.

4.2.1 Access to ICT Tools at Home

For using ICT tools in teaching-learning activities we need to invest the required money at first because there required different software for ICT and furthermore, it needs to be updated frequently. A most developing country has an economic challenge to use ICT in classroom activities as same as in Nepal. Mostly ICT teaching and learning at home more practice with Internet connectivity, laptops, and android phone. Students say, "I have an android phone, laptop, and use of ICT educational software at home.”

After this interview, I concluded that ICT only used college but more practice at home in ICT education teaching and learning. ICT had facilitated the self-learning of students. The attitude of teachers was that ICT could improve the learning strategies and teachers’ roles in a supportive and collaborative way.

However, recent figures from the Nepal Telecom Authority show that around 24 percent of Nepal now have access to some form of internet connection. The students mostly ICT used on mobile phones. ICT has already encompassed the world of mass media. ICT has been provided as one of the important tools for ICT teaching and learning in the home education system. The student used easily practice at the home.

Conclusion

In Nepal, the initiation of ICT in college education is progressing. Master Plan (2013-17) to integrate ICT into school education. This demonstrates the commitment on the part of the government. Until now, the program is not in a stable position. ICT provides a great opportunity for schools/universities in developing countries to improve their teaching and learning processes. So far, most of the schools/universities in developing countries possess basic ICT infrastructures such as internet, computers, video, audio, and mobile technology facilities that form the basis for the establishment of E-Learning.

The effects of globalization have influenced the teachers and students in their teaching and learning. Now, they both are trying to transform their roles into ICT-based activities in the classroom. They both teach and students have aware of to use of ICT tools in their pedagogy and try to incorporate them into their learning. The most convenient tools were computers, multimedia projectors, cell phones, and the internet for teachers and students. Both of them believed that ICT friendly learning environment creates more collaborative, supportive behavioral practices in the classroom. ICT tools would be useful for self-study and group work habits in learning.

Generally, the results show a positive perception that teachers hold of the use of ICT in teaching and learning. Despite the challenges associated with ICT integration in Nepal, teachers have demonstrated their willingness to use the available ICT tools for teaching and learning. In addition, teachers employ several criteria in selecting ICT tools to use in teaching and learning. Help to create more collaborative and cooperative learning. Promote both the teachers and learners to more interactive, communicative and self-learning. The ICT tools are inevitable phenomena for effective delivery of knowledge and skills in higher education teaching to meet the global needs of education.

References

Dhital, H. (2018). Opportunities and Challenges to Use ICT in Government School Education of Nepa. International Journal of Innovative Research Computer and Communication Engineering, 6(4).

GON. (2015). ICT National Policies. Kathmandu: Government of Nepal.

Hohenwarter, M. (2008). E-learning: Concepts, Issues, Application, Evaluation. Austria: Riyadh: Dar Alsolatech Publication.

Keong, C. C., Horain, S., & Daniel, J. (2005). A study on the use of ICT tools in teaching. Online Journal of Educational Technology, 4(7), 25-27.

Lam, Y., & Lawrences, G. (2002). Teacher-student role redefinition during a computer-based. Computer Assisted Language Learning, 15 (3), pp. 295-315.

Mbangwana, M. A. (2008). Introduction of ICT in schools and classrooms. Cameroon: Langaa, Bamako.

MOE. (2013). ICT Master Plan(2013-2017). Kathmandu: Ministry of Education, Government of Nepal.

MOE. (2013). Information & Communication Technology (ICT) in Education Master Plan 2013-2017. Kathmandu: Government of Nepal.

MOE. (2016). School Sector Development Program(2016-2023). Kathmandu: Ministry of Education, Government of Nepal.

Moila, M. M. (2006). The use of educational technology in teaching and learning: An investigation of South African college. Eurasia Journal of Mathematics, Science and Technology Education, 37(3), 72-75.

UNESCO. (2002). Information and communication technologies in teacher education:. Paris: UNESCO Higher Education.

UNESCO. (2014). Information and communication technologies (ICT) in education. Canada: UNESCO Institute for Statistics.

Appendices

Appendix- A: Teacher’s Interview Guideline

Name of the teacher:

Campus Name:

Campus Address:

Campus Phone No. :

1. What are the teachers’ perceptions of ICT tools in teaching?

.............................…………………………………………………………………

2. What are the teacher's perceptions and attitudes on ICT tools used in the classroom?

………………………………………………………………………………………

3. What are teachers’ perceptions in relation to ICT usage? ………………………………………………………………………………………

Appendix- B: Student’s Interview Guideline

Name of the Student:

Campus Name:

Campus Address:

Campus Phone No. :

1. What are your perceptions of the ICT facilities that are available?

………………………………………………………………………………………

2. What is your view about the current ICT state in campus?

………………………………………………………………………………………

3. What are the different types of ICT used in the classroom?

………………………………………………………………………………………

History of Mathematics Timeline in Nepal-Infinity Maths

2021-05-24T01:29:00.002+05:45

TIMELINE OF DEVELOPMENT OF MATHEMATICS IN NEPAL

Dan Bdr Budha

Student, Central Department of Education, University Campus, Kirtipur, Nepal

E-mail: budhadanbdr@gmail.com

It is difficult to declare how long ancient Nepal, when, where, and who used mathematics at first in Nepal. It is well-known mathematics was practiced very early in human civilization. So the history of mathematics is old as human civilization. It is practiced in guru Kula and different situations in the context of Nepal as other civilizations.

But it appears that Kirant ethnicity lived in Nepal more than 2,500 years ago. The kirant are a tribe of jungle and mountain people who migrated from various parts of central Asia, china, and the Himalayas and they ruled for a long time in Nepal, so we claim that Nepal is a very ancient country in the world. The brief timeline of mathematics in Nepal is listed below.

Early mathematics is practiced very beginning of the human civilization and antique age. In Guru Kula system also practices mathematics as the form of Jyoutisha as arithmetic. The tentative few dates related to mathematics developments are listed below.

Φ (576-880): Sumatitantra / Sumati Siddhanta Jyoutisha. Sumatitantra is written in basis of Varahmihira’s Surya Siddhanta written in 505.

Φ 1099: Bhaswati was written by Satyananda of Udisa (Orisa) and its commentary Balbodhani Tika was written by Daibagya Balabhadra in 1494, it is the third popular commentary of Bhaswati. Bhaswati contains addition, subtraction, multiplication, parts,, division, etc. it was 576 years ago than the establishment of Royal Observatory at Greenwich and appointment of Royal Astrologer at that observatory. At that time after completion of the study of Bhaswati then the complex study of Lilavati was starting.

Φ 1409: Dharma Patibardhan at Kathmandu had written Sumati Siddhanta Jyoutisha a book that gives the theory of calculation of planetary eclipse. It was 266 years ago than the establishment of the Royal Observatory at Greenwich and the appointment of Royal Astrologer that observatory.

Φ 1723: Daivagya Chakrapani Aryal at published his Jyoutisha manual Uttana Ganita for calculation of calendrical data like calculation of solar and lunar eclipse. It was 48 years ago than the establishment of Royal Observatory at Greenwich and appointment of Royal Astrologer at that observatory.

Φ (1758-1831): Laxmipati Pandey was the astrologer and mathematician who advised King Prithivi Narayan Shah. He wrote about 40 books, some of the notable books- Ratnadeep, Lilabati, Bhaswati, Tika, Ghira Laghava, Kalarnav Dipika, etc. He prepared the sun Dial before 83 years ago than the establishment of the Royal Observatory at Greenwich and the appointment of royal astrologer John Flamstid at that observatory. Lila Nath Pande, son of Laxmipati Pande had written Siddhanta Jyoutisha book which was the first Nepali book unpublished book.

Φ (1786-1832): Lila Nath Pande had started the comparative study in Nepali. He is as a popular writer of Jyoutisha Ganita.

Φ 1832: Brahamala Shrestha was born and had written Vichitra Ganita in 1918.

Φ (1847-1918): Gopal Pndeya was born in the Gorkha district of Nepal. Gopal Pandey was the first mathematician and writer of mathematics in the Nepali language among the known mathematics of Nepal. He had written his first mathematics book “Vyatka Chandrika” in Nepali medium 1883 to 1914. He has engineering (designed) Tundikhel at Kathmandu. He verified the lunar eclipse in Nepal.

Φ 1853: Darbar High school was established and it is the main source of education.

Φ 1877: The First Sanskrit school was established by Ranodip Singh.

Φ (1877-1940): Jaya Prithvi Bahadur shah had written Aksharank Shikha in 1901. It was a very remarkable works in Nepali mathematics.

Φ (1878-1934): Pahal Man Singh Swar had written Ankendushekhara which influenced Nepali mathematics.

Φ 1883: Chandra Shamsher was the first student of matriculation. He passed (S.L.C.) with mathematics major. Chakravarti Arithmetic, Lilavati, roots, rule of three, LCM, etc. were taught at that school. Narendranamy translated the arithmetic used for teaching in 1834 in Shrestha pathshala.

Φ 1884: Publication of first Nepali calendar. Himnath Pant (son of Toya Nath Pant) was first master’s degree in Jyoutisha in Nepal. He had worked in the preparation of calendar.

Φ 1903 (born): Harinath Pokheral wrote Brahmanda Darpan (1922) and Miti Darpan and Panchnga (1928) books in the Nepali language in Kashi.

Φ (1909-1936): Tika Ram Dhananjaya had contributed in Nepali mathematics through Sishubodhatarangini with his wife Chandrakaladevi Dhananjaya in 1933. He had contributions in Veda, Jyoutisha, Ayurveda, Panchanga, etc.

Φ (19013-2002): Naya Raj Pant occupies a central position in history of mathematics in south Asia. He had written more than 200 mathematical treaties based on number theory, trigonometry, Jyoutisha, spherical trigonometry, planetary motion and calendar, sun dial, calculus, chhanda, etc. Meru Nath Pande, Kabi Raj Pande is also the popular writer of algebra in the Nepali language at that time.

Φ (1913-2007): Prof. Keshav Dev Bhattrai was a Matriculation from Patna University was as the second M.A. degree holder in the whole of Nepal. He conducted a memorable quiz contest for school-level mathematics in olympiad mode. He taught at Trichandar College.

Φ (1922-1997): prof. Gobinda Dev Pant was appointed as a professor of mathematics in Tri Chandra College.

Φ (1915-2002): Chandrakaladevi Dhananjaya, first women mathematician/writer of mathematics in Nepal. She had written Shishubodhatarangini part one and two.

Φ 1918: Mathematics was teaching at Trichandra College at proficiency level (I.A.).

Φ 1992: Indra Nath Aryal was born and now he is the living legend of Nepali mathematics, he can express mathematics in a classical way in practical-based.

Φ 1924: The study of mathematics at the B.A. level was started at Tri Chandra College.

Φ 1925/26: Noor Datta Pande, second son (Mahila Chhora) of Gopal Pande had written Gorkha Bijaganita part one to four.

Φ 1926: Narayan Bahadur Manandhar (born 1906) was the first person who received his first master’s degree in mathematics major from Calcutta University and he taught at Trichandra College.

Φ 1930: Prof. Dhupa Ratna Bajracharya was the founder president of Nepal's mathematical society and head of the central department of mathematics at Tribhuvan University.

Φ (1941-1951): Nepali Arithmetic book was published by Khadga Man Malla to fulfil the mathematics need to service holder in Government Office.

Φ Onward 1959: Asutosh Ganguli (1961) was the first department head of mathematics for a master’s degree class in Tri Chandra College. Prof. T.P. Chaudhary, Prof. V.D. Thawani also taught mathematics.

Φ 1953: Date for training (5 months then 10 months) at Min Bhawan for mathematics teacher in Nepal. In 1956 Proficiency Certificate Level class (I.Ed.) at Chet Bhawan.

Φ 1963: Date for first mathematics curriculum in lower secondary.

Φ 1971: New Educational System Plan (NESP) is the milestone for the development of education which also supports mathematics education. From that date, mathematics education and statistics were taught at the master’s degree level University Campus, Kirtipur. Department of mathematics shift Kirtipur.

Φ 1973: First Semester class in the mathematics department of T.U. in master’s degree class.

Φ The end of the tenth years of 1990: The three pass and four pass degree also allowed for service holder in Government Office with mathematics major.

Φ 1979: Establishment of Nepal Mathematics Society (NMS).

Φ 1991: Establishment of Mathematical Education Community (MEC).

Φ 2004: Ministry of Science and Technology published a famous historical paper Mathematics in Nepali: A historical analysis written by Prof. Shankar Raj Pant was published in the scientific journal scientific world. Perhaps this is the first paper that gives the brief history of Nepali mathematics and it is as the milestone for research the historical development of Nepali Mathematics and Mathematics Education.

Φ 2008: Nepal Academy of Science and Technology (NAST) announced a mathematical report for mathematics education for 21st century new Nepal prepared by prof. R.M. Shrestha. It is a base stone for a review of Nepali mathematics with comparing mathematics in different education in Nepal. After these two works, dozens of papers are published nationally and internationally including a biography of mathematicians.

Φ 2009: Establishment of Nepal Mathematical Community (NMC).

Thanks!

Love Formula (GeoGebra)-The Infinity Mathematics

2021-05-24T01:29:00.001+05:45

Love Formula

Easy to construct of love in GeoGebra applet.

GeoGebra Link: Love

Websites for Learning Mathematics with Links-The Infinity Mathematics

2021-05-24T01:29:00.000+05:45

Websites for learning Mathematics with Links

1. E-path (OLE NEPAL)

E-Paath is a collection of digital interactive learning activities that are designed and developed at OLE Nepal and distributed freely. The E-Paath activities are based on national curriculum of Nepal. They are subject-specific and grade-specific. E-Paath is available in Nepali and English languages for grades 1 – 8.

E-Paath can run on any browser. It can be accessed online from OLE Nepal’s free digital library, E-Pustakalaya. It can also be downloaded and used for free.

Click Here: E-Paath (olenepal) Website Link: www.olenepal.org

2. A plus math

Interactive math resources for teachers, parents, and students featuring free math worksheets, math games, math flashcards, and more.

Website Link: www.aplusmath.com

3. Math TV

Over 10,000 Free Math Videos. Helpful math videos covering topics from Basic Math through Calculus

Website Link: www.mathtv.com

4. PhEt

Founded in 2002 by Nobel Laureate Carl Wieman, the PhET Interactive Simulations project at the University of Colorado Boulder creates free interactive math and science simulations. PhET sims are based on extensive education research and engage students through an intuitive, game-like an environment where students learn through exploration and discovery.

Teachers have access to simulation-specific tips and video primers, resources for teaching with simulations, and activities shared by our teacher community.

Website Link: www.phet.colorado.edu

5. Math is fun.com

We offer mathematics in an enjoyable and easy-to-learn manner, because we believe that mathematics is fun. The site aims to cover the full Kindergarten to Year 12 curriculum.

Quality is important to us. Amongst our team are:

Les Bill Gates, Graduate of Oxford University with an Honours degree in Mathematics, and a post-graduate Certificate in Education
Dianne Gentry, Bachelor of Science in Elementary Education and trained in cognitively guided math instruction
David Sevilla, Doctorate in Mathematics
Jesus Ernesto Montes, Mathematician, Professor and education enthusiast.

Also millions of people view the site and tell us when they think of improvements. You are welcome to do the same.

Website Link: www.mathsisfun.com

6. Mathad.com

MATHAD is dedicated to promoting and highlighting the contributions of members of the African diaspora to mathematics, especially contributions to current mathematical research.

Our former website was created by Professor Scott Williams of SUNY Buffalo in 1997 and we are committed to carrying on his mission.

The Mathematicians of the African Diaspora Editorial Board hereinafter referred to as "MATHAD", or the "MATHAD" ed board is a group of researchers in the mathematical sciences, and others who love and esteem mathematics. MATHAD is dedicated to promoting and highlighting the contributions of members of the African diaspora to mathematics, especially contributions to current mathematical research. We will work with individuals and organizations that share these goals and our vision of a diverse mathematical research community in which members of the African diaspora are well represented and their works are well known, respected and appreciated.

This site is proudly supported by the National Association of Mathematicians (NAM) and the Educational Advancement Foundation (EAF).

Web Site: www.mathad.com

Search Journals

7. Mathleague.org

As the largest network of local and state math competitions at the elementary, middle, and high school levels in the United States and abroad, mathleague.org runs more than 400 contests globally and reaches over 30,000 students each year.

The mathleague.org program includes a number of services focused on enhancing the quality and quantity of competitive mathematical opportunities available to students everywhere. We offer a variety of programs for students in grades 3-12.

Website Link: www.mathleague.org

• Absurd Math

Absurd Math is an interactive mathematical problem solving game series. The player proceeds on missions in a strange world where the ultimate power consists of mathematical skill and knowledge. Many of the pages have hidden clues and areas. Anytime a player needs help, they may email our staff for assistance. We try to respond within two days.

Website Link: www.learningwave.com/abmath

8. Universal math solver

The Universal Math Solver Team is one of the leading Russian companies among the firms-developers of computer programs devoted to physics and mathematics.

The company was founded by scientists and professional teaching staff in 1997. The development of our projects has involved the combined efforts of talented programmers, postgraduate students from St. Petersburg and Baltic State Universities, and dedicated scientists, professors and teachers. The main project of the company is the UMS – Universal Math Solver software, which we have been working on from the inception of the company to the present day.

Website Link: www.universalmathsolver.com

Open Access Websites

9. Google Scholar

Google Scholar provides a simple way to broadly search for scholarly literature. Search across a wide variety of disciplines and sources: articles, theses, books.

Website Link: https://scholar.google.com/

10. Books Google

Search the world's most comprehensive index of full-text books.

Website Link: https://www.books.google.com/

11. RefSeek - Academic Search Engine

Academic search engine for students and researchers. Locates relevant academic search results from web pages, books, encyclopedias, and journals.

Website Link: https://www.refseek.com/

12. Microsoft Academic

Microsoft Academic understands the meaning of words, it doesn’t just match keywords to content. For example, when you type “Microsoft,” it knows you mean the institution, and shows you publications authored by researchers affiliated with Microsoft. Similarly, Microsoft Academic knows journal titles, conference names, and many research topics. Try these queries to understand the power of semantic search and unleash it yourself!

Website Link: https://www.academic.microsoft.com/

13. ERIC - Education Resources Information Center

ERIC is an online library of education research and information, sponsored by the Institute of Education Sciences (IES) of the U.S. Department of Education.

Website Link: https://www.eric.ed.gov/

14. Open Thesis and Dissertations

Advanced research and scholarship. Theses and dissertations, free to find, free to use.

Website Link: www.oatd.org/ , www.openthesis.org

15. Dissertation Academic Book Publisher

Dissertation.com, an imprint of Universal-Publishers, was established in 1997 to provide students, researchers, and the general public with low cost access to important academic work. Since then, we have made hundreds of dissertations available online and through thousands of booksellers.

Website Link: http://www.dissertation.com/

16. ETHOS E-These Online Service

EThOS is the UK’s national thesis service which aims to maximise the visibility and availability of the UK’s doctoral research theses.

Website Link: https://www.ethos.bl.uk/

17. Find Open Access Dissertations and Theses

ProQuest Open Access Dissertations & Theses will remain freely available as part of a new and enhanced search experience at www.proquest.com.

Website Link: https://www.pqdtopen.proquest.com/

18. UIS Statistics - UNESCO

The UNESCO Institute for Statistics (UIS) is the official and trusted source of internationally-comparable data on education, science, culture and communication. As the official statistical agency of UNESCO, the UIS produces a wide range of state-of-the-art databases to fuel the policies and investments needed to transform lives and propel the world towards its development goals. The UIS provides free access to data for all UNESCO countries and regional groupings from 1970 to the most recent year available. The UIS encourages developers and researchers to build websites and applications that make rich use of UIS dissemination data. In addition to a powerful standards-based API, the UIS supports a data browser and a bulk data download service (BDDS).

Website Link: http://www.data.uis.unesco.org/

For open-access journal

19. DOJA

DOAJ is a community-curated online directory that indexes and provides access to high quality, open access, peer-reviewed journals.

Find open access journals & articles.

Website Link: https://www.doaj.org/

20. Nepal Journals Online

For Nepalese Journal

Website Link: https://www.nepjol.info/, https://www.tucl.org.np/content/nepali-journal-online

FOR FREE BOOK

21. Z-library

Part of Z-Library project. The world's largest e-book library.

Website Link: https://www.2lib.org/

1. www.bookzz.org

2. www.en.bookfi.org

3. www.libgen.org

Programmed Statistics (Question-Answers) - B.L. Agarwal : The Infinity Mathematics

2021-05-24T01:28:00.000+05:45

Programmed Statistics (Question-Answers) - B.L. Agarwal: The Infinity Mathematics

Book Link: Click the below blue (programmed statistics by b.l. Agarwal)

Programmed Statistics By B.L. Agarwal

5 Reasons to Teach Mathematical Modeling

2021-05-24T01:16:00.000+05:45

5 Reasons to Teach Mathematical Modeling

To solve modeling problems, mathematicians make assumptions, choose a mathematical approach, get a solution, assess the solution for usefulness and accuracy, and then rework and adjust the model as needed until it provides an accurate and predictive enough understanding of the situation. Communicating the model and its implications in a clear, compelling way can be as critical to a model’s success as the solution itself.

Even very young students can engage in mathematical modeling. For example, you could ask students of any age how to decide which food to choose at the cafeteria and then mathematize that decision-making process by choosing what characteristics of the food are important and then rating the foods in the cafeteria by those standards. The National Council of Teachers of Mathematics (NCTM) is providing leadership in communicating to teachers, students, and parents what mathematical modeling looks like in K–12 levels. The 2015 Focus issue of NCTM’s Mathematics Teaching in the Middle School will be about mathematical modeling and the 2016 Annual Perspectives in Mathematics Education will also focus on the topic.

1. Solving rote problems is boring. Modeling involves making genuine choices.

School mathematics is often presented as a set of steps to be followed in a particular order. Students can follow procedures without understanding (and perhaps not caring to understand) how the steps are connected and why they work. Then, they may rightly see this doing-without-understanding as a useless skill—even though correctly applying the procedures can lead to success on many standardized tests, which are developed to have predictable, standard, easy-to-grade answers. In contrast, mathematical modeling problems are big, messy, real, and open-ended. In modeling, students need to make genuine choices about what is important, decide what mathematics to apply and determine whether their solution is useful. Modeling provides opportunities for students to develop and practice mathematics-related skills, then communicate their understanding and interpretation of the problem.

2. Nobody likes to be wrong. Modeling problems have many possible justifiable answers.

When people say they dislike math, I imagine them staring at a paper with lots of X-marks all over their work. Think about how we grade school mathematics: Textbook problems provide the correct methodology, and solution manuals contain the correct answers. Problems are designed to facilitate grading, which can deemphasize creativity, elegance, efficiency, and communication. Instead, mathematical modeling problems require answers that not only use valid mathematical arguments but also make sense in context. Good models provide compelling approximations to solutions that can’t be exactly nailed down because the problem is complex, open-ended and messy. You can check out the Moody’s Mega Math Challenge orMathematical Contest in Modeling for examples of mathematical modeling problems. Of course, some models are better than others, and justifying the solution is a critical aspect of the process.

3. Contrived story problems can be mind numbing. Modeling problems matter to the end-user who needs to understand something or make a decision.

The way students generally learn mathematics in school does not resemble the way a mathematician does it or the way it is practiced in other fields, such as business, science, computing, and engineering. Problems that ask uninteresting questions about real things, such as apples, are not much of an improvement. Many people have asked me: Is there really any new math to be discovered? The information in textbooks rarely hints at interesting unanswered questions (such as the Millennium problems). In addition to the interesting abstract questions out there, mathematical modeling problems are generally practical. They relate to issues someone needs to understand or decisions someone needs to make, such as when a drug is safe and effective enough to make it available to the public. Modeling makes mathematics relevant to real problems from life.

4. Math is hard and requires practice. Modeling presents problem solving as a creative, iterative process.

When people tell you that they are bad at mathematics, they will often recount the moment they hit the wall and gave up. They recall a class, a teacher, or a test and perpetuate the idea that if you hit a wall in mathematics you are no good at it. This idea is reinforced by the fact that in school you have to learn particular ideas in a given amount of time or you fail. But here’s the truth: Every mathematician, even one called a genius, hits a wall at some point. Sometimes we get stuck on a problem for years. When we hit a wall, we have to practice harder and longer. We acquire more tools and information. We talk with our colleagues. And like an athlete who misses a shot or loses a game, we only find success if we try new strategies and do not give up. The open-ended nature of mathematical modeling problems can allow students to employ the mathematical tools that they prefer as well as practice skills they need to reinforce. The fact that the process itself involves iteration (evaluation and reworking of the model) clearly communicates that a straight path to success is unlikely.

5. The “mathematician as solitary genius” myth discourages almost everyone. Modeling is inherently a team sport.

I’d just as soon lose the term genius, but if we have to use it, here’s how I see it. A genius is someone whose brain is tickled and delighted by certain ideas. A genius is inclined to think about these ideas far more than most other people, and this perseverance enables them sometimes to think about the ideas in new ways. They are focused, creative, hard-working rule-breakers who put their work ahead of other pursuits. Their work is recognized as exceptional and groundbreaking. My problem with the term comes from the stereotype of a genius (who comes to mind for you?).

Assumptions about the characteristics of a genius can have a negative impact on those who don’t fit the mold, in terms of recognition of their work, attribution of their success to cleverness (as well as hard work), and their own wrestling with imposter syndrome. Geniuses are seen as people who don’t need any help or collaboration to succeed. But the truth is that we mathematicians often work with other people and have social lives, like anyone else. Those of us who work alone are still reading and building on the ideas of others. Real mathematical modeling problems are so big and messy that in order to solve a problem on a reasonably short deadline, a team approach is almost always valuable. The problems are multi-faceted and open to multiple approaches, so students can contribute their strengths to their team, while learning from the approaches taken by others. Everyone can help make the solution and communication stronger.

Calendar - Aptitude Questions and Answers : The Infinity Mathematics

2021-05-16T20:30:00.004+05:45

CALENDER-IQ SOLVE PROBLEM

· Odd Days:

We are supposed to find the day of the week on a given date.

For this, we use the concept of 'odd days'.

In a given period, the number of days more than the complete weeks are called odd days.

· Leap Year:

(i). Every year divisible by 4 is a leap year, if it is not a century.

(ii). Every 4^th century is a leap year and no other century is a leap year.

Note: A leap year has 366 days.

Examples:

Each of the years 1948, 2004, 1676 etc. is a leap year.
Each of the years 400, 800, 1200, 1600, 2000 etc. is a leap year.
None of the years 2001, 2002, 2003, 2005, 1800, 2100 is a leap year.

· Ordinary Year:

The year which is not a leap year is called an ordinary years. An ordinary year has 365 days.

· Counting of Odd Days:

1 ordinary year = 365 days = (52 weeks + 1 day.)

1 ordinary year has 1 odd day.

1 leap year = 366 days = (52 weeks + 2 days)

1 leap year has 2 odd days.

100 years = 76 ordinary years + 24 leap years

= (76 x 1 + 24 x 2) odd days = 124 odd days.

= (17 weeks + days) 5 odd days.

Number of odd days in 100 years = 5.

Number of odd days in 200 years = (5 x 2) 3 odd days.

Number of odd days in 300 years = (5 x 3) 1 odd day.

Number of odd days in 400 years = (5 x 4 + 1) 0 odd day.

Similarly, each one of 800 years, 1200 years, 1600 years, 2000 years etc. has 0 odd days.

· Day of the Week Related to Odd Days:

No. of days:

Day:

Sun.

Mon.

Tues.

Wed.

Thurs.

Fri.

Sat.

It was Sunday on Jan 1, 2006. What was the day of the week Jan 1, 2010?

A.	Sunday	B.	Saturday
C.	Friday	D.	Wednesday

Answer & Explanation

Answer: Option C

Explanation:

On 31^st December, 2005 it was Saturday.

Number of odd days from the year 2006 to the year 2009 = (1 + 1 + 2 + 1) = 5 days.

On 31^st December 2009, it was Thursday.

Thus, on 1^st Jan, 2010 it is Friday.

What was the day of the week on 28^th May, 2006?

A.	Thursday	B.	Friday
C.	Saturday	D.	Sunday

Answer & Explanation

Answer: Option D

Explanation:

28 May, 2006 = (2005 years + Period from 1.1.2006 to 28.5.2006)

Odd days in 1600 years = 0

Odd days in 400 years = 0

5 years = (4 ordinary years + 1 leap year) = (4 x 1 + 1 x 2) 6 odd days

Jan. Feb. March April May

(31 + 28 + 31 + 30 + 28 ) = 148 days

148 days = (21 weeks + 1 day) 1 odd day.

Total number of odd days = (0 + 0 + 6 + 1) = 7 0 odd day.

Given day is Sunday.

What was the day of the week on 17^th June, 1998?

A.	Monday	B.	Tuesday
C.	Wednesday	D.	Thursday

View Answer Workspace Report Discuss in Forum

What will be the day of the week 15^th August, 2010?

A.	Sunday	B.	Monday
C.	Tuesday	D.	Friday

Answer & Explanation

Answer: Option A

Explanation:

15^th August, 2010 = (2009 years + Period 1.1.2010 to 15.8.2010)

Odd days in 1600 years = 0

Odd days in 400 years = 0

9 years = (2 leap years + 7 ordinary years) = (2 x 2 + 7 x 1) = 11 odd days 4 odd days.

Jan. Feb. March April May June July Aug.

(31 + 28 + 31 + 30 + 31 + 30 + 31 + 15) = 227 days

227 days = (32 weeks + 3 days) 3 odd days.

Total number of odd days = (0 + 0 + 4 + 3) = 7 0 odd days.

Given day is Sunday.

Today is Monday. After 61 days, it will be:

A.	Wednesday	B.	Saturday
C.	Tuesday	D.	Thursday

Answer & Explanation

Answer: Option B

Explanation:

Each day of the week is repeated after 7 days.

So, after 63 days, it will be Monday.

After 61 days, it will be Saturday.

If 6^th March, 2005 is Monday, what was the day of the week on 6^th March, 2004?

A.	Sunday	B.	Saturday
C.	Tuesday	D.	Wednesday

Answer & Explanation

Answer: Option A

Explanation:

The year 2004 is a leap year. So, it has 2 odd days.

But, Feb 2004 not included because we are calculating from March 2004 to March 2005. So it has 1 odd day only.

The day on 6^th March, 2005 will be 1 day beyond the day on 6^th March, 2004.

Given that, 6^th March, 2005 is Monday.

6^th March, 2004 is Sunday (1 day before to 6^th March, 2005).

On what dates of April, 2001 did Wednesday fall?

A.	1^st, 8^th, 15^th, 22^nd, 29^th	B.	2^nd, 9^th, 16^th, 23^rd, 30^th
C.	3^rd, 10^th, 17^th, 24^th	D.	4^th, 11^th, 18^th, 25^th

Answer & Explanation

Answer: Option D

Explanation:

We shall find the day on 1^st April, 2001.

1^st April, 2001 = (2000 years + Period from 1.1.2001 to 1.4.2001)

Odd days in 1600 years = 0

Odd days in 400 years = 0

Jan. Feb. March April
(31 + 28 + 31 + 1) = 91 days 0 odd days.

Total number of odd days = (0 + 0 + 0) = 0

On 1^st April, 2001 it was Sunday.

In April, 2001 Wednesday falls on 4^th, 11^th, 18^th and 25^th.

How many days are there in x weeks x days?

A.	7x²	B.	8x
C.	14x	D.	7

Answer & Explanation

Answer: Option B

Explanation:

x weeks x days = (7x + x) days = 8x days.

The last day of a century cannot be

A.	Monday	B.	Wednesday
C.	Tuesday	D.	Friday

Answer & Explanation

Answer: Option C

Explanation:

100 years contain 5 odd days.

Last day of 1^st century is Friday.

200 years contain (5 x 2) 3 odd days.

Last day of 2^nd century is Wednesday.

300 years contain (5 x 3) = 15 1 odd day.

Last day of 3^rd century is Monday.

400 years contain 0 odd day.

Last day of 4^th century is Sunday.

This cycle is repeated.

Last day of a century cannot be Tuesday or Thursday or Saturday.

10.

On 8^th Feb, 2005 it was Tuesday. What was the day of the week on 8^th Feb, 2004?

A.	Tuesday	B.	Monday
C.	Sunday	D.	Wednesday

Answer & Explanation

Answer: Option C

Explanation:

The year 2004 is a leap year. It has 2 odd days.

The day on 8^th Feb, 2004 is 2 days before the day on 8^th Feb, 2005.

Hence, this day is Sunday.

11.

The calendar for the year 2007 will be the same for the year:

A.	2014	B.	2016
C.	2017	D.	2018

Answer & Explanation

Answer: Option D

Explanation:

Count the number of odd days from the year 2007 onwards to get the sum equal to 0 odd day.

Year : 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017

Odd day : 1 2 1 1 1 2 1 1 1 2 1

Sum = 14 odd days 0 odd days.

Calendar for the year 2018 will be the same as for the year 2007.

12.

Which of the following is not a leap year?

A.	700	B.	800
C.	1200	D.	2000

Answer & Explanation

Answer: Option A

Explanation:

The century divisible by 400 is a leap year.

The year 700 is not a leap year.

13.

On 8^th Dec, 2007 Saturday falls. What day of the week was it on 8^th Dec, 2006?

A.	Sunday	B.	Thursday
C.	Tuesday	D.	Friday

Answer & Explanation

Answer: Option D

Explanation:

The year 2006 is an ordinary year. So, it has 1 odd day.

So, the day on 8^th Dec, 2007 will be 1 day beyond the day on 8^th Dec, 2006.

But, 8^th Dec, 2007 is Saturday.

8^th Dec, 2006 is Friday.

14.

January 1, 2008 is Tuesday. What day of the week lies on Jan 1, 2009?

A.	Monday	B.	Wednesday
C.	Thursday	D.	Sunday

Answer & Explanation

Answer: Option C

Explanation:

The year 2008 is a leap year. So, it has 2 odd days.

1^st day of the year 2008 is Tuesday (Given)

So, 1^st day of the year 2009 is 2 days beyond Tuesday.

Hence, it will be Thursday.

15.

January 1, 2007 was Monday. What day of the week lies on Jan. 1, 2008?

A.	Monday	B.	Tuesday
C.	Wednesday	D.	Sunday

Answer & Explanation

Answer: Option B

Explanation:

The year 2007 is an ordinary year. So, it has 1 odd day.

1^st day of the year 2007 was Monday.

1^st day of the year 2008 will be 1 day beyond Monday.

Hence, it will be Tuesday.

Algebra Formulas-The Infinity Mathematics

2021-05-10T10:30:00.002+05:45

Algebra Formulas

1. Set identities

Definitions:

I: Universal set A’: Complement Empty set: Æ

Union of sets

A È B = {x | x Î A or x Î B}

Intersection of sets

Identity

A È Æ = A A Ç I = A

Set identities involving union, intersection and complement

complement of intersection and union

A È A¢ = I A Ç A¢ = Æ

De Morgan’s laws

A Ç B = {x | x Î A and

Complement

A¢ = {x Î I | x Î A}

Difference of sets

x Î B}

( A È B)¢ = A¢ Ç B¢

( A Ç B)¢ = A¢ È B¢

Set identities involving difference

B \ A = B ( A È B)

B \ A = {x | x Î B and x Ï A}

Cartesian product

B \ A = B Ç A¢

A \ A = Æ

( A \ B ) Ç C = ( A Ç C ) \ ( B Ç C )

A ´ B = {( x, y )| x Î A and y Î B}

Set identities involving union

Commutativity

A È B = B È A

Associativity

A È ( B È C ) = ( A È B ) È C

Idempotency

A È A = A

Set identities involving intersection

commutativity

A Ç B = B Ç A

Associativity

A Ç ( B Ç C ) = ( A Ç B ) Ç C

Idempotency

A Ç A = A

Set identities involving union and intersection

Distributivity

A È ( B Ç C ) = ( A È B ) Ç ( A È C ) A Ç ( B È C ) = ( A Ç B ) È ( A Ç C ) Domination

A Ç Æ = Æ

A È I = I

A¢ = I \ A

2. Sets of Numbers

Definitions:

N: Natural numbers N_o: Whole numbers Z: Integers

Z⁺: Positive integers Z^-: Negative integers Q: Rational numbers C: Complex numbers

Natural numbers (counting numbers )

N = {1, 2, 3,... }

Whole numbers ( counting numbers + zero )

N_o = {0, 1, 2, 3,... }

Integers

Z ⁺ = N = {1, 2, 3,... }

Z ^- = {..., - 3, - 2, -1}

Z = Z^- È{0} È Z = .{.., - 3, - 2, -1, 0, 1, 2, 3,... }

Irrational numbers:

Nonerepeating and nonterminating integers

Real numbers:

Union of rational and irrational numbers

Complex numbers:

C = {x + iy | x Î R and y Î R}

N Ì Z Ì Q Ì R Ì C

3. Complex numbers

Definitions:

A complex number is written as a + bi where a and b are real numbers an i, called the imaginary unit, has the property that i²=-1.

The complex numbers a+bi and a-bi are called complex conjugate of each other.

Equality of complex numbers

a + bi = c + di if and only if a = c and b = d

Addition of complex numbers

(a + bi) + (c + di) = (a + c) + (b + d)i

Subtraction of complex numbers

(a + bi) - (c + di) = (a - c) + (b - d)i

Multiplication of complex numbers

(a + bi)(c + di) = (ac - bd) + (ad + bc)i

Division of complex numbers

a + bi = a + bi × c - di = ac + bd + æ bc - ad ö i

c + di c + di c - di c² + d ^{2 (}c2 + d 2 ⁾

Polar form of complex numbers

x +iy = r (cosq +isinq) r -modulus, q -amplitude

Multiplication and division in polar form

éër₁ (cosq₁ + i sinq₁ )ùû × éër₂ (cosq₂ + i sinq₂ )ùû =

= r₁r₂ éëcos (q₁ + q₂ ) + i sin (q₁ + q₂ )ùû

De Moivre’s theorem

éër (cosq + sinq )ùûn = rⁿ (cos nq + sin nq )

4. Algebric equations

Quadric Eqation: ax² + bx + c = 0

Solution (roots):

if D=b²-4ac is the discriminant, then the roots are

(i) real and unique if D > 0

(ii) real and equal if D = 0

(iii) complex conjugate if D < 0

5. Factoring and product

Factoring Formulas

a² - b² = (a - b)(a + b)

a³ - b³ = (a - b)(a² + ab + b² )

a³ + b³ = (a + b)(a² - ab + b² )

a4 - b4 = (a - b)(a + b)(a2 + b2 )

a5 - b5 = (a - b)(a4 + a3b + a2b2 + ab3 + b4 )

Product Formulas

(a + b)² = a² + 2ab + b²

(a - b)² = a² - 2ab + b²

(a + b)³ = a³ + 3a²b + 3ab² + b³

(a - b)³ = a³ - 3a²b + 3ab² - b³

(a + b)4 = a⁴ + 4a³b + 6a²b² + 4ab³ + b⁴

(a - b)4 = a⁴ - 4a³b + 6a²b² - 4ab³ + b⁴

(a + b + c)² = a² + b² + c² + 2ab + 2ac + 2bc

(a + b + c +...)² = a² + b² + c² +...2(ab + ac + bc +...)

A Geometric Model of (a+b)2-The Infinity Mathematics

2021-05-04T16:23:00.005+05:45

A Geometric Model of (a+b)².

Introducing (a+b)². Although most, not all, algebra students accept and use the expansions for(a+b)², many students have difficulty conceptualizing these products. The following introductory expository organizer, presented in the form of a demonstration will make these products more meaningful for many students.

Being the demonstration by selecting two arbitrary lengths a and b and demonstrating that the geometric representations of a² and b² are squares having dimensions a by a and b by b, respectively. Next, consider the lengths a+b, and construct a square of dimension (a+b) by (a+) as a geometric representation of (a+b)² .Then compare the square having side (a+b) to the two squares having side a and b, respectively. The geometric representations of a², b², and (a+b)² are illustrated below in figure 1.

Figure 1: A Geometric Model of (a+b)².

Density of Love Inside Mathematica Construction-theinfinitymathematics

2021-05-03T15:07:00.003+05:45

The Density of Love Inside Mathematica/Mathematics

Manipulate[

GraphicsRow[{Show[
ContourPlot[y == 1/x, {x, 0, 10}, {y, -1, 10}, Frame -> False,
PlotRange -> {{0, 10}, {0, 10}}, PerformanceGoal -> "Quality"],
Graphics[Table[{Red, Point[{b, 1/b}]}, {b, 0.1, a, 0.1}]]],
Show[ContourPlot[x^2 + y^2 == 9, {x, -3, 3}, {y, -3, 3},
Frame -> False, PlotRange -> {{-3, 3}, {-3, 3}},
PerformanceGoal -> "Quality"],
Graphics[
Table[{Red, Point[{3 Cos[b], 3 Sin[b]}]}, {b, 0, a, 0.05}]]],
Show[ContourPlot[y == Abs[-2 x], {x, -3, 3}, {y, 0, 3},
Frame -> False, PlotRange -> {{-3, 3}, {0, 3}},
PerformanceGoal -> "Quality"],
Graphics[
Table[{Red, Point[{b, Abs[-2 b]}]}, {b, -3, a - 3, 0.05}]]],
Show[ContourPlot[x == -3 Abs[Sin[y]], {x, -3, 0}, {y, -3, 3},
Frame -> False, PlotRange -> {{-3, 0}, {-3, 3}},
PerformanceGoal -> "Quality",
PlotLabel -> Style["Dan Bdr Budha, Nepal", 6, Black]],
Graphics[
Table[{Red, Point[{-3 Abs[Sin[b]], b}]}, {b, -3, a - 3,
0.05}]]]}], {{a, 0.1,
"y=1/x & x^2+y^2=9 & y=|-2x| & x=-3|siny|: Density of Love"}, 0.1,
10}]

Mathematica and GeoGebra Plot Videos-The Infinity Mathematics

2021-05-03T13:59:00.001+05:45

Mathematica 3D Plot:

GeoGebra with Multiplication and Planet Construction

Introduction to Cryptography with Coding Theory-Maths

2021-05-01T14:00:00.009+05:45

INTRODUCTION TO CRYPTOGRAPHY

“I am fairly familiar with all forms of secret writing and am myself the author of a trifling manuscript on the subject”.

-SIR ARTHUR CONAN DOYLE

The word cryptography is derived from the Greek words Cryptos + Graphein, where cryptos mean hidden and graphein means to write. Thus, cryptography is the art of writing codes. It is the science of making communications unintelligible to all except authorized person cryptography is the only known practical means for protecting information has transmitted through public communications networks, such as those using telephone lines, microwaves, satellites, etc.

In cryptography, the codes that are used are called ciphers, the information to be the kept secret is called plain text, and the information after transformation to a secret form is called the ciphertext. The process of converting from plain text to cipher text is called encrypting (or enciphering), whereas the reverse process of changing from cipher text back to plain text is called decrypting (or deciphering).

The great roman emperor Julius Caesar used one of the earliest cryptography systems around 50 B.C. He used cryptography by replacing is a letter that occurs three places down the alphabet as below.

Plain Text: A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

Cipher Text: D E F G H I J K L M N O P Q R S T U V W X Y Z A B C

For e.g.

1. The plain text message

CAESAR SEND MONEY

Is transformed into the ciphertext

FDHVDU VHQG PRQHB

NOTE:

1. Caesar cipher technique is not very strong technique for hiding the plain text message.

2. It can be easily detectable.

The Caesar cipher can be described by easily using congruence theory. Any plain text is first expressed numerically by translating the characters of the text into digits by means of some correspondence such as following.

A	B	C	D	E	F	G	H	I	J	K	L	M
00	01	02	03	04	05	06	07	08	09	10	11	12

N	O	P	Q	R	S	T	U	V	W	X	Y	Z
13	14	15	16	17	18	19	20	21	22	23	24	25

If P denotes the digital equivalent of a plain text, letter, and C the digital the equivalent of the corresponding ciphertext letter, then

C @ P+ 3 (mod 26)

For e.g.

The letter in the message “CAESAR WAS GREAT” is converted in the digital form as,

02 00 04 18 00 17 22 00 18 06 17 04 00 19

Using the congruence C @ P+3 9mod 26) i.e. P @ C-3 @ C+23 (mod 26). We get,

05 03 07 21 03 20 25 03 21 09 20 07 03 22

NOTE:

1. There are 25 possibilities for any alphabet to be replaced by other.

proof of 1+1=2 with justification-thetnfinitymathematics

2021-05-01T06:00:00.010+05:45

PROOF OF 1+1=2 WITH JUSTIFICATION

Dan Bdr Budha

Student, Central Department of Education, University Campus, Kirtipur, Nepal

E-mail: budhadanbdr@gmail.com

The proof of a mathematical proposition is a finite sequence of statements ending in the proposition, which satisfies the following property. Each statement is an axiom drawn from a previously stipulated set of axioms or is derived by a rule of inference from one or more statements occurring earlier in the sequence. The term ‘set of axioms’ is conceived broadly, to include whatever statements are admitted into a proof without demonstration, including axioms, postulates, and definitions.

The five Peano axioms are:

1. Zero is a natural number.

2. Every natural number has a successor in the natural numbers.

3. Zero is not the successor of any natural number.

4. If the successor of two natural numbers is the same, then the two original numbers are the same.

5. If a set contains zero and the successor of every number is in the set, then the set contains the natural numbers.

Proof of the statement ‘1+1=2’ in the axiomatic system of Peano Arithmetic. For this proof, we need the definitions and axioms s0=1, s1=2, x+0=x, x+sy=s(x+y) from Peano Arithmetic. And the logical rules of inference P(r), r=t⇒P(t); P(v)⇒P(c) (where r, t; v; c; and P(t) range over terms; variables; constants; and propositions in the term t, respectively, and ‘⇒’ signifies logical implication. The following is a proof of 1+1=2: x+sy=s(x+y), 1+sy=s (1+y), 1+s0=s (1+0), x+0=x, 1+0=1, 1+s0=s1, s0=1, 1+1=s1, s1=2, 1+1=2

An explanation of this proof is as follows. s0=1 [D1] and s1=2 [D2] are definitions of the constants 1 and 2, respectively, in Peano Arithmetic, x+0=x [A1] and x+sy=s(x+y) [A2] are axioms of Peano Arithmetic. P(r), r=t⇒P(t) [R1] and P(v)⇒P(c) [R2], with the symbols as explained above, are logical rules of inference. The justification of the proof is below.

Proof of 1+1=2 with justification.

Step		Statement	Justification of Statement
S1		x+sy =s(x+y)	A2
S2		1+sy=s(1+y)	R2 applied to S1, using v=x, c=1
S3		1+s0 =s(1+0)	R2 applied to S2, using v=y, c=0
S4		X+0 =0	A1
S5		1+0 =1	R2 applied to S4, using v=x, c=1
S6		1+s0 =s1	R1 applied to S3 & S5, using r=1+0, t=1
S7		S0 =1	D1
S8		1+1 =s1	R1 applied to S6 & S7, using r=s0, t=1
S9		S1 =2	D2
S10	1+1 =2		R1 applied to s8 & S9, using r=s1, t=2

Note:

1. The mathematical assumptions used are the definitions (D1 & D2).

2. The axioms (A1 & A2).

3. The logical assumptions are the rules of inference used (R1 & R2).

Research Activities in Semester &Thesis Writing

2021-04-29T11:00:00.007+05:45

Research Activities in Semester &Thesis Writing

Outline

• What thesis is and isn’t?

• Why writing thesis?

• How to write thesis?

• Common mistakes and some tips

What is a thesis?

• Demonstration of an understanding of the state of the art

– Critical appreciation of existing work

• A novel contribution

– Evaluated systematically

What a thesis isn’t?

• What I did in the lab over the last 6 months

– I first read the background material

– I ran some experiments

– …

• A thesis is a logical reconstruction

– With a single coherent message

– Not a historical narrative

Why to write a thesis?

• It will make you famous

– Unlikely

– But YES

• It will radically change science

– Unlikely

– But YES

Why to write a thesis?

• It will advance our knowledge

– Just a little

– Main benefit is in teaching you to research

• In the process, you will learn

– How to research

– How to write

• Shorter conference & journal papers will be easy!

Thesis Message

• Write a thesis message

– 1 sentence

– 1 paragraph

– 1 page

• Everything you write should be directed at this

– Thesis (noun).

1. A proposition maintained by argument

2. A dissertation advancing original research

Thesis Message

• You’re tackling an important research problem

– E.g. Nesting Success of Vulture

• You’ve made an original contribution to its resolution

– E.g. Efficient and effective global management of carcasses

What Next?

• So, I’ve got a good thesis message

• What do I do next?

– Write the table of contents

– Logical structure of your thesis

Chapter 1: Introduction

1.1 Background

1.2 Rationale

1.3 Objectives

1.4 Limations (if any)

Chapter 2: Literature Review

Chapter 3: Materials and Methods

2.1 Study Area

2.2 Methods

Chapter 4: Results

Chapter 5: Discussion

Chapter 6: Conclusion and Recommendations

6.1 Conclusion

6.2 Recommendations

What Next?

• So, I’ve got a good thesis message

• And a table of contents

• What do I do next?

– Make a timetable

• Targets to meet

• Light at the end of the tunnel

Timetable

• “Your thesis is your baby” P. Prosser

– Give as much time as you can

• “You have to know when to let it go”

– Put a fence around what you’ve done

What Next?

• So, I’ve got a good thesis message

• And a table of contents, timetable

• What do I do next?

– Work to your timetable!

Writing Each Chapter

• Don’t start with the Introduction or Conclusion

• Start where you feel the happiest

– Typically a middle chapter

– Write outwards

– Finally Conclusions and end with the Introduction

• Write everything with your thesis message in mind

Rule of Three

• Within each chapter, repeat yourself 3 times

– Intro. We will show...

– Body. Show them…

– Concl. We have shown …

• Within thesis, repeat your contributions 3 times

– Intro chapter

– Main chapters

– Conclusion chapter

– But don’t bore reader

– E.g. in introduction be brief, in conclusions be broader

INTRODUCTION

• Gives substantive background of the research with literature overview of the theme

• Explain existing problem and status of previous efforts

• Overview of methods used to study the theme and which method the student has chosen

Note: Sets the scene against which the action of the thesis will take place

• Indicates of why the geographical location/animal/organism was chosen

• Indicates research question and hypotheses/prediction to be tested

• Indication of applied value

Three moments and formula for introduction: RCA (in sequence)

• Review: not a historical background of long span, take papers with pertinent information for background of your research, problem statements

– ask peers to comment, use your intelligence and skill

• Claim: the most important part, middle, claim your work is a worthwhile extension of the review, motivation of research (claim=0, lack of motivation)

• Agenda: end part, summarize what you will show the as your research goes on, how research works to fulfil your claim, clarify your claim, keep it short

MATERIALS & METHODS

• Study area

• Methods

– Conceptual Framing/Research Design (subheading)

– Sampling/Survey Design (subheading)

– Field/Laboratory Methods (subheading)

– Analysis

• Methods in the lab/field

– Detail procedures to give an accurate idea of what was done

– Reliable, standard, tested/verified (Published- Established Protocols), photographs and diagrams (labelled) of setup

– Materials (tool/instrument) – Describe EXACTLY what you used to do your research

Must be replicable: possible to go out in the field and repeat the study to verify/reject the findings?

• Methods used for numerical analyses: Stats. and Analysis

– Data quality and management, approaches, rational use of statistics- no use, overuse or misuse--- software (version)

• You should be able to answer

– What data did you choose to collect?

– Is some data lacking?

– Are there some practical or methodical difficulties / limitations?

– Are all the data needed to answer the objective of the study?

RESULTS

• Observation of your research

• Present results based on data collection in an order

• Text: easy to understand, no repetition

• Figures: easy to understand, self explanatory Fig. text underneath

• Tables: easy to read, and in correct format with table head and explanation of abbreviation

• Text, Figure & Table: CORRECT ORDER

• Explain and describe data, including any qualitative observations

• Say exactly what you found, patterns, trends, or relationships observed

• Use graphics – graphs, figures (visualization speaks more)

Plus Point: DO NOT repeat the methods in RESULTS!

DISCUSSION

• Interpret with scientific reasons

– Example: Regression – Intercept, slope, p, R²?

Plus Point:+ Numbers speak but what do they mean to you? +

• Critically evaluate

– Is data telling you as you wish?

– If yes, how and why?

– If no, how and why?

– Is everything alright?

Plus Point; Bonus: if you can successfully identify and address legitimate counterarguments to your thesis, your writing much stronger

• Compare to other works

– do your results speak as others have?

– do they say different stories?

– if any – what could be the reason your output is that way?

Note: Examine the amount and possible sources of variability in your data, including errors

• Develop arguments for and against your hypotheses and interpretations

+ Do not make generalized statements that are not based on your data, known facts, or reason +

• Be sure to relate your findings to other studies and cite those studies

• Draw positive conclusions from your study whenever possible

Plus Point: + Be critical on your own data and methods, or any indication of self-evaluation +

CONCLUSION

• Should be sound and toughly sustained

• Backed by what has gone before/evidence you have looked at findings

• Nothing new should be introduced at this stage

RECOMMENDATIONS

• Should be sound and well defined

• Concise and itemized

• Discreet, especially towards the findings of persons likely to be affected

• Fully considered, including their consequences, which should be stated and costed where appropriate

Common mistakes

• Informal text

– Examiners will jump on imprecision

• Opinions

– A thesis is an argument!

• Complex sentences full of long words

– A thesis should be a simple, convincing argument!

Plus Point: + Examiners greatly appreciate finding a few mistakes +

• Writing too much

– There are rules about maximum length

– But rarely rules about the minimum

– Nash’s PhD thesis

• 27 pages long

• Won him a Nobel prize

• At some point, your brain will surely become toast

– Take a break

– Eat properly, exercise, sleep …

• Toasted brain is only temporary

SOME TIPS

1. Use relevant materials ONLY

– A thesis is not a topic, it is the statement of an argument

– It is the statement from which everything else in your thesis emanates- arguments, counterarguments, examples, descriptions, implications, etc.

– Don't include irrelevant material

2. Use high-quality and relevant sources

– Don't plagiarize

3. Write how you speak

– Don't use slang

– Use short sentences

– Don't disorient your reader with abrupt changes in topic

– Instead, include appropriate transitions from one paragraph to the next

– If you simply must change topics, use a section break

4. Be succinct

– Don't use fifty words when thirty will do, five words when four will do

5. Check your language

– Nothing is more distracting than misspelled words and sloppy grammar

Thanks!

USE OF ICT IN MATHEMATICS CLASSROOM: OPPORTUNITIES AND CHALLENGES

2021-04-28T13:09:00.002+05:45

USE OF ICT IN MATHEMATICS CLASSROOM: OPPORTUNITIES AND CHALLENGES

THESIS

DAN BAHADUR BUDHA

IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR MASTER DEGREE OF MATHEMATICS EDUCATION

SUBMITTED TO

DEPARTMENT OF MATHEMATICS EDUCATION

CENTRAL DEPARTMENT OF EDUCATION

UNIVERSITY CAMPUS, KIRTIPUR,

KATHMANDU, NEPAL

APRIL, 2021.

......................................................................................................................................................................

LETTER OF CERTIFICATION

This is to certify that Dan Bahadur Budha a student of academic year 2072 / 73 with campus Roll No. 165 Exam Roll No. 7228271, thesis number 1472 and T.U. Regd. No. 9-2-29-131-2011 has completed this thesis under supervision of Mr. Lok Nath Bhattarai during the period prescribed by the rule and regulation of Tribhuvan University, Nepal. This thesis entitled "Use of ICT in Mathematics Classroom: Opportunities and Challenges" has been prepared based on results of his investigation. I, here by recommended and forward that his thesis be submitted for evaluation as the partial requirements to the degree of Master of Mathematics Education.

..……………………….

Head (Prof. Dr. Bed Raj Acharya)

Date: April 9, 2021

......................................................................................................................................................................

LETTER OF APPROVAL

This thesis entitled " Use of ICT in Mathematics Classroom: Opportunities and Challenges " submitted by Mr. Dan Bahadur Budha in partial fulfillment of the requirement for the Master's Degree in Education has been approved.

Viva Voice Committee Signature

1. Prof. Dr. Bed Raj Acharya ……………………..

(Chairman)

2. Assoc. Prof. Laxmi Narayan Yadav ……………………….

(External)

3. Mr. Lok Nath Bhattarai ……………………..

(Member)

Date: April 20, 2021

......................................................................................................................................................................

RECOMMENDATION FOR ACCEPTANCE

This is to certify that Mr. Dan Bahadur Budha has completed his M. Ed. thesis entitled Use of ICT in Mathematics Classroom: Opportunities and Challenges under my supervision during the period prescribed the rules and regulations of Tribhuvan University, Kirtipur, Kathmandu, Nepal. I recommend and forward his thesis to the Department of Mathematics Education to organize final viva-voice.

………………………..

(Mr. Lok Nath Bhattarai)

Supervisor

Date: April 20, 2021

......................................................................................................................................................................

COPYRIGHT

2021

This document is copyright material. Under the law, no parts of this document may be reproduced without the expressed permission of the researcher.

Defense Date: April 20, 2021

......................................................................................................................................................................

DEDICATION

Honestly dedicated

My parents

To my mother, Chhaita Budha for her priceless love and care, and to my Father, who sacrificed his desires and interests for my schooling and bright future.

To my elder brother, Man Bahadur Budha who support me in every step of my life.

......................................................................................................................................................................

DECLARATION

This dissertation contains no material, which has been accepted for the award of other degree in any institutions. To the best of knowledge and belief this dissertation contains no material previously published by any authors except due acknowledgement has been made.

……………………

Dan Bahadur Budha

Date: April 20, 2021

.....................................................................................................................................................................

ACKNOWLEDGEMENT

I am very much indebted to my respected supervisor Mr. Lok Nath Bhattarai Department of Mathematics Education, University Campus, Kirtipur, Kathmandu. His valuable and constructive suggestion, instruction and scholarly guidance has become the greatest valuable property of this thesis, without his constant supervision and intellectual guidance this thesis would never have been appeared in this form.

I would like to express my thank to my respected teachers Prof. Dr. Bed Raj Acharya, Head, Department of mathematics Educations, Central Department of Education, University Campus, Kirtipur, Kathmandu, and others respected teachers for their valuable comments and suggestions to bring the work in to present form. I express my sincere thanks to all my Parents and friends who encouraging and assisted to me through different angle in completing this study.

I would like to extend my thanks to campus chief, mathematics teachers and students of Mahendra Ratna Campus, Tahachal, Kathmandu for their kind co-operations, opportunity and participation conducted by the researcher during investigation of this study.

Thank you very much for all the support and guidance, assistance, encouragement, patience, advice, and sacrifice.

……………………….

Dan Bahadur Budha

ABSTRACT

Information and Communication Technology (ICT) plays various roles to make mathematics teaching learning activities more meaningful. Technology has seen a recent widespread integration into daily life, where access to vast amounts of information is now available with ease. Today’s generation of students has grown up with technology all around them in an ever-increasing manner.

This is a study on “Use of ICT in Mathematics Classroom: Opportunities and Challenges”. The objective of the study was to investigate the students excess and opportunities about ICT in learning Mathematics and the teacher’s challenges on using ICT in Mathematics Classroom. In order to achieve these goals, a college by the name of Mahendra Ratna Campus from Kathmandu District was visited for three weeks to conduct the study. This study was qualitative research type and case study in design; participants have sampled mathematics teachers and students of Mahendra Ratna Campus, Kathmandu. The major tools used for the study were observation and interview of four mathematics teachers and four students as the sample of the study. The collected data were analyzed with the help of theories and related literature reviews and a thematic approach of analysis was adopted as the result of a study.

The study concluded that the teacher and students have a positive opinion for practices of ICT in mathematics teaching and learning. Students and teachers were being motivated to learn mathematics in the new approach and ICTs provide great opportunities to improve their teaching and learning processes. Findings from the study revealed specific features of opportunities and challenges that matter for ICT integration in mathematics teaching and learning in the context of Nepal.

ACRONYMS

ICT: Information Communication and Technology

MOE: Ministry of Educations

GON: Government of Nepal

TPD: Teacher Professional Development

NCTM: National Council of Teachers of Mathematics

TU: Tribhuvan University

APA: American Psychological Association

UNESCO: United Nation Educational, Science and Cultural Organization

B.Ed.: Bachelor of Education

M.Ed.: Master of Education

SPSS: Statistical Package for Social Sciences

MS: Microsoft

LETTER OF CERTIFICATION.. i

LETTER OF APPROVAL. ii

RECOMMENDATION FOR ACCEPTANCCE.. iii

COPYRIGHT. iv

DEDICATION.. v

DECLARATION.. vi

ACKNOWLEDGEMENT. vii

ABSTRACT. viii

ACRONYMS. ix

TABLE OF CONTENTS. x

Chapter-I. 1-6

INTRODUCTION.. 1

Background of the Study. 1

Statement of the Problems. 2

Objectives of the Study. 4

Rationale of the Study. 4

Delimitation of the Study. 5

Operational Definition of Key Terms. 5

Chapter-II. 7-13

REVIEW OF RELATED LITERATURE.. 7

Empirical Review.. 7

Theoretical Review.. 11

Connectivism.. 11

Conceptual Framework. 13

Chapter-III. 14-18

METHODS AND PROCEDURES. 14

Research Design. 14

Selection of Study Site. 14

Data Collection Tools. 15

Observation. 15

Interview Guideline. 15

Data Collection Procedure. 16

Data Analysis and Interpretation Procedures. 16

Ethical Consideration. 17

Chapter-IV.. 19-35

ANALYSIS AND INTERPRETATION OF DATA.. 19

Use of ICT in Mathematics Classroom: Opportunity for Students. 19

Use of Technological Tools. 19

Use of ICT at Classroom.. 21

Students Attitudes on ICT Usages. 23

Students Opportunities for Learning. 24

ICT for Creativity and Motivation. 25

Access to ICT at Home. 27

Use of ICT in Mathematics Classroom: Teachers Challenges. 28

Unavailability of Technology Tools. 28

Lack of Implement of ICT in Classroom.. 29

Improper Training. 31

Lack of Access and ICT Infrastructure. 32

Challenges of ICT Teaching. 33

Use of ICT Teacher’s Opportunities. 34

Chapter-V.. 36-40

SUMMARY, FINDINGS, CONCLUSION AND RECOMMENDATIONS. 36

Summary and Findings. 36

Conclusion. 38

Implications of the Research. 39

Recommendations for Future Research. 40

REFERENCES. 41-42

APPENDIX-A: Interview Guidelines for Teachers. 43

APPENDIX-B: Interview Guidelines for Students. 44

Chapter-I

INTRODUCTION

Background of the Study

Nepal is a developing country, which is still behind in employing technology for teaching and learning mathematics. Traditional methods of teaching and learning are still dominant in Nepal. Normally, teachers distribute knowledge and skills to their students who in turn memorize facts, definitions, and algorithms. The paper- pencil method has a dominant role as a mathematical tool. Information and Communication Technology (ICT) has a minimal to nonexistent role in Nepal. The various challenges and opportunities of ICT in teaching and learning Mathematics in Our Country. ICT plays a strenuous role to make teaching and learning activities more meaningful (MOE, 2013)

The National Council of Teachers of Mathematics (NCTM) has emphasized the importance of using technology in mathematics education because technology can have a crucial role in teaching and learning mathematics: it both influences the mathematics that is taught and enhances students’ learning (NCTM, 2000). In practice, there appears to be little or no encouragement of students to explore mathematical ideas and concepts that they are expected to know. Technology has a minimal role at schools in Nepal. Very few schools have access to technologies, and even fewer integrate them in teaching and learning mathematics. In fact, the school-educational system is based on a traditional approach with emphasis given to drill-and-practice and procedural fluency (Bajracharya, Bhuju, & Pokhrel, 2006).

ICT is useful in mathematics for learning geometry, algebra, calculus at kindergarten to university level. ICT is dynamic easy-to-use tool interactive mathematics for learning mathematics in a unique style in which students have engaged in demonstrations, constructions, and exploration that is no available through paper-pencil (Hohenwarter, 2008).

ICT has a minimal role at a campus level in Nepal. Lack of both resources and investment are among the reason; however, a larger problem may be the low priority placed on building an education system, which will enable Nepalese young people to function better in the modern world. For example, there is no clear vision regarding the use of ICT in the classroom b teacher or student. Although the government of Nepal has initiated a school reform project in which ICT-assisted “child-friendly” teaching/learning are encourage in all school (MOE, 2007).

Therefore, this is the curiosity why many students like ICT in mathematics education. Does it enhance the quality of mathematics education? What are the student’s opportunities and Teachers Challenges to use ICT tools in learning mathematics, teaching-learning activities of ICT Classes, Application of ICT tools, ICT lab, internet facilities, and education system of ICT in mathematics education? Therefore, many researchers have concluded that students are more interested in ICT. Therefore these profiles mentioned above help to measure the use of ICT in mathematics classroom: opportunities and challenges in the context of Nepal.

Statement of the Problems

The use of ICT in Nepalese colleges and universities is very limited because of many factors including lack of availability of resources, lack of poor infrastructure, large class sizes, improper training, for stakeholders, lack of Manpower, and lack of teacher knowledge and skills to integrate ICT. The advancement of technology and its effect have changed the world. The use of technology in education has played a vital role.

Many college and universities in Nepal are still using chalk and talk methods to deliver classroom instruction. Though they have a wider knowledge of the theory of using ICT in learning classes, they do not apply it to practice. The concerned authorities do not seem to ready to integrate ICT in teaching and learning mathematics that’s why problems are seen regarding the implementation of ICT in mathematics teaching in different situations of the classroom in campus and university in Nepal.

Students can develop deeper understanding of mathematics with the appropriate use of technology. Technology can help to support investigation by students in every area of mathematics and allow them to focus on decision-making, reflection, reasoning, and problem solving. The existence, versatility, and power of technology make it possible and necessary to what mathematics students should learn as well as how they can best learn it (NCTM, 2000).

The study intends to investigate the opportunities and challenges of the use of ICT in a mathematics classroom. In Nepal, limited research has been carried out to determine factors that contribute to access and use of ICT, especially in Mathematics. There is a need for learning mathematics in Nepal to invest in the effective use of ICT in teaching and learning Mathematics.

In these concepts, this research tries to find the answer to the following research questions.

· What are the challenges of the teachers regarding teaching mathematics with ICT?

· What are the opportunities of the students regarding teaching and learning mathematics with ICT?

· What kind of Technological tools use in mathematics teaching and learning?

· How do teachers and students perceive the ICT tool in raising the achievement of the students?

Objectives of the Study

The main objective of this study is to find out the Use of ICT in mathematics classroom: opportunities and challenges. The specific objectives of this study were as follows:

· To explore the students excess and opportunities about ICT in learning Mathematics.

· To find out the teachers challenges on using ICT in Mathematics Classroom.

Rationale of the Study

This research strives to complement the existing research and enrich the current knowledge of enablers and inhibitors of technology adoption in mathematics education in Nepal. Such findings might be beneficial to stakeholders in education such as curriculum designers, school managers, teachers, and the government of Nepal including other developing countries with social and economic issues similar to Nepal.

ICT have become one of the fundamental building blocks of modern society. Many countries now regard the mastering of the basic skills and concepts of ICT as an inevitable part of the core of Mathematics education. To this end, various new models of education are evolving in response to the new opportunities that are becoming available by integrating ICT and in particular Web-based technologies, into the teaching and learning environment.

The study may enable Mathematics teachers to become better instructors in the subjects, with ICTs infrastructures that might be available to them. The study may also, benefit educational planners and policy makers to make appropriate decisions in opportunities and challenges of ICT in teaching and learning Mathematics.

Mathematics teachers need to know exactly how ICT is used as a teaching and learning tool, for their own purposes and to help students to use them. This is about the integration of ICT as a tool in the Mathematics classroom with the overall aim of increasing the effectiveness of teaching and improving students’ learning. The outlines a programme of objectives and related activities for an ICT enhanced learning environment in Mathematics teaching and learning.

Delimitation of the Study

Delimitation are boundaries that set by researcher in order to control the range of the study. The study was focuses in one subject area, ICT with mathematics and it was conducted in only Tribhuvan University affiliated Collage to Mahendra Ratna Campus Tahachal, Kathmandu. They are as follows:

· This study was concerned in Bachelors and master’s level classroom Mahendra Ratna Campus Tahachal, Kathmandu. This study included the bachelor and master level students of ICT in mathematics education.

· This study included the teacher, which teach ICT in mathematics education at Mahendra Ratna Campus Tahachal, Kathmandu.

Operational Definition of Key Terms

Operational definition of key terms refers to concepts that are observable and operation in this study with precisely single meaning. In this study, the following are the operational terms of the study.

ICT Information and Communication Technology, a range of technological tools and resources used to communicate, and to create, to disseminate, to store and manage information. Technologies do not refer to only the computers, but also broadly to Internet, Connectivity, Projectors, Calculators, mathematics software, broadcasting technologies (such as radio and television), telephones (including android mobile phones), CDs and DVDs.

Opportunities Educators have a momentous opportunity to reinvent themselves as resources for the entire in collaborating, Which students access of ICT use in mathematics include portables, graphic calculators and computerized graphing, specialized software (Google sketch-up, GeoGebra, Mathematica, Matlab, Microsoft Mathematics etc.), spreadsheets and databases, Infrastructure and internet connectivity etc.

Challenges which that educator, education administrators, and other stakeholders need to consider include educational policy and planning, infrastructure, language and content, capacity building, and financing at Mahendra Ratna Campus.

Learning Students must learn mathematics with understanding; actively Technology can help support investigation by students in every area of mathematics and allow them to focus on decision-making, reflection, reasoning, and problem solving who have studied Bachelor and master level students in Mahendra Ratna Campus.

Mathematics Mathematics is the study of numbers, quantity, space, pattern, structure, and change. In this study, mathematics means that education of mathematics, which is learning by using ICT and its materials.

Chapter-II

REVIEW OF RELATED LITERATURE

The review of literature involves the systematics identification and analysis of documents related to the study under taken review of the previous studies helps to conduct the new research in systematic manner by providing the general outline of the research study and the unnecessary duplications. This section includes empirical review, theoretical review and conceptual framework is to enhance the level of understanding of the various theoretical as well as conceptual constructs of the present study.

Empirical Review

Every researcher need to take guidance from the previous literature related to their topics. To complete my research effectively and efficiently I have reviewed article, policies, book, research work, thesis and research paper as well as different sites are listed below:

Dahal & Dahal, (2015) has made a conclusion based on his research about study entitled “Opportunities and Challenges to use ICT in Nepalese Mathematics Education” where ICTs provide great opportunity for schools/universities in developing countries to improve their teaching and learning processes. So far, most of the schools/universities in developing countries possess basic ICT infrastructure such as internet, computers, video, audio, and mobile technology facilities that form the basis for the establishment of E-learning. It argued that, schools/universities in developing countries should adopt e-learning technologies to improve teaching and learning processes. They conclude that describes about opportunities; effectiveness, efficiency, motivation, simplify abstract knowledge, instructional resources, improve students’ performance and achievement and quality, pace &accreditation of learning. Also, they describes about challenges like; geographical diversity, infrastructures, awareness & attitude, economic, readiness and trained facilitator. The implementing the ICT familiar curriculum in school to university level, the Ministry of Education Nepal, Curriculum Development Centre and other related sectors need to think for removing the challenges that we are facing. We think at first the Ministry of Education need to make and implement the suitable policies, aware programs, training programs etc. related to ICT and also local educational sectors are also require to actively involve for develop and implement the ICT familiar curriculum in each educational level.

Similarly, Dhital, (2018) conducted a research entitled” the opportunities and challenges to use ICT in Government School Education of Nepal”. This study reviews the concepts and roles of information communication technology in government school education of Nepal. He it identifies how ICT can be used to enhance quality education of government schools in Nepal. Problems such as lack of resources (viz. qualified teachers, hardware, software, electricity etc.) and poor project implementation strategies militate against these efforts. This study recommends that both government and non-government organizations should help to facilitate skilled Manpower, stabilized electricity supply, hardware resources and software resources to enhance the use of ICT in government schools. He concluded that has increased access to computers and the internet in schools, which allows for the scaling-up of the use of ICT in school education. Integrates and focuses on use of ICT in government schools. This demonstrates the commitment on the part of the government. Until now, the program is not in a stable position. The roadmap has been clear but the travel still takes a long time.

Likewise, Joshi, (2005) Wrote a research article entitled “policies, practices and barriers of ICT utilization in school education in Nepal”. The main objective of his study is to explore about existence ICT policies its practices and barriers for its utilization in school level. This study has based on the secondary source of data and those sources of data are different documents and policies related to ICT in education in context of Nepal. From this study, it has found that some ICT related policies has formulated since one dictate and some governmental and private organizations are doing some related activities in this studies, which are not sufficient. Furthermore, policies have not mentions several things. School have so many barriers for its proper utilization. Its effectiveness government should made more relevant policies, organize, several ICT based awareness program like training, seminar workshop and increase financial investment for ICT based programs in school level.

In the Same Way, Shrestha, (2015) Conducted a study on “Status of ICT use in teaching / learning mathematics” in order to find out the use of ICT in mathematics teaching and learning in heartland’s children academy. Her research design was qualitative with case study. The data has collected from primary source. Also, class 7, 8, 9and 10, and interview 4 teachers at heartland’s children academy school in Kathmandu. She has found from the study that there was neither any plan on the use of educational technology tools in mathematics teaching and learning nor inadequate teachers training on the use of educational technologies. In addition, there was a lack of relevant educational technology tools for schools. There were the major reasons for the school not to use the educational technology tools in mathematics teaching and learning.

Furthermore, Bhattrai, (2018) write an article entitle” Experiences of Teachers in diverse Classes: Teaching Mathematics through ICT”. The objectives was to analyze the experiences of mathematics teachers on diverse mathematics class by applying information communication technology integrated pedagogy. He adopted qualitative research with narrative inquiry design. The sample was taken from two mathematics teachers (1 female, 1 male) who were teaching in University Campus, Kirtipur. They were selected following a purposive and convenience sampling technique. The data was collected by The semi-structured interview was used in order to elicit in depth data from the mathematics teachers on their perception, practice and beliefs about experience of teaching in diverse mathematics classes in central department of education TU. He concluded that there are different types of diversity in the context of Nepalese mathematics classroom and the management of diversity is a great job for teachers. Although, teachers are little familiar to the diversity management skill they try to manage such type of diversity by supporting their students personally through ICT tools. Different teachers have different experiences in diverse class. The experience of teachers indicate that they are unable to include the voices and experiences of all students to prepare them for an intercultural society and workplace that helps to create opportunities to utilize project-based learning. In addition, the education system of a country should prepare students to function in today's diverse society and do not ignore or single out students and never ask a student to act as a spokesperson for his/her group and Use ICT integrated pedagogy.

Moreover, Amuke, Miheso, & Ndeuthi, (2015) carried out the research on the topics” Opportunities and Challenges: Integration of ICT in Teaching and Learning Mathematics in Secondary Schools, Nairobi, Kenya”. The objectives of the study was to examine the challenges and opportunities to ICT use in Teaching and Learning Mathematics in Secondary Schools. The research design of study was descriptive survey. The sample were taking from 24 mathematics teachers in secondary school at Nairobi, Kenya. They were used purposive sampling. The data collection tools were questionnaire, observation form, and interview guideline. They are data was interpreted by Code Sheet (SPSS) and themes, mean, frequency and percentage. The study found that has not adequately trained on ICT integration in teaching and learning mathematics in secondary schools. The researcher concluded that teachers to be trained on how to use ICT infrastructure on a regular basis and training to be done at zonal level at least after every six months.

Theoretical Review

Theories are formulated to explain, predict, and understand phenomena and, in many cases, to challenge and extend existing knowledge within the limits of critical bounding assumptions. The theoretical framework is the structure that can hold or support a theory of a research study. The theoretical framework introduces and describes the theory that explains why the research problem under study exists. All aspects of this research are related to Connectivism theory.

Connectivism

Connectivism is the integration of principles explored by chaos, network, and complexity and self-organization theories. Learning is a process that occurs within nebulous environments of shifting core elements – not entirely under the control of the individual. Learning (defined as actionable knowledge) can reside outside of ourselves (within an organization or a database), is focused on connecting specialized information sets, and the connections that enable us to learn more are more important than our current state of knowing. The Connectivism theory basically focuses in the following principles:

· Learning and knowledge rests in diversity of opinions.

· Learning is a process of connecting specialized nodes or information sources.

· Learning may reside in non-human appliances.

· Capacity to know more is more critical than what is currently known

· Nurturing and maintaining connections is needed to facilitate continual learning.

· Ability to see connections between fields, ideas, and concepts is a core skill.

· Currency (accurate, up-to-date knowledge) is the intent of all Connectivist learning activities.

· Decision-making is itself a learning process. Choosing what to learn and the meaning of incoming information is seen through the lens of a shifting reality. While there is a right answer now, it may be wrong tomorrow due to alterations in the information climate affecting the decision (Siemens, 2005).

George Siemens and Stephen Downes developed a connectivism theory for the digital age. According to (Siemens & Downes, 2015) Connectivism is a learning theory that explains how Internet technologies have created new opportunities for people to learn and share information across the world wide web and among themselves. These technologies include Web browsers, email, wikis, online discussion forums, social networks, YouTube, and any other tool, which enables the users to learn and share information with other people.

As such, Connectivism involves opportunities for peer-to-peer learning networks where learning occurs in short bursts driven by the needs and interests of the learners and where flexible learning activities encourage interaction between instructors and students and among learners (Mallon, 2013).

In this study, the Connectivism is applied in two ways: one of them is facilitate classroom and students opportunities in mathematics Learning. Second, use of ICT address teachers challenges faces in mathematics teaching.

Conceptual Framework

A conceptual framework is a graphical representation of the main concepts of the whole research. Theory and conceptual framework are interrelated. It represents the dependent and independent variables, brings clarify and their relation to each other for completion of the research work. The conceptual framework for my study has given below:

Figure 1: Conceptual Framework

The above framework demonstrates that the use of ICT in mathematics classrooms has many opportunities for students and challenges for teachers. The opportunities help students to encourage to engage in learning mathematics. Teachers challenges teaching mathematics for students to facilitate and collaborate. The researcher applied the qualitative research design and case study approach for carrying out this study. The researcher collected the data through observation and interview. Students reached to the construction of new knowledge. So the conceptual framework of the study is based on this aspect and Connectivism theory.

Chapter-III

METHODS AND PROCEDURES

Methodology is utilizes bridge to solve the research problem in systematic way. The methodology describes the methods and process applied to the entire aspect of the study. Therefore, the methodology is the most important part of the research, which was carried out to achieve the response to the problem. In fact, this chapter encompasses the discussion of research design, selection of study site, data collection tools, data gathering process, analysis and interpretation of data.

Research Design

This study adopted case study design in order to find the present status of using ICT in mathematics classroom. Its opportunities and challenges at Mahendra Ratna Campus, Tahachal. This study is qualitative and interpretive in nature. Qualitative research is a scientific method of observation to gather non-numerical data. This type of research "refers to the meanings, concepts definitions, characteristics, metaphors, symbols, and description of things" and not to their "counts or measures. This allows exploration of participants’ understanding of ICT, their experiences and classroom activities through interviews and observations (Neuman, 2006).

Selection of Study Site

This study was focused on the use of ICT in learning mathematics: opportunities and challenges. Until now, there are 62 constituent campuses in Tribhuvan University. Among them, Mahenra Ratna Campus is one of the popular and Famous Campus. Therefore, Mahenra Ratna Campus was selected as study site because, Bachelors and Masters Levels students are studying in this campus. Four mathematics teachers and four mathematics students were selected purposively as sample of the study.

Data Collection Tools

Data collection tools depend on the research design. This research is qualitative in nature. The study has based on primary and secondary data sources. Discussion, interview, observation, and collection of information during the research are the primary source for the study. In the same way literature on the theme, researches on a similar topic as well as suggestions by experts and others too were the secondary source for this study. There are different types of tools for data collecting which were as follows:

Observation

As a data, gathering devices direct observation makes an important contribution to descriptive research. Participant observation is that in which the observation is familiar and participate with the object of the study. In this study, the researcher was used participant observation where researcher was participating in the classroom. For my research, I have observed the student activity in the classroom some important data were collected.

The purpose of the classroom observation was to provide supplemental data for the study. In addition to generating interview questions and probes, Observations yield a detailed.

Interview Guideline

Interview is two-way communication between two or more persons. It is a data collection procedure including verbal communication between the researcher and respondent by telephone or face-to-face situation. I conducted semi-structured interviews probing areas that were too sensitive to explore in the early research.

I followed a process of semi-structured interviews, one of the flexible instruments for collecting data. The interview is then the most common and powerful research method, which enables participants to speak for themselves. The semi-structured interview was used in order to elicit in-depth data from the learning mathematics qualitative research at Mahendra Ratna Campus.

Data Collection Procedure

Data is the foundation of any research. Data collection refers to gathering information from vivid sources through the application of multiple data gathering methods to attain the objective of the research. Therefore, data collection is an essential part of the research. For this study, I was visited the sample campus Mahendra Ratna Campus, Kathmandu. The researcher visited the Head of Department; subject Teachers of the respective campus. First, observation was done during the teacher's normal working hours. The researcher was observing the students, teachers in their natural teaching and learning environment.

The researcher was visited the respondents and was mention the purpose of the visit before starting the interview with the respondents. For collecting information and data with related topics, the interview was conducted for teachers and students based on interview guidelines. Then I was mentioned the purpose of the study and establish a good relationship with them. Then, the researcher was take the interview door-to-door visit and face-to-face interview by the help of a structured interview schedule. After the completion of the interview. The researcher thanked the respondents for their help and co-operation.

Data Analysis and Interpretation Procedures

The information and data collected from various sources and means were analyzed meaningfully by the qualitative method. As well as the data produced out based on interviews and observation forms by using the descriptive method. All interviews were first audio-recorded by taking the informants’ permission. Secondly, data was transcribed for analyzing process. .After collecting the data from the interview schedule. It was carefully checked to remove the possible errors. Then, data were grouped based on the objectives. In this section was a discussion about different topics and sub-topics. I have analyzed the data by linked with much literature. Descriptive and interpretive analyses were used to analyze the data. The basic features of the data were described and interpreted.

Finally, interview data were analyzed through the thematic approach of analysis in which the theme of each response had been coded for generating the final theme. This analysis process involved the organization of the data, transcription of the data, coding the data, and then triangulation of the data with theory.

Ethical Consideration

A research ethics describes the various actions carried out by the researcher in a study. Ethical rules in a study according to (Creswell, 2014) contain two main areas, such as; research requirements and individual protection requirements. Individual participants and the society as a whole have the right to demand that the research conducted is of high quality and ensure that phenomenon studied is properly verified. Also, participant protection which consists of confidentiality, consent, information and utilization requirements are vital throughout the study.

The researcher made sure that the respondent’s privacy and confidentiality of the information provided were observed, these encouraged respondents to provide information more freely. The researcher tried to ensure that my research project would be more a fruitful document for all the people like research participants, teachers, the students, and the teacher educators where the sanctity of ethical issues is maintained.

Chapter-IV

ANALYSIS AND INTERPRETATION OF DATA

This is a case study related to the practice of mathematics classroom opportunities and challenges faced by students and teachers at the master level. This study focused on the use of ICT in the mathematics classroom: opportunities and challenges in the Mahendra Ratna Campus, Kathmandu. This chapter deals with the analysis and interpretation of the Data. The findings of the study were based on the research objectives of the study. Findings have shown that there are many opportunities and challenges around the use of ICT in a mathematics classroom.

The information was collected through observation and interviews with students and teachers. The interpretation of analyzed data was done using different theoretical perspectives as explained in the literature review section. For this, this chapter is organized into two sections. Section first discussed the use of ICT in mathematics classroom for students opportunities and section second discussed the use of ICT in mathematics classroom for teacher challenges.

Use of ICT in Mathematics Classroom: Opportunity for Students

In this section, I deal with the opportunity and challenges to use ICT in the mathematics classroom. For this, I took the interview with the student and class observation of master’s level. The process of taking an interview and class observation is presented below.

Use of Technological Tools

In this digital era, the use of ICT in a real classroom to teach mathematics has the most opportunities for students. The application of these related to technology in the classroom practice depends on how teachers give value to technology and the nature of learning mathematical knowledge. These technological tools have a great significance in teaching and learning mathematics. They are largely used in the classrooms or out of classrooms in mathematics learning. Technology has boomed tremendously within the past 10 years and has taken over various learning areas in Nepal. It is a necessary learning skill with a wide variety of technological tools. Technology has evolved our mathematics learning in many ways, through the adoption of tools like the internet, GeoGebra, Mathematica, Zoom, SPSS, Mat lab, Microsoft Office, Projector, etc. In the interviews, the students shared their classroom experiences of the use of technology tools in their teaching activities. In this regard, the response of the student is that:

“We use classroom in mathematics learning availability of technology tools are Geogebra, Mathematica, SPSS, Microsoft Office and Projector etc. The internet connectivity facilities and easily used technology tools in classroom and I also use of mathematics web sites and social media”.

In this concern, another student said:

“I have effectively utilized available computers and internet facilities in mathematics Lab regularly mathematics task and project work use at projector. I mostly used GeoGebra and Microsoft office used in my mathematics Lab”.

In my Classroom observation, I found that use of technological tools like, Geogebra, Mathematica, Microsoft Office, Projector, and Internet Connectivity is mostly used in Mathematics Classroom and Lab. The ICT resources are available in the classroom and they use effectively by the teacher to give regular feedback for student's work in a mathematics classroom.

After this interview, I concluded that students get more effective mathematics teaching and learning and mathematical software helps for student creativity and motivation. The student collaboration learning feels good uses of availability of technology tools in ICT.

(Siemens & Downes, 2015) Connectivism is a learning theory that explains how Internet technologies have created new opportunities for people to learn and share information across the World Wide Web and among themselves. These technologies include Web browsers, email, wikis, online discussion forums, social networks, YouTube, and any other tool, which enables the users to learn and share information with other people.

I am agreed in this situation that students ICT access in mathematics teaching and learning. The campus-level also maintains ICT lab and mathematical tools. Students used various opportunities in e-learning and worldwide community competition. The connectivism theory is also associated with the use of technology tools effectively in the use of mathematics software in their opportunities at mathematics classroom and lab. In addition, it is student-centered learning that using ICT is more effective and interesting.

Use of ICT at Classroom

By using technology in the classroom, students can develop skills essential for the 21st century. Students can gain the skills they will need to be successful in the future. Modern learning is about collaborating with others, solving complex problems, critical thinking, developing different forms of communication and leadership skills, and improving motivation and productivity. It is important to acknowledge that students are already interested and engaged in using technology. (Poudel, 2007) By using ICT in teaching mathematics, difficult problems can be solved easily and very quickly. This saves the teacher’s labor and time and the classroom will run interestingly. Also by using ICT in teaching mathematics can help teachers to express clearly, what they want to express in the class and students to understand what the teachers have expressed through the demonstration, visualization and experimentation. In this regard, response of the student is that:

“I using ICT in teaching mathematics classroom and enjoyed the class for sure. I did a lot of hard work to make my power point presentation better. While using the visualization method I felt easy in understanding the ways of solving the problems. I continued using some videos from internet to motivate”.

In this way, another student said:

“Firstly, teacher demonstrate some mathematics problems example at technology tools and give some questions. Than I use in Geogebra and Mathematica and create project work on presentation at projector. In the classroom learning more important ICT based mathematics teaching and learning opportunities at mathematics lab”.

In my observation, I found that teachers focused on the activities of individual learners rather than developing group activities in the lab. The students learning with ICT have enjoyed mathematics teaching and learning in the classroom. They have many opportunities to learn ICT. ICT changes the way students learning and easy access to ICT tools in the classroom. The use of digital technology in creating a self-learning environment.

In Conclusion, Interviews and observations in this study indicated that the use of ICT in classroom teaching could gradually shift traditional teaching and learning strategies. The participants that ICT is the most powerful weapon for discovering new knowledge. Students who use ICT in teaching-learning activities seem to be the best in the world. However, students’ self-motivation to access digital materials independently and their evolving personal skills in using digital devices to achieve their learning goals indicated the beginning of student-centered teaching.

Students Attitudes on ICT Usages

ICT will enhance the way of teaching and it opens many new opportunities for students to explore and improve their knowledge and to be creative. ICT-based tools like computers, laptops, and calculators, etc. allowing students to use Videos, images, and text together, to demonstrate their understanding of mathematical concepts.

Many countries in Europe and Asia have determined the importance of ICT and have integrated it into their schools, colleges and today it is becoming compulsory to use ICT in teaching and integrate it into subject teaching. Many of the participants in the interviews emphasized the occurrence of self-learning. They commented that the digital devices created a student-centered learning environment in the lab that allowed the students to direct their own learning. In this regard, the response of the student is that:

“The printed textbooks were helpful for the students to read texts at home and do homework. They used Mathematics Apps, Websites, and Microsoft office that helped them involve the students in mathematics learning activities”.

Similarly, response from another student said:

“ICT is a useful tool and can reach and engage students of all levels improving their overall understanding through visual and hands on methods. It allows students to progress at their own pace and encourages them to be self-motivated and work independently”.

Through observations, I noted that the participants had a strong positive attitude about using ICT in mathematics learning even though almost all of them had limited computers and a lack of ICT policies. Students more energetic to learn for ICT technology tools. Students must have the opportunity to learn from GeoGebra, audio-visual, visual, audio, print media, social media, Microsoft Office, email, and website.

Depending on findings from the interview and classroom observation, Technology colleges should develop a technologically rich curriculum through effective use of ICT and innovative e-learning to raise standards and enhance the quality of teaching and learning.

Students Opportunities for Learning

Using ICT in mathematics class makes student enjoy the audio and visual activities and the interaction among themselves and it draw the student’s attention towards learning. In general, students consider mathematics as boring and difficult subjects and if we use ICT instruments in mathematics class. It was helpful to reduce such misconceptions among such student’s.

The learning process must be expanded beyond the traditional classroom walls. The ICT program serves as a catalyst for an improved and effective learning environment in the mathematics classroom. ICT is a flexible tool to meet the learning needs of students and complement an enriched learning environment managed by the classroom teacher. In this regard, the response of the student is that:

“ICT to student-centered, and that this transformation will result in increased learning gains for students, creating and allowing for opportunities for learners to develop their creativity, problem-solving abilities, informational reasoning skills, communication skills, and higher-order thinking skills”.

According to the Information & Communication Technology (ICT) in Education

Master Plan (2013-2017) IT Policy (2010) has the policy, Expansion of access of the Internet to all schools, Coordination and collaboration with national and international institutions to develop skilled human resources for continuous, relevant and quality education. Therefore, there may be the chances of collaboration with the international institution in the learning mathematics and ICT based classroom.

In conclusion, I totally agree in studies that rely largely on self-reporting, most users feel that using ICTs make them more effective. I confidently would like to say that ICT brings fresh air into the classroom and it makes the students curious and interested towards learning mathematics.

ICT for Creativity and Motivation

ICT is supporting mathematics teaching and learning in underserved area. Using the ICT in teaching in the classroom makes the teacher and students motivate, active and creative. In this regards (Poudel, 2015) say ICT gives the good platform to students for the conceptual learning and the learning process can be conducted by using the means of the ICT more than that when we learn the content in ICT. It add the value of international dimension in learning so that learners can search new ideas so solve mathematical problems that develops creativity on the students. In this regard, response of the student is that;

“I used to be lazy in the classroom when I was learning from the traditional teaching and learning process. So, now I don't feel lazy when I am learning from the new technical tools. I have got more creative and motivate. I work create different draw image, GeoGebra, sketch, mathematics figures and using many technology tools in computer at ICT lab and home”.

Similarly, response from the student is that:

“We are motivated by the teachers as we feel that the mathematics class becomes interesting and college works are made easier by the use of ICT. When the teacher uses white board then we yawn in the class because the classroom environment is boring for me but while using ICT we try to learn every process and steps”.

In my observation, I found that through ICT students could be in touch with teachers. They can send mail to the teachers regarding their problems. ICT helps learners to develop mathematical reasoning skills. In the name of teaching, we are imposing our ideas for students but the main objective of teaching should be making the students independent.

Through this classroom observation and interview with the student, it can conclude that the learners have the perception that they can learn faster if they are taught through visualization. As mentioned earlier tools have an impact on motivating the students for learning. Some steps may be difficult to describe while teaching in the traditional approach but if ICT is used then as the student said they could see how something had happened. In addition, it has been seen as an important tool to enable and support the move from traditional ‘teacher-centric’ teaching styles to more ‘learner-centric’ methods.

Through ICT students can be in touch with teachers. They can send mail to the teachers regarding their problems. ICT helps learners to develop mathematical reasoning skills. In the name of teaching, we are imposing our ideas on them but the main objective of teaching should be making the students independent. On the other hand, some teachers want to use ICT but they don’t get sufficient tools. The students still are not getting all the ICT classes. Self-learning attitude can be developed in the students with the help of the internet and educational channels in YouTube, So that the use of ICT motivate the students therefore the use of ICT in teaching

Mathematics has a positive impact in the classroom and on the student’s motivation so it helps the conceptual learning in mathematics also increase the student’s achievement.

Access to ICT at Home

The use of ICT at home by students reflects what extent they possess the skills of ICT and its applications and can apply them in everyday use. For using ICT in mathematics teaching-learning activities we need to invest the required money at first because there required different software for mathematics and it needs to be updated frequently. Most of the developing countries have an economic challenge to use ICT in classroom activities as same as in Nepal. Mostly mathematics teaching and learning at home more practice with Internet connectivity, laptop, and android phone. I have found the following responses from the representative students based on semi-structured interviews. In this regards, the students say:

“I have a laptop and android phone with internet connectivity access at home. I used mathematical software, which has the access to computers at home and in the class as well. I will learnt different mathematics ways to software basis at home. I use creative mathematics work 2/3 hour per day”.

In this same way, another student said:

“I watch and listen to videos on YouTube while searching the internet, playing games, use mathematical software or doing homework and Project work”.

After this interview, I concluded that students frequently use ICT based mathematical tools at home. ICT has been provided as one of the important tools for mathematics teaching and learning in the home education system.

According to, (Chrisanthos, 2008) Students nowadays live in a world where ICT plays a central role in their daily lives. They enter the classroom not only having encountered rich digital experiences but also being part of a society influenced by new technologies.

In relation to the purpose of using ICT and its applications by students at home. The high ranked ICT feature was the use of Internet connectivity access. The least popular reason has for completing homework and other mathematics work. ICT tools usages for different purposes at home. Students indicated that they use the computer for solving the problems of mathematical work with the use of internet connectivity.

Use of ICT in Mathematics Classroom: Teachers Challenges

In this section, I deal with the use of ICT in the mathematics classroom: Teachers challenges. Challenges in using the ICT in teaching mathematics include the size of a classroom, infrastructure, improper training; teacher’s problems, technology tools, and lack of policy formulation and implementation. The following are challenges facing in the implementation of ICT in mathematics teaching and learning. For this, I took the interview with the teacher and observed classes of Bachelor and master’s level. The development of information and communication technology in the Nepali education system is faced with many challenges.

Unavailability of Technology Tools

The opportunity to communicate with each other by e-mail, Facebook, YouTube, GeoGebra, Mathematica, Mat lab, zoom, SPSS, Microsoft Office, interactive games have some disadvantages and advantages. Its disadvantages are that it requires more preparation for teachers, more teaching materials, and more time to prepare presentations on CD. Today is teaching process in the classroom is unimaginable without the use of ICT in mathematics teaching learning. In this regard, after asking the question teacher replied that:

“In our campus many mathematical tools like Mathematica, Mat lab, and others essential tools are not available. I prefer students to use free of cost technological tools. The computer and laptop are being used increasingly, to record homework, to Microsoft office work, and to Mathematics apps”.

In my observation, I found that the teacher uses many technological tools on campus. The use of ICT has no impact on learning in college. These activities include preparing reports or presentations using Microsoft Office software, along with using the GeoGebra, Mathematica, and other online tools on campus. ICT (compute, laptop and projector) lab which where students can easily access teaching and learning notes, assignments, and project work.

The above interview and observation concluded that worldwide e-Learning, and access to ICT use in the world community in this digital era. Teachers and students also support the use of ICT in the mathematics teaching and learning process, which helps to enhance the student’s learnings. The effectiveness of specific technology tools and software most common software used in campus classrooms seems to be the Microsoft programs Word, GeoGebra, SPSS, Mathematica, Projector, and Access. However, our campus does not sufficiently available technology tools. Mathematical software is not freely available so some application is used.

Lack of Implement of ICT in Classroom

ICT provides a great advantage in the preparation and organization of mathematics classes, as well as teaching the students, relatively using the modern technology in class, and demands constant education of teachers by attending many seminars. The use of ICT provides greater performance, visual observation, better perception, and faster learning. In the teaching process, teachers as assistants are instructing students while they are doing their tasks. ICT can bring many benefits to the classroom and the education process and can provide new opportunities for teaching professionals delivering education. Teachers are very aware of the social changes and the perceived need to keep up with the advances in technology and technology use. In this regard, the response from the Teacher is as follows:

“I use ICT to engage students by using video, audio and visuals and interactivity, and to make transitions is not easier. ICT gives a variety of ways to teach and learn. ICT is a useful tool and can reach and engage students of all levels improving their overall understanding through visual and hands on methods”.

In this concern, another Teacher said:

“I use ICT to plan my lessons. All lessons have some form of Interactive Whiteboard or PowerPoint presentation. So I very much believe we have to be up to date, we have to be using all sorts of resources and as many as we can ICT wise that allow for that good teaching. However, many students managed group by group at classroom access and also not the sufficiently available computer in campus”.

In my observation, I found that the use of ICT within the classroom enhances the learning experience. Only using ICT where relevant and where the outcomes would be positive. The technology can be a useful tool in the classroom and benefit students, most are willing to take the time to learn. But some little problems with ICT use in classroom implementation.

The interview and observation, in this response that make the students curious and interested in learning mathematics. Due to more students in the classroom, the time for each student in the ICT room gets less so that it becomes a difficult task for the teacher to complete the target of the curriculum. In order to make use of ICT within teaching and learning, it may be necessary for teachers to alter their conceptions in terms of technology, students, teaching, and learning. One of the greatest challenges in ICT use in education is balancing educational goals with economic realities.

Improper Training

For the successful and effective use of ICT tools, teacher training is of most importance, and ICT very useful for teachers. One of the preliminary steps in implementing any ICT-based educational approach is teacher perception, unless the teacher fully comfortable with a new approach to teaching, providing students with computers. That is why training related to the specific subject with appropriate use must be essential for the teacher. According to Coley, Cardler, and Engle, for successful and effective ICT tools usage, teacher training is almost important. In this regards, a teacher says that:

“I wish we could move from this chalkboard approach to white board and effective use of ICT in instruction. It will make teaching easier and facilitate students’ understanding. At the academic training like seminar, ICT training and other Mathematics community is not proper organized by particularly trained for teachers to become ICT literate to them to be able and get information from the internet”.

Another teacher said:

“Our Collage does not have any training schedule for the teachers. Some teachers are only send for training twice a year and such training were about mathematics Seminar and using mathematics application teaching learning process. It is possible up to now for me to participate in any seminar conducted on mathematics”.

The above teachers' view indicated that though they were willing to participate in the training in a certain interval, they were not getting it because the campus has no proper schedule for the teachers' training. The teachers were not being participated in such training that was related to teacher’s professional development. Training could be very important and necessary for teachers for their professional development because to come with a fresh and new mind in the classroom is fruitful and hence helpful to increase students' achievement. However, teachers learned to web sites, YouTube, and other resources' own teaching processes. Therefore, such training has been limited to the formality of trainers and trainees.

Lack of Access and ICT Infrastructure

Effective teaching and learning Mathematics using ICT is determined by the availability of ICT infrastructure in the schools. Access and the available infrastructures remain the main factors that influence the mathematical learning and teaching use of ICT.

ICT Infrastructures are all the information and communications technology infrastructure and systems (including software, hardware, firmware, networks, and the company websites) that are used in an organization. ICT infrastructure and skilled human resources are core components of ICT in education. Availability of ICT in the community environment provides an opportunity to use various forms of ICT for different purposes. The ICT access hardware infrastructure needs to be in place with supporting elements such as electricity, maintenance, and technical services. Effective teaching and learning Mathematics using ICT is determined by the availability of ICT infrastructure in the college. In this regards, the teachers responded as:

“Computer are not sufficient, poor connectivity, infrequent electricity supply, the number of students in classrooms, having almost a hundred plus with almost no space for circulation. All of that you know compact the difficulties that go with using ICT usage in the classroom”.

Similarly, another teacher said:

“Only ICT teachers are allowed to use the College labs. For a subject teacher like me, to come here with my students, I need to start first by taking permission from my head of the department in charge of my subject area. The head of the department then asks for permission from the collage discipline masters, who make a request to the ICT monitor in charge of the College multi-media Centre”.

In my observation, I concluded that the ICT infrastructure is less availability in campus. Large class sizes make it difficult for teachers to employ interactive teaching strategies or to gain insight into the difficulties experienced by students. Large classes pose problems for all students but students who are under-prepared are particularly affected.

Depending on findings from the classroom observation and interview, responses from many of the teachers in ICT classrooms their positive interest to incorporate ICT in their classrooms. The interest in integrating ICT could not effectively use ICT tools because of poor networks and lack of electricity in the classrooms.

Challenges of ICT Teaching

Teachers need specific professional development opportunities in order to increase their ability to use ICT for formative learning assessments, individualized instruction, accessing online resources, and for fostering student interaction and collaboration. ICT technologies and other aspects of digital culture have changed the ways people live, work, play, and learn, impacting the construction and distribution of knowledge and power around the world. The development of information and communication technology in mathematics education is faced with many challenges. In this regards, the teachers responded as:

“ICTs have not been used as a way of acquiring new knowledge and skills in campus of Nepal due to inadequacy of curriculum content and limited access to ICTs. Other challenges include inadequate funding, lack of basic infrastructure, lack of qualified personnel; our context is the required physical infrastructure for implementing, sustainability and lack of policy formulation and implementation”.

In the above teacher’s interviews, I conclude that the digital device and access to ICT facilities is a major challenge facing Nepali College. In our context, we are facing various problems and challenges for using ICT in the mathematics classroom. In most of the developing country has an economic challenge to use ICT in classroom activities as same as in Nepal.

According to, National Curriculum Formwork-2007 and ICT in education master plan (2013-017) focuses on ICT familiar curriculum in every subject but we need to know our ground reality that is the lack of trained course facilitators for all subjects to use ICT in classroom activities. Especially in mathematics classroom there need to use different mathematical software in different ways so at first need to provide opportunities for facilitator to gain implementing knowledge and skills of ICT in mathematics.

In Conclusion, some major challenges for using ICT in a Nepalese mathematics classroom. Challenges in using the ICT in teaching mathematics include the size of the classroom, Infrastructure, and funding, lack of qualified personnel, and lack of policy formulation and implementation.

Use of ICT Teacher’s Opportunities

According to the Information & Communication Technology (ICT) in Education Master Plan 2013-2017) IT Policy (2010) has the policy, Expansion of access of the Internet to all College, Coordination and collaboration with national and international Institutions to develop skilled human resources for continuous, relevant and quality Education. Therefore, there may be the chances of collaboration with the international institution in the learning mathematics and ICT based classroom. In this regard, the one teacher says:

“ICT make teaching job easier, ICT promote individualized interactivity, ICT improves delivery of mathematical resources, and ICT offers a wide access to global knowledge, ICT facilitate interaction with resources”.

In this same way, another teacher said that:

“ICT has the ability to make learning occur anytime at any place, through the use of ICT access to mathematics education has been wide and limitless, and teachers can learn and get access to mathematics educational resources anywhere and at any time. There are varieties of mathematics materials on the internet such as virtual classes, electronic books, electronic libraries that are accessible 24 hours everywhere ICT has made mathematics education resources easily be available, easily accessible”.

From the above information, I found that teaching mathematics using ICT is more effective and more interesting. It is student centered learning that can assist to boost up their computer skills as well as lesion be learnt is meaningfully. The most significant factor for continuing the development of teachers’ ICT-related skills is for them to have regular access to functioning and relevant ICT equipment. The study identified the following factors: - teachers’ positive attitude, teachers’ competence in ICT use, accessibility of ICT facilities, professional development, and availability of technical support.

Chapter-V

SUMMARY, FINDINGS, CONCLUSION AND RECOMMENDATIONS

This chapter synthesizes the analysis of the data gathered from primary and secondary sources as findings of the study and draws conclusion of the study. This chapter also deals with the finding, conclusion and implications of the study and presents a summary of the research findings, conclusion, recommendations of the study and suggestions for further research.

Summary and Findings

Literature on mathematics teaching and learning has shown that there is a consensus on the need to enforce our student's problem solving and higher-order thinking skills in mathematics so that they can be captured in pursuing successful careers.

This study was qualitative with a case study type. The researcher himself developed a questionnaire under the guidance of a supervisor. The questionnaire, classroom observation, and interview schedule were the main tools of this study. The responses were collected from mathematics teachers and students of sampled campus, in the Kathmandu district, selected by the purposive sampling method. Also, interview data analyzed based on the thematic approach.

It is obvious that in general information technology and in particular, calculator, computer and software major changes in what to teach. It is more efficient with changes in how to teach rather than what to teach. A typical way to do so is to replace older ways of communication with new possibilities offered by information technology and internet connectivity. Thus, ICT helps the students to become more active in the education process. Particularly, ICT tools have also great potential to affect presenting the content of the university mathematics.

Based on analysis and interpretation of the data, the major findings of this study are presented below:

· ICT has provided an opportunity to each individual for unlocking creativity systematically through active participation, which is a key element of constructivism learning.
· The use of ICT promoted independent and self-regulated learning that are important for unlocking student’s potential and enables students to develop invaluable confidence.
· The use of ICT helped students and teachers to embed mathematical concepts is visual.
· There is a facility of ICT and internet for selection and use of teaching materials to teach mathematics in a modern way.
· There are sufficient teaching materials in college and teachers are using available teaching materials as well.
· The campus has no proper schedule for refreshing training to deal with new challenges that take place during teaching-learning activities.
· ICT infrastructures were limited in the college and Mathematics teachers did not the sufficient seminars and training programs on how to use ICT in teaching and learning Mathematics.
· The use of ICT in teaching mathematics can make the teaching process more effective as well as enhance the student's capabilities in understanding basic concepts.
· Students get more effective mathematics teaching and learning and mathematical software help for student creativity and motivation. The student collaboration learning feels good uses of availability of technology tools in ICT.
· The use of ICT in classroom teaching could gradually shift traditional teaching and learning strategies. The participants that ICT is the most powerful weapon for discovering new knowledge.
· The study was identified as barriers to using ICT in teaching teacher competence and confidence, teaching experience, inadequate infrastructure, lack of training, and lack of technical support.
· Teachers and students also support the use of ICT in the mathematics teaching and learning process, which helps to enhance the student’s learnings.
· The most significant factor for continuing the development of teachers’ ICT-related skills is for them to have regular access to a functioning and relevant ICT equipment.

Conclusion

From the above-stated findings of this study, it can be concluded that teaching-learning activities of mathematics are satisfactory to construction and purchase of teaching materials, selection of teaching materials, use of teaching materials and method, teachers' training and its transfer in real classroom teaching, trainers with their knowledge, skill, experience. It is found that necessary teaching materials are available and teachers are using available teaching materials too. According to teachers, we can use teaching materials because of crowded class, a large number of students, inappropriate campus environment, and divide the group by group in the classroom teaching.

Both lecturers and students are competent in basic ICT applications such as Microsoft word processor, GeoGebra, Mathematica, e-mail, excel, and the like. However, the majority of lecturers have lack competence in the pedagogical use of ICTs to enhance education delivery for which they required proper training given to them for success. The policy emphasizes that the use of ICT in teaching and learning can equip the growing generation of youths with skills and integrate them into the global technological market. The ICT is essential and useful to conduct the mathematics lesson at the campus level. It is more effective in comparison to the traditional method. Teaching mathematics through ICT, there is the active participation of students and teachers will benefit from teaching and learning.

In addition, in this digital era, ICT use in the classroom is important for giving students and teachers challenges and opportunities to learn and apply the required 21st-century skills. ICT has made the world come closer day by day. After a few years, any gadget will be mandatory among children or aged people. This represents that the coming generation without the internet will be unimaginable. So as to motivate mathematics educators to apply elements of ICT in their teaching. This could maintain the positive changes and perceptions of students regarding learning mathematics.

Implications of the Research

Every research has implications in different sectors. The study entitled “use of ICT in mathematics classroom: opportunities and challenges” has based on the findings, the following are potential implications;

· Teachers should also be provided with adequate technological resources, technical support and administrative support to encourage them successfully use ICT in teaching and learning.
· Teacher should be urged in on using mathematics lesson in accordance with policy provisions of penetrating ICT tools in university level curriculum.
· Traditional approach has a lot of countenance in mathematics teaching and learning and ICT based mathematics class may be panacea for it.
· Teachers should be given sufficient training on how to use ICT in teaching and learning processes to acquire the requisite knowledge and skills in integrating the technology in classrooms.
· This study has reported enhancing classroom uses of technology, providing technology training, providing technology infrastructure and resources.

Recommendations for Future Research

The researcher is of the opinion that further research can be carried out in the following areas.

· A study to be done on ICT pedagogical practices in teachers training colleges and universities in Nepal.
· A study to be conducted on the effectiveness of using technology tools in teaching and learning Mathematics.
· A research can be done to involve several universities in the country in order to determine challenges and opportunities for integration of ICT in the mathematics Classroom.
· The study about problems related to mathematics curriculum, textbook, and its relevancy to the context of the multicultural classroom can be one of the areas for further study.
· It is helpful to find out the challenge and opportunities of teachers and students in mathematics classrooms.
· Further research should also be designed to investigate the experiences of lecturers and students on ICT opportunities and challenges in mathematics education delivery at the University of Nepal.

REFERENCES

Amuke, S., Miheso, M., & Ndeuthi, S. (2015). Opportunities and challenges: Integration of ICT in eaching and learning mathematics in secondary schools, nairobi, kenya. Journal of Education and Practice, 6(15).

Bajracharya, D., Bhuju, D. R., & Pokhrel, J. R. (2006). Science, research and technology in nepal. UNESCO, Kathmandu.

Bhattrai, L. N. (2018). Experiences of teachers in diverse classes:Teaching mathematics through ICT. International Education & Research Journal, 4(8).

Chrisanthos, I. (2008). The use of ICT in primary mathematics in Cyprus: the case of GeoGebra (Master's thesis).

Cohen, L., Manion, L., & Morrison, K. (2013). A Guide to teaching Practice. New Delhi: Cambridge University Press.

Creswell, J. W. (2014). Research design qualitative, quantitative, and mixed methods approaches. Thousand Oaks, CA: SAGE Publications.

Crowther, D. T. (1997). The Constructivist Zone. Electronic Journal of Science Education: Retrieved fromhttp://wolfweb.unr.edu/homepage/jcannon/ejse/ej.

Dahal, B., & Dahal, N. (2015). Opportunities and challenges to use ICT in nepalese mathematics education. Second National Conference on Mathematics Education: Retrieved Fromhttps://www.researchgate.net.

Dhital, H. (2018, April). Opportunities and challenges to use ICT in government school education of nepal. International Journal of Innovative Research in Computer adn communication engineering, 6(4).

Hohenwarter, M. (2008). E-learning: Concepts, issues, application, evaluation. Austria: Riyadh:Dar Alsolatech Publication.

Joshi, D. (2005). Policies, practices and barriers of ICT utilization in school education in nepal. International Journal of Research in Social Science, 7(2).

Koohang, A. (2009). A learner-centered model for blended learning design. International Journal of Innovation and Learning, 6(1), 76-91.

Mallon, M. N. (2013). Extending the learning process: Using the theory of connectivism to inspire student collaboration. Kansas Library Association College and University Libraries Section Proceedings, 3, 18-27.

MOE. (2007). School sector reform: Draft for consultation and dissemination. Kathmandu: Authors.

MOE. (2013). Information & communication technology (ICT) in education master plan 2013-2017. Kathmandu: Government of Nepal.

NCTM. (2000). Principles and standards for school mathematics. Reston Virginia: Authors.

NCTM. (2000). The national council of teachers of mathematics. Retrieved from www.nctm.org: https://www.nctm.org/uploadedFiles/Standards_and_Positions/PSSM_ExecutiveSummary.pdf

Neuman, W. L. (2006). Social research methods: Qualitative and quantitative approaches. Boston: Pearson /AandB.

Plan, I. M. (2013-2017). Information & Communication Technology (ICT). Kathmandu: Government of Nepal.

Poudel, S. (2015). Teacher and student perception on the use of ICT in mathematics teaching (An unpublished dissertation of master of degree). Kathmandu University, Nepal.

Poudel, Y. N. (2007). Use of ICT in teaching mathematics (An unpublished dissertation of master of degree). Tribhuvan University, Nepal.

Shrestha, R. (2015). Status of ICT use in teaching / learning mathematics. An unpublished master thesis, Department of Mathematics Education, T.U.: Kirtipur, Kathmadu.

Siemens , G., & Downes, S. (2015). "Connectivism (Siemens, Downes)"in learning theories. Retrieved from https://www.learning-theories.com/connectivism-siemens-downes.html.

Siemens, G. (2005). Connectivism:A learning theory for the digital age. Retrieved From http://www.itdl.org/journal/jan_05/article01.htm.

APPENDIX-A: Interview Guidelines for Teachers

Name of the Teachers………………College …Name…………………Date:……….

Address…………………………… Gender………………

Dear Sir/Madam,

I am Dan Bdr Budha, a postgraduate researcher from the Mahendra Ratna Campus, Tahachal, Kathmandu, Nepal, carrying out a research on “Use of ICT in Mathematics Classroom: Opportunities and Challenges” under the supervision of Mr. Loknath Bhattrai a lecture of Department of Mathematics Education. I shall be grateful for your kind cooperation and participation in making this task a success.

This interview aims to get your views about the use of Information and Communication Technologies (ICTs) in Mathematics Classroom opportunities and challenges. This study is strictly for academic purpose and will be treated with high confidentiality.

This interview with mathematics teacher taken in the basis of following statements.

Ø How long have you been teaching?
Ø Proper training
Ø Availability of technological tools (like Internet, Mathematical software, projector etc.)
Ø Teachers interest and Students interest
Ø Challenges face to learning/teaching mathematics using ICT
Ø Implement of ICT in mathematics classroom
Ø Engage your learners to learn by using ICT
Ø Knowledge about technologies
Ø Opportunity to use of ICT

APPENDIX-B: Interview Guidelines for Students

Name of the Students…………College Nam…….……….Date……… Address……………………….. Gender…………

Dear Student,

This interview with mathematics students taken in the basis of following Statements.

Ø Do you have a computer at home?
Ø Computer basic skills
Ø Use of technological tools (like mathematical software, internet, projector etc.)
Ø ICT facilities mathematics task
Ø Engage in ICT based learning activities
Ø Effective learning in ICT classroom
Ø Effectively use computer and internet
Ø Internet access in ICT Lab
Ø Opportunities in using ICT
Ø Challenges in using ICT

USE OF ICT IN MATHEMATICS CLASSROOM: OPPORTUNITIES AND CHALLENGES

2021-04-28T09:59:00.003+05:45

USE OF ICT IN MATHEMATICS CLASSROOM: OPPORTUNITIES AND CHALLENGES (Post Graduate Thesis)

TEACHING UDERGRADUATE MATHEMATICS (Small Review)

2021-02-13T13:31:00.000+05:45

TEACHING UDERGRADUATE MATHEMATICS

1. Algebra:

Algebra (from Arabic al-jebr meaning "reunion of broken parts") is the branch of mathematics concerning the study of the rules of operations and relations, and the constructions and concepts arising from them, including terms, polynomials, equations and algebraic structures. Algebra is a branch of mathematics that deals with relations, operations and their constructions. It is one of building blocks of mathematics and it finds a huge variety of applications in our day-to-day life.

The word “algebra” means many things. Apart from its significance as a core subject of mathematics, Algebra helps students and kids a lot in developing an overall understanding of other advanced branches of mathematics such as Calculus, Geometry, Arithmetic etc. Basic algebra is the first in a series of higher-level math classes students need to succeed in college and life. Algebraic Expression: Rhetorical Algebra, Syncopated Algebra and Symbolic Algebra. Conceptual Stages: Geometric Stages, Static equation solving stage, Dynamic functional stage, Abstract Stage.

Because many students fail to develop a solid math foundation, an alarming number of them graduate from high school unprepared for college or work. Many end up taking remedial math in college, which makes getting a degree a longer, costlier process than it is for their more prepared classmates. And it means they’re less likely to complete a college-level math course. For middle-schoolers and their parents, the message is clear: It’s easier to learn the math now than to relearn it later.

Some area of Mathematics with the word algebra in the Name. They are following,

ü Elementary algebra.

ü Abstract algebra.

ü Linear algebra.

ü Boolean algebra.

ü Modern algebra.

ü Commutative algebra.

ü Computer algebra.

ü Universal algebra.

ü Systematic algebra.

ü Classical algebra etc.

Algebra emerged at the end of the 16th century in Europe with the work of François Viète. The most important Area of algebra is described below.

2. Classical Algebra:-

i. Introduction:

The start of the classical discipline of algebra developments included several related trends, among which the following deserve special mention: the quest for systematic solutions of higher order equations, including approximation techniques; the rise of polynomials and their study as autonomous mathematical entities; and the increased adoption of the algebraic perspective in other mathematical disciplines, such as geometry, analysis, and logic. During this same period, new mathematical objects arose that eventually replaced polynomials as the main focus of algebraic study. The classical algebra uses finding roots or values of unknowns symbols instead of specific numbers, arithmetic operations to establish procedures for manipulating symbols.

The development of classical algebra can be traced to the ancient period Where Algebra Comes From.

ii. Contents:

• systems of equations

• number and equations

• Equations and Their Solutions.

• Numerical Solution of Equations.

• Introduction to cryptography

• Polynomial equation and complex number.

iii. Period:

Classical algebra has been developed over a period of 4,000 years ago.

3. Abstract Algebra:-

i. Introduction:

School algebra can be seen as a generalization of arithmetic in which the variables are numbers and the expressions and equations are formed with the four arithmetic operations. Abstract algebra is a generalization of school algebra in which the variables can represent various mathematical objects, including numbers, vectors, matrices, functions, transformations, and permutations, and in which the expressions and equations are formed through operations that make sense for the particular objects: addition and multiplication for matrices, composition for functions, and so on. This section provides a short sketch of abstract algebra in order to highlight ideas of structure and to present the terms, concepts, notations, and perspectives that undergird the research questions and subsequent analysis.

Abstract algebra consists of axiomatic theories that provide opportunities to consider many different mathematical systems as being special cases of the same abstract structure. The theories are called axiomatic because the structures are defined by axioms. Group theory is “one of the oldest (and also one of the simplest) of axiomatic theories”

ii. Contents:

· Groups theory

· Rings theory

· Fields theory

· Modules theory

· Vector space

· Functions and integers

· Galois Theory

iii. Period:

In the 19^th century algebra was no longer restricted to ordinary number systems. Algebra expanded to the study of algebraic structures.

4. Modern Algebra:-

i. Introduction:

Modern algebra, also called abstract algebra, branch of mathematics concerned with the general algebraic structure of various sets (such as real numbers, complex numbers, matrices, and vector spaces), rather than rules and procedures for manipulating their individual elements. During the second half of the 19th century, various important mathematical advances led to the study of sets in which any two elements can be added or multiplied together to give a third element of the same set. The elements of the sets concerned could be numbers, functions, or some other objects.

A definitive treatise, Modern Algebra, was written in 1930 by the Dutch mathematician Bartel van der Waerden, and the subject has had a deep effect on almost every branch of Mathematics. The study of groups, rings, fields is not only the students first introduction to modern mathematical thinking but provides some of the essential crutches. Abstract algebra emerged around the start of the 20th century, under the name modern algebra. Its study was part of the drive for more intellectual rigor in mathematics. Initially, the assumptions in classical algebra, on which the whole of mathematics (and major parts of the natural sciences) depend, took the form of axiomatic systems.

ii. Contents:

Ø Group theory

Ø Modulus and vector spaces

Ø Ring theory

Ø Field and Galois theory

iii. Period:

The end of the 19th and the beginning of the 20th century saw a tremendous shift in the methodology of mathematics. Abstract algebra emerged around the start of the 20th century, under the name modern algebra.

5. Linear Algebra:-

i. Introduction:-

The origins of the concepts of a determinant and a matrix, as well as an understanding of their basic properties, are historically closely connected. Both concepts came from the study of systems of linear equations. Linear algebra is the branch of mathematics concerning vector spaces and linear mappings between such spaces. It includes the study of lines, planes, and subspaces, but is also concerned with properties common to all vector spaces. The branch of mathematics that deals with the theory of systems of linear equations, matrices, vector spaces, determinants, and linear transformation. Or the part of algebra that deals with the theory of linear equations and the linear transformations.

Branch of algebra concerned with method of solving system of linear equations, more generally, the mathematics of linear transformation and vector spaces. The term "linear algebra" is also used to describe a particular type of algebra. Techniques from linear algebra are also used in analytic geometry, engineering, physics, natural sciences, computer science, computer animation, advanced facial recognition algorithms and the social sciences (particularly in economics). Because linear algebra is such a well-developed theory, nonlinear mathematical models are sometimes approximated by linear models.

ii. Contents:

ü Fields and Vector spaces

ü Linear transformations

ü Matrix theory

ü Eigenvalue and eigenvectors

ü Subspace, span and basis

ü Theory of Determinants

ü Linear Coding Theory

ü Linear Equations

iii. Period:

The emergence of the subject came from determinants, values connected to a square matrix, studied by the founder of calculus, Leibnitz, in the late 17^thcentury, Gabriel Cramer devised Cramer's Rule for solving linear systems in 1750 and 19^th century.

6. Conclusions:

I am at the end of my individual assignment. This work was given as a part of University campus curriculum. I am very grateful to the school authority for providing a golden platform for the creative work. I express my gratitude to the subject teacher Mr. Abatar subedi for his guidance and support.

The topic was very interesting and I learned a lot of things about “algebra ”. Such works develoapp the creativity of the students and also increase their knowledge base. I hope to get such works in future days. Once again I am grateful to everyone who was involved in this work.

REFRENCE:-

- - Alan sultan and alice F. artz (2011). The mathematics that every secondary school mathematics - teacher needs to know. Routledge

- - Wikipedia and various related websites.

- -Powerpoint of Subject teacher etc.

difference between curvature and torsion

2021-02-10T12:48:00.001+05:45

1. What is the difference between curvature and torsion?

- Space curve are uniquely determined by two scalar quantities, called curvature and torsion.

S.N.	Curvature	Torsion
1.	-Curvature measures deviation of a curve from a straight line.	-Torsion measures deviation of a curve from a plane.
2.	-Rate of change in the direction of tangent line.	-Rate of change in the direction of bi-normal line.
3.	-Straight line has zero curvature.	-Plane curve has zero torsion.
4.	-The expression of curvature is t¢ =kn.	-The expression of torsion is b¢ =-tn.
5.	-The magnitude of curvature is denoted by k (Kappa).	- The magnitude of torsion is denoted by t (Tau).

PROPOSAL AND REPORT WRITING- The Infinity Mathematics

2021-02-05T19:46:00.000+05:45

PROPOSAL AND REPORT WRITING

Research Proposal

ü A research proposal is an overall plan, scheme, structure and strategy designed to obtain the answers to the research questions or problems that constitute the research project.

ü It is a statement of intent or a plan of action. It helps to the researcher for engaging in genuine enquiry, finding out about something worthwhile in a particular context.

ü What, how and why of the research?

Why Research Proposal

ü Gives you an opportunity to think through your project carefully, and clarify and define what you want to research

ü Provides you with an outline and to guide you through the research process

ü Link your proposed work with the work of others,

ü Communication between researcher and supervisor

ü Document to apply for a budget

Component of Proposal

ü Title

ü Introduction

ü Literature review

ü Methodology

ü References

Title of the Study

ü Must give the reader a sense of what you are doing or examining

ü Do not make it too general and too long

ü Should be no more than 15 words

ü Catchy and attention-grabby

Introduction

· Background of the study

· Problem of the statement

· Objectives of the study

· Research questions and hypothesis (if applicable)

· Rationale or significance of study

· Delimitation

· Operational definition

Literature Review

Ø Theoretical literature

Ø Empirical literature

Ø Theoretical framework

Ø Conceptual framework

Methodology

Research Design

Ø Population and sample

Ø Instruments and validation

Ø Data collection

Ø Data analysis

Ø Ethical issues

Ø Timelines and budget (if required)

Research Report

v A report is a statement of the results of an investigation or of any matter which definite information is required.

v Final product of the research

v A formal statement or document of a research process and its results

v Means of communication between researcher and readers

v Good report –accurate, clear, free of ambiguity, local and concise writing

Essential Qualities of a Research Report

v Professionalism

v In-depth knowledge of the subject

v Concentration

v Writing skills

Components of Research Report

v Preliminary part

v Main part

v Reference part

Preliminary Part

v Title page

v Recommendation page(if applicable)

v Approval lertter(if applicable)

v Acknowledgement

v Abstract

v Table of contents

v List of tables

v List of figures(if applicable)

v Abbreviation

According to Education Dean of Tribhuvan University

v Title page

v Declaration

v Recommendation *

v Approval *

v Abstract

v Acknowledgments

v Table of contents

v List of tables

v List of figures

v Acronyms/ abbreviations

Main Part

v Introduction

v Review of literature

v Methodology

v Data analysis and interpretations

v Summary, conclusion and implications

According to Education Dean of Tribhuvan University

Chapter I: Introduction

· Background of the Study

· Statement of the problem

· Objectives of the Study

· Research Question or Hypothesis (if necessary)

· Significance of the Study

· Delimitations of the Study

· Operational definition of the key terms

Chapter II: Review of Related Literature and Conceptual Framework

· Review of Theoretical Literature

· Review of Empirical Literature/Previous Studies

· Implications of the review for the Study

· Theoretical/Conceptual Framework

Chapter III: Methods and Procedures of the Study

· Design and method of the Study

· Population, sample and sampling strategy

· Study area/field

· Data collection tools and techniques

· Data Collection Procedures

· Data Analysis and Interpretation Procedure

Chapter IV: Analysis and Interpretation of Results

· •Analysis of Data and Interpretation of the results

· •Summary/Discussion of Findings

Chapter V: Conclusions and Recommendation

ü Conclusions

ü Recommendation

-Policy related

-Practice related

-Further research related

Reference Sections

ü References

ü Appendix

ü Index

ü Maps and pictures

Citation and Referencing as per APA format (American Publication Manual of American Psychological Association, 6th Edition, 2010)

-Appendices

{Dean office}

Research Report

Φ Title

Φ Abstract

Φ Introduction

Φ Literature review

Φ Methodology

Φ Results and discussion

Φ Summary, conclusion and implications

Φ References

Φ Appendices

APA Referencing

v American psychological association 6thedition

v In-text citation and end-text referencing

Language

ü Language in an APA paper should be:

· Clear: be specific in descriptions and explanations

· Concise: condense information when you can

· Plain: use simple, descriptive adjectives and minimize figurative language

APA Writing

ü Your report should:

· be typed,

· double-spaced,

· have 1” margins,1’’-left

· use 10-12pt. Standard font (ex. Times New Roman), and

· be printed on standard-sized paper (8.5”x 11”)

General APA Format

ü Your report should include four major sections:

Title page

Abstract

Main Body

References

APA in-Text Citations

ü The APA system of referencing uses in text references or citations to acknowledge someone else's words, thoughts or ideas that have been included in your work. Information required in the text of your assignment includes:

· the author(s)'s surname(s)

· the year of publication

· The page number or paragraph number for non-paginated sources (direct quotes only).

Punctuation of Citations

Direct Quotes

ü Direct quotes show where another person's original thoughts, words, ideas, images etc. have been useddirectlyin someone else's work.

ü Follow these steps to use direct quotes in your assignments.

· Copy theexactwords from the original source.

· Usequotation marks " "at the beginning and end of the copied text.

· Referencethe author, year and page number information.

Direct Quotes Short (Less than 40 Words)

Long Direct Quotes

ü For citations of 40 words or more, block quotes should be used. A block quote is indented and written on a new line. Itdoes not have quotation marks around it.

Paraphrasing

v Paraphrasing is when you use someone else's ideas and put them in your own words.

v Even though you are not using the original author's exact words, you must still cite the source.

v By presenting the information in your own words, you demonstrate your understanding of the material that you have read.

Citing of Paraphrase

Using Multiple Source

End-Text Referecing

ü Books

· Book author(s) or editor

· Year of publication

· Book title (in italics)

· Publication information: place: publisher

Journal Article

v Article author(s)

v Date of publication

v Article title

v Journal title (in italics)

v Volume number (in italics), (issue in brackets if required), page numbers

v Digital object identifier (DOI): used for electronic publications. If no DIO is given for online journal articles, use the homepage URL of the journal.

Examples

Websites

v Author(s) / organization's name

v Date last modified (if there is no date, n.d.can be used)

v Title of page

v Website URL

Plagiarism

ü the presentation of the work, idea or creation of another person as if it were your own

ü a form of cheating

ü a serious offence with serious consequences.

ü Examples of plagiarism:

· copyingsentences or paragraphs word-for-word from a sourcewithout proper citation

· puttingsomeone else's words, thoughts, ideas into your own words (paraphrasing) butfailing to cite your sourcewith a proper citation

· piecing together textsfrom one or more sourceswithout appropriate citation

· copyingor submitting whole parts of computer fileswithout acknowledging their sources

· copyingor submitting the whole or a part of another student's work.

To avoid plagiarism you must cite the source.

Proposal and Report Writing- The Infinity Mathematics

2020-12-24T02:00:00.001+05:45

PROPOSAL AND REPORT WRITING

For Download: Click the Red Underline Letter Below,

Proposal and Report Writing

Download Link: https://drive.google.com/drive/u/0/folders/1nKWqHeGyeodzr-L9ynbCOxDuP8LkPTDk

Report Writing Format

2020-12-15T14:16:00.000+05:45

Report Writing Format

General Guidelines

1. Use 8 ½ x 11” white paper.

2. Make 1 inch margins on the top, bottom, and sides.

3. The first word in every paragraph should be indented one half inch.

4. APA recommends using Times New Roman font, size 12.

5. Double space the entire paper.

6. Include a page header known as the “running head” at the top of every page.

a. To create the running head/page header, insert page numbers justified to the right-hand side of the paper (do not put p. or pg. in front of page numbers).

b. Then type “TITLE OF YOUR PAPER” justified to the left using all capital letters.

c. If your title is long, this running head title should be a shortened version of the title of your entire paper.

APA Paper Components

The paper should include these four major sections:

1. Title Page

2. Abstract

3. Main Body

4. References

1. Title Page

This page should contain four pieces: the title of the paper, running head, the author’s name, institutional affiliation, and an author’s note. Create the page header/running head as described above.

*Please note that only on the title page, your page header/running head should include the words “Running Head” before your title in all capitals. The rest of the pages should not include this in the page header.

Note: Make title page based on the questions given to you.

· The title of the paper should capture the main idea of the essay but should not contain abbreviations or words that serve no purpose

· It should be centered on the page and typed in 12-point Times New Roman font. Do not underline, bold, or italicize the title.

a. Your title may take up one or two lines, but should not be more than 12 words in length.

b. All text on the title page should be double-spaced the same way as the rest of your essay.

c. Do not include any titles on the author’s name such as Dr. or Ms.

d. The institutional affiliation is the location where the author conducted the research.

2. Abstract

Begin with the Running title. Then -

1. On the first line of the page, center the word “Abstract” (but do not include quotation marks).

2. On the following line, write a summary of the key points of your research. Your abstract summary is a way to introduce readers to your research topic, the questions that will be answered, the process you took, and any findings or conclusions you drew.

3. This summary should not be indented, but should be double-spaced and less than 150 words.

4. If applicable, help researchers find your work in databases by listing keywords from your paper after your summary. To do this, indent and type Keywords: in italics. Then list your keywords that stand out in your research.

3. The Body

Begin with the Body of the paper. Then -

a. Start with the Running title.

b. On the next line write the title (do not bold, underline, or italicize the title).

c. Begin with the introduction. Indent.

d. The introduction presents the problem and premise upon which the research was based. It goes into more detail about this problem than the abstract.

e. Begin a new section with the Method. Bold and center this subtitle The Method section shows how the study was run and conducted. Be sure to describe the methods through which data/information was collected.

f. Begin a new section with the Results. Bold and center this subtitle. The Results section summarizes the data. Use graphs and graphs to display this data (if necessary).

g. Begin a new section with the Discussion. Bold and center this subtitle. This Discussion section is a chance to analyze and interpret your results.

ü Draw conclusions and support how your data led to these conclusions.

ü Discuss whether or not your hypothesis was confirmed or not supported by your results.

ü Determine the limitations of the study and next steps to improve research for future studies.

** Throughout the body, in-text citations are used and include the author’s/authors’ name(s) and the publication year. In APA format, page numbers are not used in in-text citations.

Note: Total length of the paper should be within 1200 to 1500 words excluding abstract and references.

4. References

On a new page, write your references. Then -

1. Begin with a running title

2. Center and bold the title “References” (do not include quotation marks, underline, or italicize this title)

3. Alphabetize and Double-space all entries

4. Every article/source mentioned in the paper and used in your study should be referenced and have an entry.

Possible Headings

Background of the study

Objective of the study

Methods of study

Use of ……..Software in Nepalese context

Use of ………..software in International context

Discussion

Conclusion

References

List of Mathematics and Mathematics Education Journals

2020-12-04T16:54:00.000+05:45

For the Learning of Mathematics

An International Journal of Mathematics Education.

The journal is published three times a year, in February, June and November. Internet: http://flm.math.ca/. (Address: FLM Publishing Association, c/o MSTE Group, Faculty of Education, A234 McArthur Hall, Queen's University, Kingston, Ontario, Canada K7L 3N6)

The journal aims to stimulate reflection on mathematics education at all levels, and promote study of its practices and its theories: to generate productive discussion; to encourage enquiry and research; to promote criticism and evaluation of ideas and procedures current in the field. It is intended for the mathematics educator who is aware that the learning and teaching of mathematics are complex enterprises about which much remains to be revealed and understood.

The National Council of Teachers of Mathematics

Web Address: http://www.nctm.org . (Address: 1906 Association Drive, Reston, VA 20191-1593, USA)

The National Council of Teachers of Mathematics is a public voice of mathematics education supporting teachers to ensure equitable mathematics learning of the highest quality for all students through vision, leadership, professional development and research in United States of America. It publishes different journals for members:

(a) Teaching Children Mathematics

Teaching Children Mathematics (TCM) is an official journal of the National Council of Teachers of Mathematics and is intended as a resource for elementary school students, teachers, and teacher educators. The focus of the journal is on intuitive, exploratory investigations that use informal reasoning to help students develop a strong conceptual basis that leads to greater mathematical abstraction. TCM is published nine times a year, monthly August through May, with a combined December/January issue.

(b) Mathematics Teaching in the Middle School

Mathematics Teaching in the Middle School (MTMS) is an official peer-reviewed journal of the National Council of Teachers of Mathematics and is intended as a resource for middle school students, teachers, and teacher educators. The focus of the journal is on intuitive, exploratory investigations that use informal reasoning to help students develop a strong conceptual basis that leads to greater mathematical abstraction. MTMS is published nine times a year, monthly August through May, with a combined December/January issue and a yearly focus issue in February.

(c) Mathematics Teacher

Mathematics Teacher solicits submissions from high school mathematics teachers, university mathematicians, and mathematics educators and strongly encourages manuscripts in which ideas relate to classroom practice. MT is published nine times a year, monthly August through May, with a combined December/January issue.

(d) Mathematics Teacher Educator

This is a new online journal which will be published from Summer 2012 onwards. The Mathematics Teacher Educator will contribute to building a professional knowledge base for mathematics teacher educators that stems from, develops, and strengthens practitioner knowledge. The journal will provide a means for practitioner knowledge related to the preparation and support of teachers of mathematics to be not only public, shared, and stored, but also verified and improved over time (Hiebert, Gallimore, and Stigler 2002). Mathematics Teacher Educator will be a scholarly, peer-reviewed journal for practitioners. Initially, two issues of the journal will be published each year.

(e) Journal for Research in Mathematics Education

The Journal for Research in Mathematics Education (JRME), an official journal of the National Council of Teachers of Mathematics, is devoted to the interests of teachers of mathematics and mathematics education at all levels-preschool through adult. JRME is a forum for disciplined inquiry into the teaching and learning of mathematics. The editors encourage the submission of a variety of manuscripts: reports of research, including experiments, case studies, surveys, philosophical studies, and historical studies; articles about research, including literature reviews and theoretical analyses; brief reports of research; critiques of articles and books; and brief commentaries on issues pertaining to research. The JRME is published five times a year, November, January, March, May, and July.

The Mathematical Association (MA), United Kingdom

Web address: http://www.m-a.org.uk/jsp/index.jsp (Address: The Mathematical Association, 259 London Road, Leicester LE2 3BE, UK)

history is located within a broad context of changes in the educational system, developments in

educational and mathematical thought, the growth of professionalism, and wider social, political and economic forces which influence the curriculum. MA reports and publications became standard references in the growing international interest in mathematics education throughout the 20th century.

MA publishes a number of journals:

(a) Mathematics in School

Mathematics in School is a lively and resource packed A4 journal aimed at teachers of primary and secondary pupils, students in training and all those with a professional interest in mathematics education. Contents include contributions from mathematics practitioners at all levels and its pages reflect the best of current thinking and practice by exploring further development and sharing practical experience. Readers will find helpful advice on general teaching methods and each issue guarantees numerous articles of relevance and a book/product reviews section. Importantly, the wealth of material used in every issue has photo copy rights thereby providing busy teachers with hands on classroom resources.

(b) The Mathematical Gazette

15-20 age range and expositions of attractive areas of mathematics. Regular sections include letters, extensive book reviews and a problem corner.

(c) Primary Maths

Primary Mathematics is issued three times a year. The content is often but not always themed and tries to blend ideas for classroom activities with articles about research, and some writing intended to provoke discussion, as well as reviews and up to date news. The editor is always delighted to receive copy, especially from classroom teachers, and is happy to give help and/or advice on the presentation and style of these.

(d) Equals

Equals Mathematics and Special Educational Needs is a resource for those working to ensure that all pupils will benefit from mathematics. Classroom teachers need the best support to develop good practice in line with current initiatives and it is the aim of Equals to provide this support in a number of practical ways. Age range: 3-18+ years.

Equals is produced by teachers and curriculum/SEN specialists dedicated to opening up mathematics to low attainers. In practical terms it provides support through the exchange of ideas to help teachers reveal the excitement and applicability of mathematics to those who have in the past found the subject inaccessible and/or irrelevant.

(e) Mathematical Pie

Mathematical Pie is an eight-page A5 magazine published three times a year. It is aimed at pupils from 10 to 14 years of age, but is read by all age groups. Each issue contains a variety of problems and challenges, stimulating mathematical activity. The questions vary in their difficulty so that there are suitable starting points for all ages of student. Mathematical Pie Notes are produced to enable the problems to be easily adapted for schools and to show possible extensions into further activity.

Mathematical Pie has shown itself to be an easy and enjoyable method of involving students in extra-curricular activity. For those who enjoy mathematics it is a must.

(f) Symmetry Plus

Symmetry Plus is a bright, colourful and lively magazine containing articles, puzzles, problems and competitions for all those who enjoy their mathematics. It is aimed at pupils and students of all ages, but especially those from 10 to 18 years. It has 16 colour pages in A4 format and is published three times a year (spring, summer and autumn).

Mathematical Association of America (MAA)

Web address: http://www.maa.org (Address: Mathematical Association of America, 1529 Eighteenth Street, N.W., Washington, D.C. 20036-1385, USA)

The MAA is a non-profit, independent, membership organization. It all began in 1894 with the American Mathematical Monthly - and ever since, the MAA has been providing mathematicians with the best expository articles, engaging problems, and articles devoted to teaching collegiate mathematics. In 1915, we became the MAA. It publishes the following journals:

(a) The American Mathematical Monthly

The American Mathematical Monthly publishes articles, notes, and other features about mathematics and the profession. Its readers span a broad spectrum of mathematical interests and abilities. Authors are invited to submit articles and notes that bring interesting mathematical ideas to a wide audience of Monthly readers.

(b) Mathematics Magazine

The Mathematics Magazine is published by the Mathematical Association of America bimonthly except July/August. Mathematics Magazine aims to provide lively and appealing mathematical expositions that are attractive and accessible to undergraduates or in stimulating student investigations.

(c) The College Mathematics Journal

The College Mathematics Journal is designed to enhance classroom learning and stimulate thinking regarding undergraduate mathematics. It publishes articles, short Classroom Capsules, problems,

solutions, media reviews and other pieces. All are aimed at the college mathematics curriculum with emphasis on topics taught in the first two years.

(d) MAA Focus

MAA FOCUS is the news magazine of the MAA. It contains information about MAA activities, news about mathematics and the mathematical community, and lively articles about interesting new (or sometimes not so new) ideas in mathematics, mathematics education, and related areas. It is published six times a year and is received by all members of the MAA.

Association of Teachers of Mathematics (ATM)

Web address: http://www.atm.org.uk . (Address: 7 Prime Industrial Park, Shaftesbury Street, Derby DE23 8YB, U.K. International Phone Number: +44 1332 346599 Email: admin@atm.org.uk)

The Association of Teachers of Mathematics (ATM) was established in 1950 to encourage the development of mathematics education such that it is more closely related to the needs of the learner. There are about 4 000 members - mainly teachers in primary and secondary schools. The ATM provides opportunities to bring together all concerned with mathematics education for all age ranges. It produces policy statements and publishes response to National and Government initiatives. ATM publishes the following journals:

(a) Mathematics Teaching

Mathematics Teaching is the journal of the Association of Teachers of Mathematics. It is a professional journal sent to all members of the Association. It is not a refereed journal.

(b) Micromath

Though it does not exist anymore, but articles from Micromath, those that we feel still have relevance or interest today, can still be found from the website.

School Science And Mathematics Association (SSMA)

Web Address: http://www.ssma.org/ (Address: School Science and Mathematics Association, Curriculum and Foundations, Bloomsburg University, 400 East Second Street, Bloomsburg, PA 17815-1301, USA)

The School Science and Mathematics Association is an inclusive professional community of researchers and teachers who promote research, scholarship, and practice that improves school science and mathematics and advances the integration of science and mathematics. SSMA focuses on

promoting research-based innovations related to K-16 teacher preparation and continued professional

enhancement in science and mathematics. Target audiences include higher education faculty members, K-16 school leaders and K-16 classroom teachers.

SSMA publishes an international journal, School Science and Mathematics; a newsletter, Mathematics-Science Connector; and two monograph series, Topics for Teachers and Classroom Activities.

(a) School Science and Mathematics

The SSMA Journal, School Science and Mathematics, is now published by Wiley Blackwell Publishers. It is published monthly from October through May.

(b) Published Monographs

The School Science and Mathematics Association publishes monographs in two series: Classroom Activities and Topics for Teachers. Classroom Activities provide science and mathematics activities for use in the classroom and are primarily intended for K-12 classroom teachers. Topics for Teachers present research-based emphasize leadership issues and/or targeted science and mathematics educators and school leaders.

The American Mathematical Society (AMS)

Web Address: http://www.ams.org (Address: 201 Charles Street, Providence, RI 02904-2294 USA)

The AMS, founded in 1888 to further the interests of mathematical research and scholarship, serves the national and international community through its publications, meetings, advocacy and other programs, which (i) promote mathematical research, its communication and uses, (ii) encourage and promote the transmission of mathematical understanding and skills, (iii) support mathematical education at all levels, (iv) advance the status of the profession of mathematics, encouraging and facilitating full participation of all individuals, and (v) foster an awareness and appreciation of mathematics and its connections to other disciplines and everyday life.

Journals Published by the AMS

The AMS has published peer-reviewed journals of the highest quality in mathematical research for over 100 years. Each journal is unique in its offering of articles, book reviews, and reports. And each is managed by editors who are prominent in their fields. In addition to publishing and distributing printed journals, the AMS offers searchable electronic versions. Articles are posted before they are included in an issue, so the electronic versions are available prior to the print versions.

(a) Print and Electronic Journals

to the print versions. Access to Abstract pages and article references that include links to MathSciNet® reviews is available free to anyone. Subscribers to electronic versions of AMS journals automatically receive free access to two electronic-only AMS journals, Conformal Geometry and Dynamics and Representation Theory.

(i) Bulletin of the American Mathematical Society

(ii) Journal of the American Mathematical Society

(iii) Mathematics of Computation

(iv) Memoirs of the American Mathematical Society

(v) Notices of the American Mathematical Society

(vi) Proceedings of the American Mathematical Society

(vii) Transactions of the American Mathematical Society

(b) Electronic-Only Journals

(i) Conformal Geometry and Dynamics

(ii) Electronic Research Announcements of the American Mathematical Society (1995-2007)

(iii) Representation Theory Translation Journals

(i) St. Petersburg Mathematical Journal

(ii) Sugaku Expositions

(iii) Theory of Probability and Mathematical Statistics

(iv) Transactions of the Moscow Mathematical Society

《小學數學教師》(XIAOXUE SHUXUE JIAOSHI)

由上海教育出版社編 SHANGHAI JIAOYU CHUBANSHE [雙月地址：上海永福路 123 號，上海教育出版社。郵編：200031)

《小學數學教師》是一份小學數學教育的專業性期。本雜誌是把握教改?絡，理論聯系實際，

文章短小精悍，富有新意，既注重提高教師的教育思想水平，又力求對教師的教學有直接的幫助。

《中小學數學 (初中版)》(ZHONG XIAO XUE SHUXUE)

由中國教育學會主辨 (ISSN 1006-3439) [月地址：北京西三環北路 105 號，首都師範大學數學樓 401 室。郵編：100037)

《中小學數學 (初中版)》是以指導中小學數學教學和學習的月刊。它具有嚴謹性、導向性、實用性和先備性的豐富文章。

《中學生數學》(ZHONGXUESHENG SHUXUE)

由中國數學會普委會主辦 [月刊] (地址：北京西三環北路 105 號，首都師範大學數學系。郵編： 100037)

《中學生數學》含有不同類型的文章。包括有學好基礎知識、思路與方法、數學史話、趣味數學、競賽之窗等豐富內容。

《統計教育》(Statistical Education)

由國家統計局統計教育中心、中國統計教育學會主辦 [雙月刊] (地址：北京市西城區月壇南街75 號，《統計教育》編輯部。郵編：100826)

《統計教育》包含有關統計教育、統計教育改革、統計工作、統計教材建設、信息窗等豐富文章。

《數學教學》(SHUXUE JIAOXUE)

由華東師範大學數學系主辦 [雙月刊] (地址：上海中山北路 3663 號，華東師範大學出版社。郵編：200062)

《數學教學》是刊登有關數學開放題研究，數學教學研究、數學應用研究、現代教學技術、考試之窗等豐富文章。

Stages of Algebra:

2020-11-23T12:56:00.005+05:45

Stages of Algebra:

Algebraic Expression: Rhetorical Algebra, Syncopated Algebra and Symbolic Algebra.

Conceptual Stages: Geometric Stages, Static equation solving stage, Dynamic functional stage, Abstract Stage.

Liberation of Algebra: Role of Hamiltonian Quaternion (1,i,j,k), Grassmann hypercomplex numbers x₁e₁+x₂e₂+…+x_ne_n,Caley Matrix algebra. (See History of mathematics for detail)

a. Structures of modern algebra and their teaching

Twentieth century mathematics is characterized by its emphasis on the systematic investigation of a number of abstract mathematic structures. Many such basic structures come under Abstract Algebra. The study of groups, rings, fields is not only the students first introduction to modern mathematical thinking but provides some of the essential crutches used by mathematicians morning and evening. What constitute abstract structures in mathematics? Crudely speaking, these may be viewed as decorations on a set eg. A topological space is a set with a prescribed collection of subsets to be called open sets satisfying some specific axioms. Axioms are considered as ‘self -evident truths’. Today many textbooks avoid the word ‘axiom’ with ‘properties’.

For example: In the defining the group you can write: A group (G,*) is a set G together with a binary operation * on G, such that the following properties (axioms) are satisfied:…..

The introduction of abstract mathematical structures in the curricula in Nepal was late by several decades when compared to many advanced countries. During the last generation specially at the advanced level were introduced to this effect in several stages.

Modern algebra can be classified into abstract and linear algebra.

Abstract Algebra:

What Is Abstract Algebra?

Abstract algebra consists of axiomatic theories that provide opportunities to consider many different mathematical systems as being special cases of the same abstract structure. The theories are called axiomatic because the structures are defined by axioms.

Group theory is “one of the oldest (and also one of the simplest) of axiomatic theories” (Bourbaki, 1950, p. 224).

Consider, for example, the following four mathematical systems:

1. The integers {… , -3, -2, -1, 0, 1, 2, 3, …} under the operation of addition. This

system is denoted Z.

2. The whole numbers less than a given whole number n, {0, 1, 2, … , n – 1}, under the operation of addition, where addition is given by the remainder after dividing the usual sum by n. This system is denoted Z_n.

3. The translations of the plane, where the operation is given by composition, that is, following one translation by another.

4. The set of 2 2 matrices of real numbers with determinant 1, under matrix

multiplication.

Each of these examples consists of a set of elements (numbers or translations) together with an operation that specifies how to combine two of the elements to get an element that is also in the set. Because the operation combines two elements, it is often called a binary operation. In order to talk about these examples simultaneously, the operation is denoted by *, where the interpretations are addition, addition “modulo n,” composition,

and matrix multiplication, respectively, in the four examples.

With some work, it is possible to see that each of these systems satisfies the following axioms:

1. Associativity. For any three elements, x, y, and z, in the set (not necessarily distinct),

(x*y)*z = x*(y*z).

2. Identity. There is an element, e, in the set, such that for any x in the set,

e*x = x =x*e. (For addition of integers, the identity is 0; for addition modulo n, the identity is 0; for translations of the plane, it is the “identity” translation that leaves every point fixed; for matrices under multiplication, it is the “identity” matrix with 1s on the diagonal and 0s elsewhere.)

3. Inverse. For each element x in the set, there is an element y in the set such that x*y = e = y*x.

A fourth (or zero) axiom, closure, is built into the requirements of a binary operation: that the combination of two elements gives an element that still lies in the set. It should be pointed out that commutativity is not one of the axioms, and it is not hard to see that matrix multiplication is not commutative.

Any set and operation that together satisfy these axioms is said to be a group. When the operation is also commutative, the group is said to be Abelian. The advantage of the axiomatic approach is that any result (i.e., theorem) that can be proved on the basis of the axioms alone necessarily applies to all four examples and also to any other mathematical system that satisfies the axioms.

The important results in group theory depend upon a collection of related concepts. A subgroup, for example, is a subset of a group, which is itself a group under the group’s operation. The role of structure again returns to the fore with the concept of isomorphism. On a high level, the group axioms define an algebraic structure that applies to a broad collection of mathematical systems. The axioms create the rudimentary structure to which all groups must conform. At a lower level, every specific group is a mathematical system with its own internal structure. An important abstraction can occur when two groups appear in different settings and yet are “essentially the same.” The intuitive idea is that two groups are structurally the same, or isomorphic, if they differ only in the names of their elements and operation. Demonstrating that two groups are isomorphic requires finding a renaming that preserves the group operation. Such a renaming, which is essentially a function that takes elements from one group to the other, is called an isomorphism.

It should be pointed out that the above mathematical systems and other standard examples may not be familiar to undergraduates in a first course in abstract algebra. Thus, some of the student’s energy must be spent trying to build some familiarity with the examples.

Taken together, these examples and the concepts of group, subgroup, and isomorphism constitute the fundamental concepts of group theory for the purpose of this study.

I distinguish as “advanced concepts of group theory” those concepts that require the construction of new objects. Given a subgroup H, one can create a left coset of the subgroup by multiplying an element a of the group on the left by each of the elements in the subgroup. The coset is denoted aH. When the set of left cosets forms a group by extending the group operation to the cosets, the resulting group is called a quotient group, and the subgroup that gave rise to the cosets is said to be normal.

Other important mathematical structures are rings and fields. In ring theory, there are two operations, typically called multiplication and addition. Examples are the arithmetic of integers, of matrices, and of polynomials in one variable with integer coefficients. A field is essentially a ring in which multiplication is commutative and division is also possible, except, of course, division by zero. Examples are the rational numbers, the

complex numbers, and the integers modulo p, where p is prime.

The Big Ideas of Abstract Algebra

A course in abstract algebra is the place where students might extract common features from the many mathematical systems that they have used in previous mathematics courses, such as calculus, linear algebra, and school algebra. Students have opportunities to develop deeper understandings of concepts such as identity, inverse, equivalence, and function. What is shared, for example, by the identity for multiplication of real numbers, the identity matrix, and the identity function? What is the common idea behind the

inverse of a function, the inverse of a matrix, and the multiplicative inverse of a number?

In abstract algebra, students can also learn about the importance of precise language in mathematics and about the role of definitions in supporting such precision. Mathematics is also about noticing when things are the same and being able to describe how they are different. In abstract algebra, this naïve notion of “sameness” becomes formalized in the concept of isomorphism.

Thus, it is clear that the concepts in abstract algebra provide guiding themes, principles, and sensibilities that pervade mathematics. It is not so clear, however, what sequence of topics from abstract algebra can be constructed to help students recognize and appreciate such themes. And, in particular, it is not clear whether an abstract algebra course intended for mathematics majors, as it is typically taught, can serve such a role.

When the population of students in an abstract algebra course includes future teachers (which may be almost always), these big ideas, such as inverse and identity, are particularly important because they can help teachers connect advanced mathematics with high school mathematics in ways that can strengthen and deepen their understandings of the mathematics they will teach. Of course, it is also crucial that future teachers are able to employ those new understandings in their teaching, but that concern takes us beyond the scope of this study.

Sfard (1995) gives a detailed a description of the historical development of algebra with strong connections to the teaching and learning of both school and abstract algebra, providing compelling support for the claim that historical-critical and psychogenetic studies should converge (Piaget & Garcia, 1989, p. 108). According to Sfard, group theory arose out of the work of Lagrange and Ruffini, who noticed that methods of solving polynomial equations depended on permutations of the roots. Soon permutations and then, with Cauchy, operations on those permutations became objects of attention.

Galois defined the notion of a group by declaring interest in the structure imposed on the permutations by the so-called substitutions. Cayley freed the concept from any commitment as to the nature of the elements, focusing instead on the manipulations.

With the invention of the concept of group, the seeds had been planted for algebra to become a science of abstract structures.

Kleiner (1986) describes four lines of inquiry that coalesced toward the end of the nineteenth century to form the area we now call abstract algebra. First, the techniques from classical algebra for solving polynomial equations led to the permutation groups.

Second, questions in number theory led to the finite Abelian groups. Third, attempts to unify and organize geometry led to transformation groups. Finally, roots in analysis led to investigation of continuous transformation groups. One response to this account is to use historically important problems to provide pedagogical and intellectual motivation in the teaching of abstract algebra (see Kleiner, 1995).

Nicholson’s (1993) account of the slow historical development of the concept of quotient group can provide additional sources for cognitive roots to be exploited. She suggests several obstacles that were overcome by the mathematics community during the development of this concept. First, the community needed an abstract concept of group that was not dependent on any particular representation. Second, the community needed the concept of equivalence (modulo a subgroup). Finally (and most importantly), the community needed to realize that the elements of the quotient group are not like the elements of original group, but are equivalence classes—sets. All of these historical developments provide clues about what might be the issues for students learning the subject

Group Theory: The notion of group did not simply spring into existence, however, but is rather the culmination of a long period of mathematical investigation. The first formal definition of an abstract group in the form in which we use it appearing in 1882. The definition of an abstract group has its origins in extremely old problems in algebraic equations, number theory and arose because very similar techniques were found to be applicable in a variety of situations.

We illustrate with a few of the disparate situations in which the ideas later formalized into the notion of an abstract group were used:

1. In number theory the very object of study, the set of integers, is an example of a group. Consider for example what we refer to as “Euler’s Theorem” : for every integer ‘a’ relatively prime to ‘n’.

This was proved in 1761 by Euler using “group theoretic” ideas of Lagrange, long before the first formal definition of a group.

2. Investigations into the question of rational solutions to algebraic equations of the form y²=x³-2x there are infinitely many points such as (0,0), (-1,1), (2,2), (9/4,-21/8)… . today the curve above is referred to as an “elliptic curve” and these questions are viewed as two different aspects of the same thing- the fact that this geometric operation on points can be used to give the set of points on an elliptic curve the structure of a group.

3. By 1824 it was known that there are formulas giving the roots of quadratic, cubic and quartic equations. In 1824 Abel prove that such a formula for the roots of a quintic is impossible [the general equation of degree n cannot be solved by radicals for n>4]. The proof of this theorem is based on the idea of examining what happens when the roots are permuted amongst themselves. The collection of such permutations has the structure of a group ‘permutation group’. This idea culminated in the beautiful work of Evarste Galois in 1830-32 working with explicit group of substitutions. He was the first person who used the word “group”. Today this work is referred to as Galois Theory. Similar explicit groups were being used in geometry as transformation group by Cayley around 1850, Jordan by 1867, Klein by 1870.

Concepts contained in group theory

Binary Operation:

Modular Algebra:

- Concept of equivalence relation: The relation a b(mod n) is the equivalence relation. How?

Different examples of group: dihedral group, symmetric group, matrix group, quaternion group etc.

Subgroups:

Definition and examples. eg: Intersection of two subgroup of any group is subgroup but union may not be. For eg: ({0,6},+₁₂) and ({0,4,8},+₁₂) are two subgroup of group (z,+₁₂) of integer modulo 12 but what about the union.

Centre, Centerlizer and Normalizer: C_G(H)<N_G(H)<G

Cyclic Groups and Cyclic subgroups, normal subgroups etc.

Quotient Groups and Homomorphism

Definition and examples

Cosets and Lagrange’s Theorem

Isomorphism theorems

Composition Series and the Holder program

Transposition and the alternating group

Group Actions

Direct product and Abelian group

Nilpotent and solvable group.

Ring Theory:

The theory of groups is concerned with general properties of certain objects having an algebraic structure defined by a single binary operation. The study of rings is concerned with objects possessing two binary operations (addition and multiplication) related by the distributive laws. Some concepts of ring theory are analogues for the basic points of development in the structure theory of groups. In particular, subrings, quotient rings , ideals (analogues with normal subgroup) and ring homomorphism. The general theory of ring is arise naturally from the presence of two binary operations. Questions concerning multiplicative inverse leads to the notion of fields and eventually to the construction of some specific fields such as finite fields. The study of the arithmetic (divisibility, GCD etc) of rings leads to the notion of primes and unique factorizations and are then applied to rings of polynomials.

Structure of content:

1. Basic definition and examples:

2. Polynomial rings, matrix rings, and group rings

3. Ring homomorphisms and quotient rings

4. Ideals and properties

5. Euclidean domain, PID and UFD

6. Polynomial ring (simple concepts)

Module Theory:

The use of modules was pioneered by one of the most prominent mathematicians Emmy Nother, who led the way in demonstrating the power and elegance of this structure. The vector spaces are just special types of modules which arise when the underlying ring is a field. If R is a ring the definition of an R-module M is closely analogous to the definition of a group action where R plays the role of the group and M the role of the set.

1. Basic definitions and Examples

2. Quotient Modules and module homomorphism

3. Generation of modules, Direct Sums, and free Modules

4. Tensor Product of Modules

5. Exact Sequences-Projective, injective and flat module.

Vector Spaces

1. Definition and Basic Theory

2. The matrix of a linear transformation

3. Dual vector spaces

Field Theory:

1. Basic theory of field etensions

2. Algebraic extensions

3. Spliting fields

Definitions:

Groupoid, Semigroups, Monoids, Groups and Abelian Groups:

1. A nonempty set G together with binary operation * is said to be a group (G, *) if the following postulates (axioms/properties) holds under the binary operation * in G.

i. G is closed under *, ie. (Closure axiom)Obvious on binary operation.

ii. G is associative under *, i.e (Associative)

iii. There exists an element e in G, called an identity of G such that for all a we have a*e=e*a=a.

iv. For each a there is an element , called an inverse of a, such that a*

2. The group (G,*) is called abelian (or commutative) if a*b=b*a for all a,b

i	i,ii	i,ii,iii	i-iv	1,2
Groupoid (Quasi group)	Semigroup	Monoid	Group	Abelian Group

Rings:

Definition

1) A ring R is a set together with two binary operations + and x (called addition

and multiplication) satisfying the following axioms:

(i) (R. +) is an abelian group,

(ii) x is associative: (a x b) x c = a x (b x c) for all a, b, c R,

(iii) the distributive laws hold in R : for all a, b, c R

(a+b)xc=(axc)+(bxc) and ax(b+c)=(axb)+(axc).

(2) The ring R is commutative if multiplication is commutative.

(3) The ring R is said to have an identity (or contain a I) if there is an element I R with lxa=axl=a for all a R.

Definition. A ring R with identity 1, where 1 0 is called a division ring (or skew

field) if every nonzero element a R has a multiplicative inverse, i.e., there exists

b R such that ab = ba = I. A commutative division ring is called a field.

Module Theory:

Definition: Let R be a ring (not necessarily commutative nor with I). A left R -module

or a left module over R is a set M together with

1. a binary operation + on M under which M is an abelian group, and

2. an action of R on M (that is, a map R x M M) denoted by rm, for all r R

and for all m M which satisfies

i. (r + s)m = rm + sm, for all r, s R, m M,

ii. (rs)m = r(sm), for all r, s R, m M, and

iii. r(m + n) = rm + rn, for all r R, m, n M.

If the ring R has a 1 we impose the additional axiom:

iv. 1m = m, for all m M.

Vector Space

Let F be a field. A vector space over F consists of an abelian group V under addition together with an operation of scalar multiplication of each element of V by each element of F on the left s.t

i. av

ii. a(bv)=(ab)v

iii. (a+b)v=(av)+(bv)

iv. a(u+v)=au+av

v. 1v=v.

Ring	Field	Module	Vector Space
· Two binary operations + and	Two binary operations + and	Two binary operations + and	Two binary operations + and
· (R,+) is abelian group, (R, is a semigroup with distributive property.	(F,+) is an abelian group and ( ) is abelian group.	(M,+) is an abelian group and scalar multiplication (rm is closed and distributive over scalar.	(V,+) is an abelian group, v and scalar multiplication is closed and distributive, 1v=v.
· Every ring is an R-module	F is a F-module, F is vector space over F.	If R is a division Ring then unitary R-module is called vector space.	V is an F module.
·		Module is a generalization of vector space.
·
·
·

Subgourp:

A non-empty subset H of G is said to be subgroup of G if H itself form a group under same binary operation as in G.

For example:

1. Set of integer is the subgroup of the set of Real number under addition binary operation.

2. The set A={(1), (123),(132)} is subgroup of S₃ under permutation multiplication.

Some important results in subgroup:

1. A nonempty subset H of group (G,*)is a subgroup iff ab^-1

2. A non empty finite subset H of group G is a subgroup of G iff ab , a,b

3. The intersection of two subgroup of a group is also a subgroup. But Union may not be subgroup.

Sub-Rings:

A nonempty subset S of a ring R is said to be a sub ring of R if S itself forms a ring under the same binary operations of R.

For example:

1. The ring (Z,+,*) is a subring of (Q,+,*)

2. The set 2Z={2n:n is a sub ring of (Z,+,*).

Note:

1. A nonempty subset S of a ring R is a sub ring of R if for each a,b i) a-b ii) a*b

2. The intersection of two subrings of a ring is also a subring.

Normal Subgroup:

A subgroup H of a group G is a normal (invariant) subgroup of G if g^-1Hg=H for all g .

Thus normal subgroups are precisely those important subgroups of a group having the property that for the cosets(left and right are the same), the induced operation is well defined and the cosets form a group.

Ideal: (Analogue of the definition of a normal subgroup)

An additive subgroup (N,+) of a ring R satisfying rN and Nr for all r is an ideal (or two sided ideal) of R.

Every ideal I is the subring of R but every subring may not be ideal of R

For example: Let Z be the set of integers and I=2Z is the set of even integer which is an ideal of R.

But Z is the subring of Q. But Z is not ideal of Q. For let, 3/5 , 2 but 3/5.2 . So Z is not ideal of Q.

Factor/Quotient Group:

Quotient Ring: (Analogue of the definition of the factor group): If N is an ideal in a ring R, then the ring of cosets r+N under the induced operations is the quotient ring, or factor ring or residue class ring of R modulo N and is denoted by R/N.

Group Homomorphism:

Let (G,*) and (G’,*) be two group. The mapping is said to be group homo if

For Example: The mapping Is the group homo but the mapping is not the group homo.

Ring Homomorphism:

Let (R,+,*) and (R’,+,*) be two rings, a mapping is said to be ring homo if a) f(a+b)=f(a)+f(b) and f(a*b)=f(a)*f(b)

Module Homomorphism:

Let M and N are any two R-module. The function is said to be R-module homomorphism if f(a+b)=f(a)+f(b), f(ra)=rf(a) a,b

Show by example every group homo is module homo.

Also module homo may not be ring homo and vice versa.

Let M and N be two arbitrary abelian groups and Z be the Z module.

Let be group homomorphism. Let a,b . We have f(a+b)=f(a)+f(b)

Let then

f(na)=f(a+a+… to n times)

= f(a)+f(a)+… to n times

=n f(a). f(na)=nf(a).

Hence, each group homo is an Z-module Homo.

In the ring of integer Z, the function defined as by f(z)=2z, z

f is module homo:

Since f(m+n)=f(m)+f(n)

And f(rm)=f(m+m+…+r times)

= f(m)+f(m)+…+f(m) r times= rf(m).

Hence f is module homo.

Bur for ring homo: Let f is module homo then f(m+n)=f(m)+f(n) and

f(rm)=2rm=r.2m f(r).f(m). So f is not ring homo.

Let us consider the ring of complex number C. Defined by f(x)=

F is ring homo:

1. f(x+y)= = =f(x)+f(y).

2. f(xy)= =f(x).f(y). So f is ring homo.

But for module homo:

1. f(x+y)= = =f(x)+f(y).

2. f(i.i) . f(i.i)=f(-1)=-1 and if(i)=1.

Hence f is not module homo.

Fundamental theorem of group homo, ring homo and module homo.

- Let be onto group homo. Then G/ker

- Let be ring homo with R onto R’ with kernel N then R/N

- Let is an onto module homo with kernel K then M/K

Compare and contrast these theorems.

Difficulties in learning Algebra:

In response to the difficulties students usually have with Lagrange’s theorem, Johnson

(1983) notes that the traditional proof involves cosets and equivalence relations, both of which are new concepts to most students. As Lagrange’s theorem is usually used to prove the more intuitive theorem that the order of an element divides the order of the group, Johnson suggests proving the latter result first, for it follows quite naturally from the decomposition of a permutation into disjoint cycles. Of course, this approach assumes the students are familiar with permutation groups, and such an assumption might be unwarranted. Holton and Wenzel (1993) describe an abstract algebra course in which Lagrange’s theorem is preceded by cooperative learning via examples. Rejecting the traditional approach of “exposition, exhortation and regurgitation” (p. 883), they found that students were able to conjecture the theorem and many of the necessary lemmas. Although it was not a formal research study, the description of the classroom environment was compelling.

Groups and Binary Operations

“Is Z₃ a subgroup of Z₆?” The short answer to this question is no because the operations in the two groups are different. More specifically, because Z₃ is the set {0, 1, 2} under addition modulo 3, and Z₆ is the set {0, 1, 2, 3, 4, 5} under addition modulo 6, the operations are not the same. For example, 2 + 2 is 4 in Z₆ But 1 in Z_3.Nonetheless, the subset{0,2,4} of Z₆ is simultaneously a subgroup of Z₆ and isomorphic to Z₃. From this sense Z₃ is subgroup of Z₆.Two reasons for students’ difficulties with this question. First, although students think of a group as a set, they are not always sufficiently aware of the operation (Dubinsky et al., 1994). Some students use a powerful result inappropriately, saying that Z₃ is a subgroup of Z₆ by Lagrange’s theorem because 3 divides 6 (Hazzan & Leron, 1996).

Just as a group is a set with structure provided by an operation, a subgroup is not merely a subset of a group but rather a substructure, and the structure is provided by the operation of the group. General insight into the structure can be provided by Lagrange’s theorem, which says that in a finite group the order of a subgroup (the number of elements in the subgroup) must be a factor of the order of the group. The converse of the theorem is false in general.

Linear Algebra (Student Learning Opportunities)

i. Linear Maps and Matrices

ii. Bilinear Forms and Standard Operators

iii. Algebraic Properties of Linear Transformation

iv. Spectral Theorem and Primary decomposition theorem

b. Prepare any three lessons for teaching from algebra of bachelor level using different strategies at least one of them must be in PBL model.

List of Mathematics and Mathematics Education Journals

2020-11-18T07:22:00.000+05:45

List of Mathematics and Mathematics Education Journals

1. For the Learning of Mathematics

An International Journal of Mathematics Education.

2. The National Council of Teachers of Mathematics

Web Address: http://www.nctm.org . (Address: 1906 Association Drive, Reston, VA 20191-1593, USA)

(a) Teaching Children Mathematics

(b) Mathematics Teaching in the Middle School

Mathematics Teaching in the Middle School (MTMS) is an official peer-reviewed journal of the National Council of Teachers of Mathematics and is intended as a resource for middle school students, teachers, and teacher educators. The focus of the journal is on intuitive, exploratory investigations that use informal reasoning to help students develop a strong conceptual basis that leads to greater mathematical abstraction. MTMS is published nine times a year, monthly August through May, with acombined December/January issue and a yearly focus issue in February.

The Mathematics Teacher, an official journal of the National Council of Teachers of Mathematics, is devoted to improving mathematics instruction from grade 8-14 and supporting teacher education programs. It provides a forum for sharing activities and pedagogical strategies, deepening understanding of mathematical ideas, and linking mathematics education research to practice. Mathematics Teacher solicits submissions from high school mathematics teachers, university mathematicians, and mathematics educators and strongly encourages manuscripts in which ideas relate to classroom practice. MT is published nine times a year, monthly August through May, with a combined December/January issue.

(d) Mathematics Teacher Educator

(e) Journal for Research in Mathematics Education

3. The Mathematical Association (MA), United Kingdom

Web address: http://www.m-a.org.uk/jsp/index.jsp (Address: The Mathematical Association, 259 London Road, Leicester LE2 3BE, UK)

The MA was the first teachers’ subject association to be formed in England, in 1871, as the Association for the Improvement of Geometrical Teaching, the original catalyst being the need to develop and to lobby for alternatives to the then standard treatment of geometry. The Association’s history is located within a broad context of changes in the educational system, developments in educational and mathematical thought, the growth of professionalism, and wider social, political and economic forces which influence the curriculum. MA reports and publications became standard references in the growing international interest in mathematics education throughout the 20th century.

#MA publishes a number of journals:

(a) Mathematics in School

(b) The Mathematical Gazette

The Mathematical Gazette readership is a mixture of school teachers, college and university lecturers, educationalists and others with an interest in mathematics. This is one of the World's leading journals in its field, publishing articles about the teaching and learning of mathematics with a focus on the 15-20 age range and expositions of attractive areas of mathematics. Regular sections include letters, extensive book reviews and a problem corner.

(d) Equals

(e) Mathematical Pie

(f) Symmetry Plus

4. Mathematical Association of America (MAA)

Web address: http://www.maa.org (Address: Mathematical Association of America, 1529 Eighteenth Street, N.W., Washington, D.C. 20036-1385, USA)

(a) The American Mathematical Monthly

(b) Mathematics Magazine

The College Mathematics Journal is designed to enhance classroom learning and stimulate thinking regarding undergraduate mathematics. It publishes articles, short Classroom Capsules, problems,

solutions, media reviews and other pieces. All are aimed at the college mathematics curriculum with emphasis on topics taught in the first two years.

(d) MAA Focus

5. Association of Teachers of Mathematics (ATM)

Web address: http://www.atm.org.uk . (Address: 7 Prime Industrial Park, Shaftesbury Street, Derby DE23 8YB, U.K. International Phone Number: +44 1332 346599 Email: admin@atm.org.uk)

(a) Mathematics Teaching

Mathematics Teaching is the journal of the Association of Teachers of Mathematics. It is a professional journal sent to all members of the Association. It is not a refereed journal.

(b) Micromath

Though it does not exist anymore, but articles from Micromath, those that we feel still have relevance or interest today, can still be found from the website.

6. School Science And Mathematics Association (SSMA)

Web Address: http://www.ssma.org/ (Address: School Science and Mathematics Association, Curriculum and Foundations, Bloomsburg University, 400 East Second Street, Bloomsburg, PA 17815-1301, USA)

enhancement in science and mathematics. Target audiences include higher education faculty members, K-16 school leaders and K-16 classroom teachers.

SSMA publishes an international journal, School Science and Mathematics; a newsletter, Mathematics-Science Connector; and two monograph series, Topics for Teachers and Classroom Activities.

(a) School Science and Mathematics

The SSMA Journal, School Science and Mathematics, is now published by Wiley Blackwell Publishers. It is published monthly from October through May.

(b) Published Monographs

7. The American Mathematical Society (AMS)

Web Address: http://www.ams.org (Address: 201 Charles Street, Providence, RI 02904-2294 USA)

Journals Published by the AMS

(a) Print and Electronic Journals

The electronic versions of most AMS and AMS-distributed journals are free to print subscribers. Articles are posted before they are included in an issue, so the electronic versions are available prior to the print versions. Access to Abstract pages and article references that include links to MathSciNet® reviews is available free to anyone. Subscribers to electronic versions of AMS journals automatically receive free access to two electronic-only AMS journals, Conformal Geometry and Dynamics and

Representation Theory.

(i) Bulletin of the American Mathematical Society

(ii) Journal of the American Mathematical Society

(iii) Mathematics of Computation

(iv) Memoirs of the American Mathematical Society

(v) Notices of the American Mathematical Society

(vi) Proceedings of the American Mathematical Society

(vii) Transactions of the American Mathematical Society

(b) Electronic-Only Journals

(i) Conformal Geometry and Dynamics

(ii) Electronic Research Announcements of the American Mathematical Society (1995-2007)

(iii) Representation Theory

#Translation Journals

(i) St. Petersburg Mathematical Journal

(ii) Sugaku Expositions

(iii) Theory of Probability and Mathematical Statistics

(iv) Transactions of the Moscow Mathematical Society

8. 《小學數學教師》(XIAOXUE SHUXUE JIAOSHI)

由上海教育出版社編 SHANGHAI JIAOYU CHUBANSHE [雙月地址：上海永福路123號，上海教育出版社。郵編：200031)

《小學數學教師》是一份小學數學教育的專業性期。本雜誌是把握教改?絡，理論聯系實際，文章短小精悍，富有新意，既注重提高教師的教育思想水平，又力求對教師的教學有直接的幫助。

9. 《中小學數學 (初中版)》(ZHONG XIAO XUE SHUXUE)

由中國教育學會主辨 (ISSN 1006-3439) [月地址：北京西三環北路105號，首都師範大學數學樓401室。郵編：100037)

《中小學數學 (初中版)》是以指導中小學數學教學和學習的月刊。它具有嚴謹性、導向性、實用性和先備性的豐富文章。

10. 《中學生數學》(ZHONGXUESHENG SHUXUE)

由中國數學會普委會主辦 [月刊] (地址：北京西三環北路105號，首都師範大學數學系。郵編：100037)

《中學生數學》含有不同類型的文章。包括有學好基礎知識、思路與方法、數學史話、趣味數學、競賽之窗等豐富內容。

11. 《統計教育》(Statistical Education)

由國家統計局統計教育中心、中國統計教育學會主辦 [雙月刊] (地址：北京市西城區月壇南街75號，《統計教育》編輯部。郵編：100826)

《統計教育》包含有關統計教育、統計教育改革、統計工作、統計教材建設、信息窗等豐富文章。

12. 《數學教學》(SHUXUE JIAOXUE)

由華東師範大學數學系主辦 [雙月刊] (地址：上海中山北路3663號，華東師範大學出版社。郵編：200062)

《數學教學》是刊登有關數學開放題研究，數學教學研究、數學應用研究、現代教學技術、考試之窗等豐富文章。

The Infinity Mathematics

A list of Regular and Irregular Verbs-[English Verbs]

USE OF ICT IN CLASSROOM: TEACHERS AND STUDENTS PERCEPTION ON ICT TOOLS (SEMINAR PAPER)

History of Mathematics Timeline in Nepal-Infinity Maths

TIMELINE OF DEVELOPMENT OF MATHEMATICS IN NEPAL

Love Formula (GeoGebra)-The Infinity Mathematics

Websites for Learning Mathematics with Links-The Infinity Mathematics

Websites for learning Mathematics with Links

1. E-path (OLE NEPAL)

2. A plus math

3. Math TV

4. PhEt

5. Math is fun.com

6. Mathad.com

7. Mathleague.org

8. Universal math solver

Open Access Websites

9. Google Scholar

10. Books Google

11. RefSeek - Academic Search Engine

12. Microsoft Academic

13. ERIC - Education Resources Information Center

14. Open Thesis and Dissertations

15. Dissertation Academic Book Publisher

16. ETHOS E-These Online Service

17. Find Open Access Dissertations and Theses

18. UIS Statistics - UNESCO

For open-access journal

19. DOJA

20. Nepal Journals Online

FOR FREE BOOK

21. Z-library

Programmed Statistics (Question-Answers) - B.L. Agarwal : The Infinity Mathematics

5 Reasons to Teach Mathematical Modeling

Calendar - Aptitude Questions and Answers : The Infinity Mathematics

Algebra Formulas-The Infinity Mathematics

1. Set identities

Definitions:

Union of sets

Intersection of sets

Set identities involving union, intersection and complement

De Morgan’s laws

Complement

Difference of sets

Set identities involving difference

Cartesian product

Set identities involving union

Set identities involving intersection

Set identities involving union and intersection

2. Sets of Numbers

Definitions:

Natural numbers (counting numbers )

Whole numbers ( counting numbers + zero )

Integers

Z - = {..., - 3, - 2, -1}

Real numbers:

Complex numbers:

3. Complex numbers

Definitions:

Equality of complex numbers

Addition of complex numbers

Subtraction of complex numbers

Multiplication of complex numbers

Division of complex numbers

De Moivre’s theorem

5. Factoring and product

Factoring Formulas

Product Formulas

A Geometric Model of (a+b)2-The Infinity Mathematics

Density of Love Inside Mathematica Construction-theinfinitymathematics

Mathematica and GeoGebra Plot Videos-The Infinity Mathematics

Introduction to Cryptography with Coding Theory-Maths

INTRODUCTION TO CRYPTOGRAPHY

proof of 1+1=2 with justification-thetnfinitymathematics

PROOF OF 1+1=2 WITH JUSTIFICATION

The five Peano axioms are:

Research Activities in Semester &Thesis Writing

Outline

What is a thesis?

What a thesis isn’t?

Z ^- = {..., - 3, - 2, -1}