An American Anti-theist

Happy Independence Day!

2010-07-04T10:44:00.000-07:00

On this 4th of July, as we observe the continuing collapse of our economic system and the incipient socialist takeover of the United States, let us try to remind ourselves of the meaning of Independence, its principles and necessity.

"Independence is the recognition of the fact that yours is the responsibility of judgement and nothing can help you escape it -- that no substitute can do your thinking, as no pinch-hitter can live your life." -- Ayn Rand

"There's no way to rule innocent men. The only power any government has is the power to crack down on criminals. Well, when there aren't enough criminals, one makes them. One declares so many things to be a crime that it becomes impossible for men to live without breaking laws. Who wants a nation of law-abiding citizens? What's there in that for anyone? But just pass the kind of laws that can neither be observed nor enforced nor objectively interpreted and you create a nation of law-breakers." -- Ayn Rand

"Whoever claims the right to redistribute the wealth produced by others is claiming the right to treat human beings as chattel." -- Ayn Rand

"It is error alone which needs the support of government. Truth can stand by itself." -- Thomas Jefferson

"He who permits himself to tell a lie once, finds it much easier to do it a second and third time, till at length it becomes habitual; he tells lies without attending to it, and truths without the world's believing him. This falsehood of the tongue leads to that of the heart, and in time depraves all its good dispositions." -- Thomas Jefferson

"A man's moral sense must be unusually strong if slavery does not make him a thief." -- Thomas Jefferson

"I never submitted the whole system of my opinions to the creed of any party of men whatever, in religion, in philosophy, in politics, or in anything else, where I was capable of thinking for myself. Such an addiction is the last degradation of a free and moral agent. If I could not go to heaven but with a party, I would not go there at all." -- Thomas Jefferson

"A slender acquaintance with the world must convince every man, that actions, not words, are the true criterion of the attachment of his friends, and that the most liberal professions of good will are very far from being the surest marks of it." -- George Washington

"Arbitrary power is most easily established on the ruins of liberty abused to licentiousness." -- George Washington

"Government is not reason, it is not eloquence — it is force! Like fire, it is a dangerous servant and a fearful master. Never for a moment should it be left to irresponsible action." -- George Washington

"Power always sincerely, conscientiously, de très bon foi, believes itself right. Power always thinks it has a great soul and vast views, beyond the comprehension of the weak." -- John Adams

"We ought to consider what is the end of government, before we determine which is the best form." -- John Adams

http://www.youtube.com/watch?v=mWv5VZWlwRQ

The Declaration of Independence

IN CONGRESS, JULY 4, 1776
The unanimous Declaration of the thirteen united States of America

When in the Course of human events it becomes necessary for one people to dissolve the political bands which have connected them with another and to assume among the powers of the earth, the separate and equal station to which the Laws of Nature and of Nature's God entitle them, a decent respect to the opinions of mankind requires that they should declare the causes which impel them to the separation.

We hold these truths to be self-evident, that all men are created equal, that they are endowed by their Creator with certain unalienable Rights, that among these are Life, Liberty and the pursuit of Happiness. — That to secure these rights, Governments are instituted among Men, deriving their just powers from the consent of the governed, — That whenever any Form of Government becomes destructive of these ends, it is the Right of the People to alter or to abolish it, and to institute new Government, laying its foundation on such principles and organizing its powers in such form, as to them shall seem most likely to effect their Safety and Happiness. Prudence, indeed, will dictate that Governments long established should not be changed for light and transient causes; and accordingly all experience hath shewn that mankind are more disposed to suffer, while evils are sufferable than to right themselves by abolishing the forms to which they are accustomed. But when a long train of abuses and usurpations, pursuing invariably the same Object evinces a design to reduce them under absolute Despotism, it is their right, it is their duty, to throw off such Government, and to provide new Guards for their future security. — Such has been the patient sufferance of these Colonies; and such is now the necessity which constrains them to alter their former Systems of Government. The history of the present King of Great Britain is a history of repeated injuries and usurpations, all having in direct object the establishment of an absolute Tyranny over these States. To prove this, let Facts be submitted to a candid world.

He has refused his Assent to Laws, the most wholesome and necessary for the public good.

He has forbidden his Governors to pass Laws of immediate and pressing importance, unless suspended in their operation till his Assent should be obtained; and when so suspended, he has utterly neglected to attend to them.

He has refused to pass other Laws for the accommodation of large districts of people, unless those people would relinquish the right of Representation in the Legislature, a right inestimable to them and formidable to tyrants only.

He has called together legislative bodies at places unusual, uncomfortable, and distant from the depository of their Public Records, for the sole purpose of fatiguing them into compliance with his measures.

He has dissolved Representative Houses repeatedly, for opposing with manly firmness his invasions on the rights of the people.

He has refused for a long time, after such dissolutions, to cause others to be elected, whereby the Legislative Powers, incapable of Annihilation, have returned to the People at large for their exercise; the State remaining in the mean time exposed to all the dangers of invasion from without, and convulsions within.

He has endeavoured to prevent the population of these States; for that purpose obstructing the Laws for Naturalization of Foreigners; refusing to pass others to encourage their migrations hither, and raising the conditions of new Appropriations of Lands.

He has obstructed the Administration of Justice by refusing his Assent to Laws for establishing Judiciary Powers.

He has made Judges dependent on his Will alone for the tenure of their offices, and the amount and payment of their salaries.

He has erected a multitude of New Offices, and sent hither swarms of Officers to harass our people and eat out their substance.

He has kept among us, in times of peace, Standing Armies without the Consent of our legislatures.

He has affected to render the Military independent of and superior to the Civil Power.

He has combined with others to subject us to a jurisdiction foreign to our constitution, and unacknowledged by our laws; giving his Assent to their Acts of pretended Legislation:

For quartering large bodies of armed troops among us:

For protecting them, by a mock Trial from punishment for any Murders which they should commit on the Inhabitants of these States:

For cutting off our Trade with all parts of the world:

For imposing Taxes on us without our Consent:

For depriving us in many cases, of the benefit of Trial by Jury:

For transporting us beyond Seas to be tried for pretended offences:

For abolishing the free System of English Laws in a neighbouring Province, establishing therein an Arbitrary government, and enlarging its Boundaries so as to render it at once an example and fit instrument for introducing the same absolute rule into these Colonies

For taking away our Charters, abolishing our most valuable Laws and altering fundamentally the Forms of our Governments:

For suspending our own Legislatures, and declaring themselves invested with power to legislate for us in all cases whatsoever.

He has abdicated Government here, by declaring us out of his Protection and waging War against us.

He has plundered our seas, ravaged our coasts, burnt our towns, and destroyed the lives of our people.

He is at this time transporting large Armies of foreign Mercenaries to compleat the works of death, desolation, and tyranny, already begun with circumstances of Cruelty & Perfidy scarcely paralleled in the most barbarous ages, and totally unworthy the Head of a civilized nation.

He has constrained our fellow Citizens taken Captive on the high Seas to bear Arms against their Country, to become the executioners of their friends and Brethren, or to fall themselves by their Hands.

He has excited domestic insurrections amongst us, and has endeavoured to bring on the inhabitants of our frontiers, the merciless Indian Savages whose known rule of warfare, is an undistinguished destruction of all ages, sexes and conditions.

In every stage of these Oppressions We have Petitioned for Redress in the most humble terms: Our repeated Petitions have been answered only by repeated injury. A Prince, whose character is thus marked by every act which may define a Tyrant, is unfit to be the ruler of a free people.

Nor have We been wanting in attentions to our British brethren. We have warned them from time to time of attempts by their legislature to extend an unwarrantable jurisdiction over us. We have reminded them of the circumstances of our emigration and settlement here. We have appealed to their native justice and magnanimity, and we have conjured them by the ties of our common kindred to disavow these usurpations, which would inevitably interrupt our connections and correspondence. They too have been deaf to the voice of justice and of consanguinity. We must, therefore, acquiesce in the necessity, which denounces our Separation, and hold them, as we hold the rest of mankind, Enemies in War, in Peace Friends.

We, therefore, the Representatives of the united States of America, in General Congress, Assembled, appealing to the Supreme Judge of the world for the rectitude of our intentions, do, in the Name, and by Authority of the good People of these Colonies, solemnly publish and declare, That these united Colonies are, and of Right ought to be Free and Independent States, that they are Absolved from all Allegiance to the British Crown, and that all political connection between them and the State of Great Britain, is and ought to be totally dissolved; and that as Free and Independent States, they have full Power to levy War, conclude Peace, contract Alliances, establish Commerce, and to do all other Acts and Things which Independent States may of right do. — And for the support of this Declaration, with a firm reliance on the protection of Divine Providence, we mutually pledge to each other our Lives, our Fortunes, and our sacred Honor.

The Montessori Classroom Part II: Sensorial

2010-06-24T19:23:00.000-07:00

For Part I: Practical Life, click here.

The Sensorial area focuses on the isolation and identification of essential characteristics of physical reality to increase a child’s perceptual range and introduce skills for ordering one’s thoughts in a manner conducive to supporting later explorations in mathematical reasoning and language development. It follows introduction to the Practical Life area but may be explored concurrently after the basic prerequisite skills are acquired by the student. This essay will attempt to summarize the purpose of the Sensorial curriculum area, its relevance to the curriculum, the nature and theory of the material design and sequence, the principles active in presenting the work to a child, the concept of the ‘Three Period Lesson’, and how Sensorial prepares the student for future studies in math and language.

The Sensorial area is designed to expand the range and depth of sense perceptions by a child. Percepts are composed of sensory data refined into algorithms of experience. That is to say that the creation of any perception is composed of the repetitive observation of certain sensory characteristics. When a particular sensory experience has been repeated so much that it becomes automatically identifiable, then it becomes integrated into a percept. Percepts are what we access when we perceive something. It is an awareness of a certain quality of an object as opposed to other qualities. Our perception expands as our distinctions in sensory definition become more subtle. For instance, a newborn baby most likely has access only to a very confused array of sensory impressions. As the baby gains experience in noticing differences between these sensations, the baby gains the ability to integrate certain senses into percepts. For example, length, color, size, weight, and so on. The more experience the child obtains, the more refined that child’s perceptual distinctions become. The child becomes aware of graded differentiations which aid its mind in ranking and ordering the attributes of objects in its environment. Children move through this progression naturally. There are sensitive periods that the child passes through which are like windows of opportunity for the child to acquire a wide variety and depth of skills. When a child is in the sensitive period for the development of a particular skill or perception, that child can show amazing command of concentration and repetition for mastery. As the child acquires more depth and variety of perceptions and builds their experience, the child eventually acquires the ability to integrate those perceptions into concepts. This is the child’s first foray into abstraction and opens the door to all later conceptual knowledge. As such, the ability to make unit-based discriminations with various sense perceptions would seem to stand at the very base of human knowledge.

The Sensorial area encourages the refinement of this skill by making available to the child sets of materials which isolate one sensory characteristic and requires the child to master the grading, matching, and distinction of that characteristic. For example, the Red Rods are a series of red rods of various lengths, all graded in differences of 10cm. The shortest is 10cm, the longest is 1m. Through the mastery of this material, a child will gain a refined perception of length measurement based on accepted and functional units. Repetition is built into the design and layout of the materials to encourage mastery and internalization. The Red Rods are ordered once on the rug and then returned to the same order on the shelves. Other Sensorial materials provide similar experiences with other perceptions. Children have a sensitive period for ordering their environment and the activities in Sensorial appeal directly to this predilection. The controlled practice of these skills is also intended to help children reorganize and classify information that they have already internalized. In some cases, a child may have internalized a distorted or inaccurate sense of length or size or some other perceptual faculty. Attention to organizing the materials in a carefully graded unit sequence will enhance their appreciation of perceptions in context and help them correct mistakes in percept integration and the organization of those perceptions in their mind. Furthermore, the fact that all introductory materials isolate one sense perception acts as an early warning system to alert the teacher of any potential disabilities which could impede the child’s progress. This diagnostic function makes it easier for the teacher to quickly assess the needs of the children and offer such support and intervention as would be required. Additionally, the Sensorial materials utilize a child’s need to move, develop muscular control and tactile memory, and help prepare the students for later studies in math and language through developing appreciation of 1:1 correspondences in the matching of identical sets of variegated degree. An example of the latter would be the Thermic Tablets, where the child must find the tablets of matching surface temperature. There is only one tablet of each material, there is only one answer, and the child need not be corrected by the teacher for the differences are self-evident. A more in-depth discussion of how Sensorial prepares children for math and language will follow later. However, it would first be proper to provide an explanation of what exercises are included in the Sensorial area, how are they arranged, and what is the underlying rationale for their design.

The Sensorial area is divided into sections based on each of the five senses: visual (sight), muscular-tactile (touch), auditory (sound), olfactory (smell), and gustatory (taste). The primary sensitivities of young children are to the visual and muscular-tactile senses. Because of this, the greater part of the sensorial materials focus on these two senses, and between these are predominantly based on visual discrimination. The progression of the materials follows a logical chain of building complexity which seeks to develop a series of sense perceptions focusing on just one aspect at a time.

The first materials in Sensorial are dedicated to refining a child’s visual sense of size. The Knobbed Cylinders are a series of 4 similar works. Each one is a block of wood with ten cylinders cut out. Each cylinder has a knob on top by which to be grasped. The cylinders themselves vary by one dimension (either diameter or height) and later a combination of two dimensions (diameter and height). The child practices removing and replacing the cylinders to refine their perception of these differences. These are followed by the Pink Cubes, which are stacked from largest to smallest to develop a sense of order and refine perception of size and height. Next are the Brown Quadrilateral Prisms, which are sequenced horizontally from thickest to thinnest. These refine the perception of thickness. The Red Rods, as stated previously, develop perception of length. Finally the Colored Cylinders are the twin of the Knobbed Cylinders except they are color coded, have no knobs, and have no accompanying wood blocks to serve as a control of error. These represent a step into the abstraction of the previously introduced dimensions from a highly controlled relationship into recognition in the environment—that is, where the control of error is only evident if the dimension being graded is perceived by the child. Previously, the control of error would depend on whether or not all cylinders fit flush into their holes. Once the Colored Cylinders are introduced, the child can now sequence the cylinders based on their visual perception of the graded variation in size. This concept of control of error is a critical point in the design strategy of the materials. Every set of materials must isolate one aspect of sense perception and, for each set, error must be instantly recognizable by the child as they work.

The next sequence of materials focuses on building the perception of various forms. These start with a series of works which expose the child to a broad representation of geometric shapes in two and three dimensions. These are followed by the Constructive Triangles, which are a series of boxes of triangles which are used to construct various geometric shapes from equilateral triangles to rhomboids and trapeziums. Next comes a series of three-dimensional cube-shaped puzzles. Each one focuses on developing visual awareness of an algebraic concept as a concrete spatial relationship years before it would be reintroduced in abstract mathematical form. These are followed by the Square of Pythagoras, which introduces the visual perception of the difference of squares, and the Leaf Cabinet, which introduces children to the study of more abstract geometric forms and prepares them for the study of biology.

The last sequence of materials developing visual perception focuses on defining distinctions of color, and tint. The first of the Color Boxes contains only a set of pairs of primary colors. The six tiles are simply randomized and paired up. The other boxes increase the depth of a child’s distinctions by providing greater variations of color and requiring the child to organize and match them accordingly.

After the visual works come the other four senses. First is the Muscular-Tactile sense. The Fabric Boxes and Tactile Boards develop a child’s sense of touch and texture. The Baric Tablets refine the perception of relative weight. The Thermal Tablets and Cylinders require the matching of materials based on surface temperature. The Auditory, Olfactory and Gustatory senses are refined with primarily stand-alone materials. The Sound Cylinders are used to refine the sense of hearing by requiring the child to match like pairs of cylinders which generate different sounds when shaken. The Smelling Cylinders refine the sense of smell by likewise requiring the child to match like pairs of scent. The Tasting Bottles also require the matching of like pairs based on different tastes: sweet, sour, salty, spicy, or bitter.

All the materials above follow a consistent strategy in design. All the materials involve the grading or matching of variations in a specific, isolated quality. All include a self-evident control of error. All support the development of gross motor skills by requiring the child to physically move the materials a fair distance, assemble them, and then return them to their original place and orientation. They also proceed in the necessary logical sequence of moving from concrete realizations of the perception involved to more abstract realizations. Just as with the Knobbed and Colored Cylinders, the work with geometric shapes moves from handling real objects in the Geometric Cabinet to identification of abstract representations of shape in the form of line drawings on cards. There are also certain guidelines in the presentation of the materials during a lesson which ensure that attention is drawn to the essential characteristics concerned.

First, the teacher must decide when it is appropriate to introduce a child to a given work. Has the child mastered the skills required to handle the materials? Are their fine motor skills sufficiently developed from exercises in Practical Life? Have they indicated an interest in the materials? Have they already had sufficient experience with the preceding materials? Is their maturity such that they can be entrusted with carrying large or delicate objects and treat them with respect? Have the ground rules for showing respect for their peers and the environment been properly established? If the teacher is confident that the answers to these questions are positive, then the next step is to invite the child to a lesson on the proper use of the new material.

The form of the invitation communicates an undercurrent of meaning. This meaning is highly relevant to the child’s perception of the teacher-student relationship and the social dynamic of the educational environment. If the invitation takes the form of a command, the child may interpret this as an authoritarian interaction where the teacher is trying to impose their own will upon the desires of the child. It is because of this that this step is called, “invitation”. If the student asks the child to come and learn this work, the child feels they have a choice and will be less likely to resist instruction. Also, this can serve as a check to see if the child is ready to engage the work for any number of reasons from lack of confidence to lack of normalization. Either way, even a “no” answer would be informative and direct the teacher to assess possible reasons for the hang-up or delay. Forcing the lesson would have no effect. You can put information, in any form, in front of a person’s eyes, but their mind must be actively engaged in the material to learn. The child will learn when the time is right.

When the child is ready and accepts the lesson, the teacher names the material. The names may seem arbitrary but they actually represent the distinguishing characteristic of the work to the child and expose them to the actual vocabulary that they will need in later academic pursuits. For example, “the Pink Cubes” are called the “Pink Tower” in AMI teacher programs, or they could be called the “Pink Blocks” or “Wood Blocks”. The difference is that while being pink and cube-shaped, they could still be arranged in a variety of patterns. Therefore, the name “Pink Cubes” represents more their essential defining features than “Pink Tower”. Also, the word “cube” is an academic word useful in geometry and mathematics. It is better to use these words as soon as possible and in a concrete and physical context. Early exposure to academic language helps children to adopt precise vocabulary without having to comprehend the abstract reasoning for the distinctions. Even better, such attention to precision of language allows children to mentally arrange, with clear distinctions, a variety of subtle concepts—and this without later having to untangle them from vague and imprecise terminology. An added benefit is that the use of these mysterious sounding words from the adult vocabulary will help to entice the children to be curious about the materials and give them an added sense of pride and accomplishment when they have mastered them. Imagine the glint in a child’s eye as they boast that they have mastered the quadrilateral prisms.

The next series of steps helps the child understand how best to prepare the materials for work. The teacher must clearly indicate where the materials are stored in the classroom and he should be familiar with its initial orientation. This is so the child can be successful in finding, retrieving, working on, and then returning the materials properly. Likewise, the teacher should always carry the materials in the manner that they desire the child to carry them. Children learn by watching. Also, some materials are quite large compared to a child’s frame and careful forethought about how best to hold the materials is essential to classroom harmony. Before this, however, the teacher must decide if these materials should be used on a rug or at a table. Some materials will be too large to use at most any table in an average classroom. Some may be small, but have a large number of pieces that must be laid out over a large space. The child, too, is a factor. A sufficiently normalized child who can focus on their work may be well able to handle a complex set of materials on a rug without incident. However, a less focused child may need the visual and physical order and boundaries imposed by the limits of a table and chair.

Once the material has been brought to the rug or table, the physical position of the teacher in relation to the child becomes an issue. Most material instructions assume a right-handed teacher teaching a right-handed student in a one-on-one situation. In the event of a group lesson, the teacher may want to sit opposite the group and reverse the presentation, although this runs the risk of the children reversing the procedure in their minds and doing things backwards. The teacher may be left-handed, or the student may be. Depending on the essential nature of the work it may be necessary to reverse hands or seating position so that the line of sight is not blocked by arm and hand position. Once these issues have been resolved, the lesson proper may begin.

The activity, or principal action of the presentation, must be clearly named. For example with the Red Rods, the teacher would say, “I am going to grade the red rods from longest to shortest.” The teacher should state the action before it is begun. This is closely connected with another aspect of a lesson, which is the arrangement of the materials prior to the principal action. Once again with the Red Rods, they are usually brought to the rug in a certain sequence dictated by their initial position in the classroom and then placed on the rug in a random orientation. Once this is completed, the teacher would name the principal action as stated above and then proceed to arrange the rods in the stated sequence. The random orientation is usually consistent throughout the manipulatives and thus aids in handling new materials. For instance, matching or sorting lessons usually require the materials to be laid out in a line above the work space before they are matched, sorted, or reassembled. The teacher must also decide when, how, and to what extent the child should be allowed to actively participate and to engage the materials during the progress of the lesson. It will be easier to retain the focus of some children by allowing them to touch the materials. Although some lessons will require being shown to completion before the child will be able to appreciate what must be done. The teacher must decide based on experience and familiarity with the given student. Finally, the teacher must demonstrate how to return the materials to their original condition and place in the classroom. Reversing procedures is not something which comes naturally to some children, so it is best to demonstrate the full clean-up process.

Now that the main principles for presenting the materials have been discussed, the method of actively teaching nomenclature must be addressed. The model used by Montessori is based on Seguin’s Three Period Lesson. The Three Period Lesson is presented after the child has already been introduced to a set of materials and had ample opportunity to manipulate the materials for themselves. The rationale is that the child must have had enough experience to develop the ability to perceive the essential characteristics of the materials necessary for their manipulation before they hope to attach a name to that characteristic. Learning to subsume those percepts into the concept of a word describing essential characteristics is the fundamental operation of conceptual abstraction.

In the first ‘period’, the teacher isolates two objects from the materials which differ the most. The teacher then presents those materials in juxtaposition to emphasize their essential difference. At this point the teacher names that difference. For example, with the Geometric Solids, the teacher would place the cube and sphere next to each other. They would say, “This is a cube” while pointing to the cube. Then the teacher would say, “This is a sphere” while pointing to the sphere. Depending on the level of the child, the teacher could perhaps then introduce some other forms such as cylinder, prism, pyramid and others. Generally, though, it is best to keep the first lessons as simple as possible. Also the same set of materials can sometimes be used to introduce various concepts. The Pink Cubes can, for example, be used to introduce the distinction between highest and lowest as well as largest and smallest or even ordinal numbers like “first, second, third”.

In the second period, the teacher tests the child for recognition of the vocabulary taught in the first. The teacher could use a sequence of simple commands to see if the child is properly recognizing the terms. Once again using the Geometric Solids as an example, the teacher could say, “Point to the cube.” If the child correctly executes the command, then the teacher would move on. “Put the sphere under the rug.” If the child happened to select the cylinder by mistake, the teacher would correct in a positive manner. “That is a cylinder. This is a sphere. Put the sphere under the rug.” As long as the child fails to properly recognize the commands with verbal cues only, the teacher continues with the second period. It is important to note here that the teacher never corrects sternly. The teacher must always maintain a calm and nurturing disposition. This process can continue as long as necessary and can be built on in later sessions to further develop vocabulary. Once the teacher is confident that the child can respond to verbal cues, instruction enters the third period.

In the third period, the teacher prompts the child to produce the vocabulary taught in the first two periods. To test the child’s retention of the vocabulary, the teacher makes sure to use no verbal cues. Pointing to the cube, the teacher simply asks, “What’s this?” If the child says, “It’s a cube!” then the child has successfully demonstrated their knowledge and no further guidance is necessary. If the child cannot answer, then the teacher knows that further assistance is necessary and should return to the second period.

The method of applying the Three Period Lesson after the experience of developing perceptual awareness is highly effective in preparing children for work in Mathematics and Language. That the process teaches children technical nomenclature has already been discussed. Almost more important is the series of foundational principles that work with the Sensorial materials helps children acquire. Children not only learn to name objects but to perceive subtle similarities and differences between forms. This is a critical skill in developing the ability to differentiate between written characters—a fundamental reading skill called letter recognition. This is also helpful in helping children recognize the differences between written numbers—a prerequisite skill for all formalized mathematics. Sensorial also prepares the children for comprehension of the base-10 decimal system. All graded materials such as the Pink Cubes and Colored Cylinders have ten pieces to be removed and replaced in a set sequence. They also prime the children for unit measurement because all materials differ in unit differences based on the metric system. This means that as they develop their awareness of the qualities of the materials, they develop a physical appreciation of the unit multiplication of surface area and volume. The Constructive Triangles help prime children for later explorations in formulating geometric proofs and the Knobbed Cylinders help children develop an appreciation for 1:1 correspondence, the awareness that one number corresponds to one thing. Once children realize this, it opens them up to be able to combine numbers through adding, removing them through subtraction and then on to other higher functions. The Knobbed Cylinders can also be seen as introducing the children to the concept of an empty set, or zero. The sight of the wood block with all pieces removed is a perfect visual image of a null set placeholder.

Children are also primed for studies in Language through use of the Sensorial materials. The grading and sequencing of parts is always conducted left-to-right and top to bottom. The layout of the materials on the shelves follows the same pattern. This is because it is the standard pattern for written English and most other European languages. It is interesting to note, that this sequencing and layout can be adjusted in countries where the standard layout is right to left or top to bottom. Children engage in basic problem solving skills like trying to determine logical sequencing and gradation, finding the missing piece, memorization, deconstruction and reassembly. These are fundamental skills used in reading to fill-in meaning from contextual clues, to remember sight words, and to blend together phonetic compounds. Comparing like parts to a larger whole is also integral to breaking apart compound words and longer words for easier reading and comprehension. Finally, the independent, one-on-one nature of the Sensorial materials enables children to develop a sense of self-motivation and a positive attitude towards self-correction. These are necessary for maintaining a positive and productive future attitude in the study of any academic discipline. Nonetheless, the potential for group learning and peer mentoring ensures that if the child has the inclination, they can be fully supported by friends working together to mutual advantage.

The Practical Life area prepares the children for meaningful exploration and participation in their environment and daily lives. Sensorial helps children expand the breadth and depth of their perceptual apparatus and helps prime their minds for the patterns of order and scale which form the foundation for later studies in mathematics and language. Sensorial also introduces students to technical terminology in geometry, mathematics, and biology. The hands-on, individualized paradigm introduced in Practical Life is further developed in Sensorial and helps instill a heightened sense of concentration, independence, and confidence—all skills necessary to ensuring that future explorations of academic disciplines are self-motivated and fulfilling.

John Allison - A Living Example of the Objectivist Ethics

2010-04-18T19:34:00.000-07:00

I saw this video lecture today and I was captivated. Allison perfectly synthesizes the Objectivist ethics into a practical, matter-of-fact, and easy to understand presentation. I highly recommend this, especially if you're a new-comer to Ayn Rand's work and are having difficulties understanding what she's really all about. But I also think it would be refreshing for veterans in the philosophy as well. As always, why not check it out and decide for yourself?

http://www.youtube.com/watch?v=twolXLHBmgQ