chapter 26 representative ideas from ways of knowing through the realms of meaning by william allan...

Copyright © 2011 by William Allan Kritsonis/All Rights Re-served

26

REPRESENTATIVE IDEAS

INSIGHTS

1. The educator is faced with the difficult task of selecting from the rich resources of authentic knowledge that comparatively small portion that will best serve his students.

2. Content should be chosen so as to exemplify the representative ideas of the disciplines.

3. A “representative idea” is an idea that repre-sents the discipline in which it occurs.

4. Representative ideas are concepts that afford an understanding of the main features of the disci-pline.

5. Representative ideas exist because disci-plines have form, pattern, or structure.

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586 PART THREE:THE CURRICULUM FOR GENERAL EDUCATION

6. Representative ideas are the organizing prin-ciples of the discipline. They exhibit its distinctive logic.

7. Representative ideas are clearly of great im-portance in economizing learning effort.

8. A thorough understanding of these ideas is equivalent to a knowledge of the entire discipline.

9. Representative ideas are therefore at once and the same time principles of growth and princi-ples of simplification.

10. An understanding of the very ideas that make a discipline fertile, causing knowledge in it to ex-pand rapidly, is also the basis for simplifying the task of learning the discipline.

11. The use of representative ideas is one way of solving the problem of quantity in knowledge by means of qualitative principles of selection.

12. Representative ideas are elements the under-standing of which makes it unnecessary to learn large numbers of particular items of knowledge.

13. Some components within a subject are more representative than others.

14. The less representative components are those that draw attention to particular aspects of the subject rather than to the essential patterns of the whole.

15. The ideas comprising a discipline may be ar-ranged in a hierarchical order.

16. At the top (first in representative quality) be-long those few concepts that characterize the dis-cipline in all its parts.

17. At the bottom of the hierarchy appear the host of individual results of inquiry in the disci-pline, reflecting applications of the general con-cepts to particular cases and holding within speci-fied conditions.

18. A hierarchy of concepts can be constructed for each of the fundamental patterns of meaning.

REPRESENTATIVE IDEAS 587

19. The main objective is that some defensible organization of ideas in each discipline be achieved.

20. The working out of patterns of representative ideas within the several disciplines is a task that only specialists in the disciplines themselves can really satisfactorily accomplish.

21. Only experts with intimate understanding of their disciplines can make dependable judgments concerning the relative precedence of concepts and the ways in which ideas fit together in the pat-tern of the entire discipline.

22. Representative ideas have no place in the ac-tual content of instruction at the introductory stages.

23. The most fundamental ideas are usually not appropriate as explicit content until a fairly ad-vanced stage of understanding has been reached.

24. The less comprehensive ideas are, the more easily they can be understood by the beginning student.

25. The function of representative ideas is to guide the selection of learnable content so that it will exemplify the characteristic features of the disciplines.

26. The place of the representative ideas is not in the first instance on the lips of the teacher, but in his mind, to direct him in the choice of learning ex-periences that will illustrate the ideas he has in mind.

27. In the beginning stages representative ideas are for the guidance of the teacher (or the curricu-lum maker) and not directly for the student.

28. The essential point is that at every stage of instruction the representative ideas should govern what is taught.

29. A good teacher chooses each item or experi-ence with the deliberate purpose of giving sub-


stance to certain basic concepts that are distinc-tive and representation of the discipline studied.

30. The distinctively human goal in learning is to expand meanings beyond particulars to the larger patterns of understanding.

31. Human fulfillment consists in enriching and deepening comprehension through the ever-ex-panding integration of experience.

32. The aim of teaching is comprehensive under-standing.

33. The way to achieve comprehensive under-standing in teaching is to choose particular materi-als for instruction that in an unusual degree exem-plify the pattern of the subject as a whole.

34. A drastic reduction in the amount of what has to be learned can be effected by the use of repre-sentative materials.

35. Of greatest importance is the consequence that a student taught by the use of representative ideas understands meaning fully.

36. Good teachers have always practiced the art of communicating the essence of their subject by means of unusually illuminating specific examples.

37. What is required is a clear recognition of the close relation between efficiency in learning and knowledge of the characteristic ideas of the disci-plines.

38. Great opportunities exit today for the ad-vancement of education through the joint efforts of experienced classroom teachers, curriculum ex-perts, and scholars in the disciplines in providing study materials constructed on sound principles from both pedagogy and the theory of knowledge.

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SELECTION OF CURRICULUM CONTENT DISCRIMINATES

BETWEEN DISCIPLINED AND UNDISCIPLINED MATERIALS

The first principle for the selection of curriculum con-tent discriminates between disciplined and undisci-plined materials. Other principles are required to guide the choice of materials within the disciplines. The need for such guidance has been occasioned by the explo-sion of knowledge—an explosion due largely to the ac-tivity of workers within the disciplines themselves. The educator not only has to choose authentic knowledge in place of commonsense opinion; he has the even more difficult task of selecting, from the rich resources of au-thentic knowledge, that comparatively small portion that will best serve his students. The second, third, and fourth principles of curricular selection, which will be explained in the present and the following two chap-ters, are designed to guide this choice within the disci-plines.

CONTENT SHOULD BE CHOSEN TO EXEMPLIFY THE

REPRESENTATIVE IDEAS OF THE DISCIPLINES

The second principle is that content should be cho-sen so as to exemplify the representative ideas of the disciplines.

The Term Representative IdeaAs the term suggests, a “representative idea” is

an idea that represents the discipline in which it occurs. It is a typical idea in the sense that it reveals the type or kind of the discipline. It is a characteristic idea in the sense that it manifests the character of the discipline. Representative ideas are concepts that afford an under-standing of the main features of the discipline. They are not minor or subordinate ideas; they disclose the essence of the discipline. They are elements of the sub-ject that stand for the whole or important aspects of it.


They are aspects within which the image of the com-plete discipline or major portions of it is contained. They are epitomes of the subject.

Representative Ideas Have Form, Pattern, or Structure

Representative ideas exist because disciplines have form, pattern, or structure. A representative con-cept represents the pattern of the discipline. It charac-terizes the structure of that field of inquiry. It is an idea that enables one to distinguish one discipline from an-other. The assertion that disciplines have form means that their various components fit together according to some scheme of coordination. They cohere in some sys-tematic fashion. A discipline is not merely a collection of various and sundry ideas. It has a characteristic logic that provides a standard for judging whether or not any given item belongs to the discipline, and if it does, how it fits together with the other components of the field. Representative ideas are the organizing principles of the discipline. They exhibit its distinctive logic.

Representative Ideas help in Economizing Learn-ing Effort

Representative ideas are clearly of great impor-tance in economizing learning effort. If there are certain characteristic concepts of a discipline that represent it, then a thorough understanding of these ideas is equiva-lent to a knowledge of the entire discipline. If knowl-edge within a discipline is organized according to cer-tain patterns, then a full comprehension of those pat-terns goes far toward making intelligible the host of particular elements that fit into the design of the sub-ject.

From the existence of consistent patterns within disciplines it follows that the metaphor of an explosion of knowledge is not really an apt one. For an explosion normally suggests uncontrolled, chaotic expansion. If


knowledge is developing within organized disciplines according to specified patterns, then an organic metaphor would seem more appropriate for the in-crease in knowledge. For example, it might be better to say that knowledge is showing exuberant healthy growth. The reason for its growth is that certain fruitful concepts have been discovered that enable continuous, productive learning to take place. These fruitful con-cepts are simply the representative ideas described above.

Representative Ideas are Principles of Growth and Simplification

Representative ideas are therefore at one and the same time principles of growth and principles of simpli-fication. They are principles of growth because the pat-terns they reveal prove to be productive of further in-sight, yielding more and more particular exemplifica-tions of what they typify. They are principles of simplifi-cation because they provide a kind of map of the disci-pline that keeps one from getting lost in the details. This is a surprising fact, that an understanding of the very ideas that make a discipline fertile, causing knowl-edge in it to expand rapidly, is also the basis for simpli-fying the task of learning the discipline.

Representative Ideas are Very Special ElementsThe use of representative ideas is one way of solv-

ing the problem of quantity in knowledge by means of qualitative principles of selection. Representative ideas are not components of a discipline chosen at random. They are very special elements within it, selected for their representative qualities. They are of such a quality that they stand for large quantities of material. Repre-sentative ideas are elements the understanding of which makes it unnecessary to learn large numbers of particular items of knowledge.


Representativeness is a Matter of DegreeWhat has been said so far may have given the im-

pression that a discipline is made up of two kinds of ideas—representative and unrepresentative ones—and the recommended principle of selection is to teach the representative rather than the unrepresentative. Such a view is misleading. It is not actually possible to divide the contents of a discipline into two compartments on the basis of representativeness. There is a sense in which any item of knowledge belonging within a disci-pline represents that discipline; if it is properly placed in one discipline rather than in another, it may be said to represent that discipline. Representativeness is actually a matter of degree. Some components within a subject are more representative than others in that they more clearly reveal its pervasive essential features. The less representative components are those that draw atten-tion to particular aspects of the subject rather than to the essential patterns of the whole.

Disciplines Arranged in Hierarchical OrderThe ideas comprising a discipline may be arranged in a hierarchical order. AT the top (first in representative quality) belong those few concepts that characterize the discipline in all its parts. Next come certain corol-lary ideas suggested by the primary ones. On the next lower level appear certain important concepts that serve as organizing principles for large subdivisions of the discipline, and below these are ranked many more particular ideas that prove useful in the detailed devel-opment of the various special problems and areas of the subject. At the bottom of the hierarchy appear the host of individual results of inquiry in the discipline, re-flecting applications of the general concepts to particu-lar cases and holding within specified conditions.

Further Analysis of Representative Ideas


The analyses of the various fundamental patterns of meaning in Chapters 5 to 20 were intended to iden-tify certain representative ideas in the disciplines, showing both the most essential ones and some with lower orders of representative power. At the highest level are the ideas that characterize the general logical type of a discipline. For example, at the most general level, a language is characterized as a conventional symbolic structure, and this distinguishes language knowledge from empirical, esthetic, personal, moral, and synoptic knowledge. Each of these other realms is characterized by representative concepts of the same high order of generality.

In the general realm of symbolics different repre-sentative ideas typify the several constituent disci-plines. For example, the concepts of phoneme, mor-pheme, and syntactical classes apply to ordinary lan-guage but not to mathematics or to the nondiscursive symbolic forms. The fundamental ideas of set, complete abstraction, and logical consistency are typical of math-ematics but not necessarily of the other symbolic fields. Similarly, the ideas of presentational form and of figura-tive meaning pertain characteristically to the nondiscur-sive symbolic forms.

At a lower order of representativeness in the symbolics are such important ideas as inflection in ordi-nary language, variable in mathematics, and gesture in nondiscursive symbolic forms. At the bottom of the rep-resentative hierarchy are particular words and word se-quences, particular mathematical propositions, and par-ticular presentational symbols.

Hierarchy of ConceptsIn this manner a hierarchy of concepts can be con-

structed for each of the fundamental patterns of mean-ing discussed in Part Two. At the top appear those ideas that are shown to be fundamental to the entire realm of meaning. Next come the characteristic features of the


constituent disciplines, followed by ranks of important organizing concepts in the various divisions and subdi-visions of each subject. Probably no single order of precedence of concepts can be defended as the right one. Different points of view can be taken regarding or-ganizing principles. For example, mathematicians are not agreed as to whether number or set is the more characteristic idea for mathematics; a satisfactory hier-archy of concepts can be arranged either way. The main objective is that some defensible organization of ideas in each discipline be achieved. It is hoped that the analyses of the disciplines in Part Two may illustrate in a general and tentative way the lines along which such organization can proceed.


Red means stop.Green means go.

Yellow means caution.The speed limit sign prescribes

maximum speed, but not minimum speed. The driver on the right has the right of way at a four way stop sign.

No passing on a double yellow stripe. To a licensed automobile driver, this is common sense. Unless a representa-

tive idea has been forwarded, driving a car from point A to point B, the unfamiliar

could be confused. Can a student comprehend the elements of a lesson without knowing what

it is leading to?


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THE TASK OF THE SPECIALIST OR EXPERT IS TO WORK OUT PATTERNS OF REPRESENTATIVE IDEAS WITHIN THE

DISCIPLINES

The working out of patterns of representative ideas within the several disciplines is a task that only specialists in the disciplines themselves can really satis-factorily accomplish. Only experts with intimate under-standing of their disciplines can make dependable judg-ments concerning the relative precedence of concepts and the ways in which ideas fit together in the pattern of the entire discipline. The specialists who undertake this work also need a degree of philosophical interest and competence. They need to become critically aware of their enterprise as a whole and to be capable of de-veloping interpretive categories in which to express the inter-relationships of ideas within the subject.

TEACHING FIRST THE MOST REPRESENTATIVE

IDEAS WOULD BE A MISTAKE

If it is granted that disciplines have characteristic features and that it is possible to construct hierarchies of representative ideas, it still remains to be explained how these qualitatively special concepts are to be used by the teacher. It might appear that the answer to the crisis in learning is to select and teach first the most representative ideas, that is, the ones at the top of the hierarchy, then to move on to the next lower level, and so on down toward the particularity and detail of the lowest level, as far as time permits. Such a view of the principle of representative ideas in teaching is quite mistaken. Instruction on such a basis would prove com-pletely ineffective.

CONTENT SHOULD BE CHOSEN TO EXEMPLIFY THE

REPRESENTATIVE IDEAS OF THE DISCIPLINE—THESE IDEAS ARE HIGHLY ABSTRACT

The principle as stated early in this chapter was that content should be chosen so as to exemplify the


representative ideas of the disciplines. The italics are important. It was not said the representative ideas themselves should be taught as explicit concepts. These ideas are of a highly abstract nature. They be-long to the philosophical analysis of the disciplines. They have no place in the actual content of instruction at the introductory stages. For example, the represen-tative idea of the principle of conservation is not an ap-propriate topic for explicit abstract treatment in the early stages of physical science. The analytical concept of the musical idea is not a suitable way to begin the study of music. The idea of personal knowledge as be-ing concrete, existential, and intersubjective is not of direct value for beginning instruction in that field, any more than the idea of the logical distinction between fact and obligation would be appropriate as an explicit topic in elementary moral teaching. The representative ideas of history as the reenactment of unique events, of religion as ultimate commitment, and of philosophy as interpretation of meanings are likewise not helpful as specific material for basic instruction in the synoptic disciplines.

The most fundamental ideas are usually not appro-priate as explicit content until a fairly advanced stage of understanding has been reached. They are high ab-stractions that are not meaningful except to persons who possess a considerable fund of knowledge in the subject to which they apply. The less comprehensive ideas are, the more easily they can be understood by the beginning student.

REPRESENTATIVE IDEAS GUIDE THE SELECTION LEARNABLE CONTENT SO THAT IT WILL EXEMPLIFY THE

CHARACTERISTIC FEATURES OF THE DISCIPLINE

What, then is the use of the representative ideas if they are not suitable from the beginning as curriculum content? Their function is to guide the selection of learnable content so that it will exemplify the character-


istic features of the disciplines. The place of the repre-sentative ideas is not in the first instance on the lips of the teacher, but in his mind, to direct him in the choice of learning experiences that will illustrate the ideas he has in mind. For example, in the arts not much would be learned if the teacher talked about individual per-ceptual forms. What is required is a series of experi-ences all of which exemplify concern for the unique per-ceptual object. In the study of history the student would not be helped very much initially by talk about relevant evidence or about history being the best possi-ble explanation of the present. He would be assisted by specific experiences judicially chosen to illustrate the meaning of relevance and the manner of using present data as the evidence for the construction of history.

AT EVERY STAGE OF INSTRUCTION, THE REPRESENTATIVE IDEAS SHOULD GOVERN WHAT IS TAUGHT

In the beginning stages representative ideas are for the guidance of the teacher (or the curriculum maker) and not directly for the student. Later they may be made explicit for the student and may prove as use-ful to him in advancing and epitomizing his own under-standing as they are for the teacher. The essential point is that at every stage of instruction the representative ideas should govern what is taught. Every particular should manifest the larger concept that it illustrates. The poor teacher piles item upon item of information and experience, only making certain that each contribu-tion falls within the subject being pursued. The good teacher, by contrast, chooses each item or experience with the deliberate purpose of giving substance to cer-tain basic concepts that are distinctive and representa-tion of the discipline studied.

TEACHING THROUGH THE USE OF REPRESENTATIVE IDEAS

The manner in which representative ideas should be used in teaching is summed up in Alfred North


Whitehead’s dictum that “the problem of education is to make the pupil see the wood by means of the trees.”1 The wood is the subject as a whole. The trees are the particular instances chosen to exemplify the whole. This is the approach to teaching through the use of representative ideas, as advocated in the foregoing pages.

1 The Aims of Education, New American Library of World Litera-ture, Inc., New York, 1949, p. 18.


Teaching Using the Trees OnlyBy way of contrast, three other common ap-

proaches to teaching may be noted. The first is to teach by using the trees only. This is the method of simple accumulation of knowledge, piece by piece, without any consideration for the relationships among the parts or for the structure of the whole. This is the way resorted to by those who are confused about the meaning of the multiplicity of experiences presented by modern life. They take refuge in particularity, heaping up fragments of existence without regard to their co-herence or direction. While students may become ab-sorbed in this flow of miscellaneous experience, they sooner or later feel its emptiness, finding in the arbi-trary juxtaposition of ideas no satisfactory basis for per-sonal fulfillment.

Teaching Use the Wood OnlyA second type of teaching is in direct contrast

with the first. This is the way of teaching by using the wood only. Such teaching is concerned only with gen-eral principles. It is the way of the theoretically minded person, who loves abstractions above all. Concrete in-stances he regards as beneath his notice, for he dwells in the lofty atmosphere of pure idea. This kind of teach-ing would be tolerated, if at all, only at the higher aca-demic levels. Children and young people would gain nothing from it and would properly react strongly against it, because it is too remote from their concrete experience.

This unsatisfactory second type is one that might readily be confused with the method of teaching by the use of representative ideas. These ideas are general concepts that represent the wood—the discipline as a whole. To economize learning effort it might be urged that these representative ideas be taught, leaving out all unnecessary details. As pointed out earlier, such teaching would be empty. The students would learn


nothing from it. They would at most learn how to repeat certain philosophical generalities about the various fields of study. The students would have no real under-standing either of the disciplines or of the general ideas they had learned to utter.

For example, a student of mathematics might know that the discipline has to do with abstraction, sets, deductive inference, and postulational method and yet not really understand the subject at all, be-cause he had never seen and savored these elemental ideas through specific illustrations. Again, a student who knew history in the abstract sense that he could describe the subject as the reenactment of unique past events, using relevant evidence, would not really un-derstand history unless these abstractions had first been brought to life for him by particular illuminating il-lustrations.

Teaching By Using the Trees By Means of the Wood

A third approach to instruction is to help the stu-dent see the trees by means of the wood. Here the em-phasis is on the particular instance, and the generaliza-tions are used to make the individual case intelligible. For example, music may be studied with the ultimate objective of understanding particular musical composi-tions, and representative concepts, such as rhythm and harmonic texture, may be introduced only when needed to render certain features of the individual works intelligible, but there may be no attempt to com-prehend the larger meaning of music as a significant human activity. Again, language may be studied purely for the sake of speaking it, and representative ideas like morpheme and paradigmatic class (regardless of whether or not such technical terms are used) may be introduced only to clarify certain meanings or construc-tions that prove difficult in the course of studying the


language, rather than to afford an understanding of the significance of the language enterprise as a whole.

The distinctively human goal in learning is to ex-pand meanings beyond particulars to the larger pat-terns of understanding. Human fulfillment consists in enriching and deepening comprehension through the ever-expanding integration of experience. Seeing the trees is not appropriate as an ultimate goal of learning.

It is doubtful that one could understand the wood by which to see the trees if he had not first been shown the wood by means of the trees. In the music example above, it is doubtful the general concepts of rhythm and harmonic texture would have any clarifying power when applied to particular compositions unless these ideas had earlier become meaningful in themselves through vivid particular exemplifications. In the lan-guage instance it is doubtful that the general ideas of morpheme and paradigmatic class would be of any help in particular situations unless these concepts had al-ready become significant through carefully chosen illus-trations directed at illuminating their meaning.

THE AIM OF TEACHING IS COMPREHENSIVE UNDERSTANDING

We return to the proposition that the aim of teach-ing is comprehensive understanding. The way to achieve comprehensive understanding in teaching is to choose particular materials for instruction that in an un-usual degree exemplify the pattern of the subject as a whole. Another way of stating this is to say that the par-ticulars of instruction should be representative, typical, or paradigmatic materials, their representativeness be-ing measured by how well they show the typical fea-tures of the discipline they are supposed to illuminate.

A STUDENT TAUGHT BY THE USE OF REPRESENTATIVE

IDEAS UNDERSTANDS MEANING FULLY


A drastic reduction in the amount of what has to be learned can be effected by the use of representative materials. The student comes to an implicit understand-ing of the characteristic features of the disciplines step by step. By the consistent nature of his experiences in connection with a given discipline he gains an intimate sense of its basic patterns, so that he can make sound judgments regarding materials in it and can readily fa-miliarize himself with new knowledge as it develops in the field. Of greatest importance, however, is the con-sequence that a student taught by the use of represen-tative ideas understands meaning fully. he possesses a power of inner appropriation, by which he feels himself at home in the universe of meanings.

The purpose of representative ideas is to define what the final out-come of education in that discipline

should be. In some cases a more gen-eral statement of what is to be accom-plished will be more successful than in

others. If the student athlete is told that the object of the race is to run to the other end of the track faster than

everyone else, he/she will probably un-derstand. If the young flutist is told that the object of music is to play a


concerto for the esthetic enjoyment of the audience, success will probably be

harder to come by. Teachers must then be trained in how to present the material to be learned in a way that will bring the student to the desired level of achievement. How does the

teacher determine whether or not the final outcome has been achieved as

expected?


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REPRESENTATIVE MATERIALS INCREASE EFFICIENCY INLEARNING AND KNOWLEDGE OF THE REPRESENTATIVE

IDEAS OF THE DISCIPLINES

Teaching by the use of representative materials is not a recent innovation. Good teachers have always practiced the art of communicating the essence of their subject by means of unusually illuminating specific ex-amples. What is required in the contemporary situation is a deliberate cultivation of such teaching, based on a clear recognition of the close relation between effi-ciency in learning and knowledge of the characteristic ideas of the disciplines. Some of the best new instruc-tional materials, particularly in mathematics and the sciences, have been prepared by the cooperative ef-forts of scholars in the disciplines and teachers at the various grade levels affected. The value of these mate-rials is due in large measure to the fact that they unite the necessary pedagogical specificity with a high de-gree of discipline representativeness. More such materi-als for the teacher’s use are urgently needed in all ar-eas of the curriculum. Since the individual teacher sel-dom has the time or ingenuity to create his own repre-sentative materials, he must normally make use of pub-lished guides. Great opportunities exist today for the advancement of education through the joint efforts of experienced classroom teachers, curriculum experts, and scholars in the disciplines in providing study mate-rials constructed on sound principles from both peda-gogy and the theory of knowledge.

WAYS OF KNOWING

1. Why is the first principle for the selection of cur-riculum content to discriminate between disci-plined and undisciplined materials?

2. Why is the second principle for the selection of curriculum content to choose content that exem-plifies the representative ideas of the disciplines?


3. What is a “representative idea”?4. What is the form, pattern, or structure of repre-

sentative ideas?5. How do representative ideas help in economiz-

ing the learning effort?6. How are representative ideas both principles of

growth and principles of simplification?7. Why are representative ideas very special ele-

ments?8. How is representativeness a matter of degree?9. How are ideas comprising a discipline arranged

in a hierarchical order?10. Why is it important to know how the hierarchy

of concepts can be constructed for each of the fun-damental patterns of meaning?

11. Why is the task of the specialist or expert to work out the patterns of representative ideas within the disciplines?

12. Why does the specialist or expert need to have a certain degree of philosophical interest and com-petence?

13. Why would teaching first the most representa-tive ideas be a mistake?

14. Why should content be chosen so as to exem-plify the representative ideas of the disciplines?

15. How are representative ideas highly abstract?16. Why is it that the less comprehensive ideas are,

the more easily they can be understood?17. How are representative ideas used to guide in

the selection of learnable content so it will exem-plify the characteristic features of the discipline?

18. Why is it critically important that at every stage of instruction that the representative ideas govern what is to be taught?

19. How does the good teacher choose each item or experience with the deliberate purpose of giving substance to certain basic concepts that are dis-


tinctive and representative of the discipline stud-ies?

20. What does Alfred North Whitehead’s dictum mean that “the problem of education is to make the pupil see the wood by means of the trees”? (Source: The Aims of Education, New American Li-brary of World Literature, Inc., New York, 1949, p. 18.)

21. Why is the aim of teaching comprehensive un-derstanding?

22. How do we achieve comprehensive understand-ing as a teacher?

23. How can teaching by the use of representative ideas cause the student to possess a power of in-ner appropriation, by which he feels himself at home in the universe of meanings?

24. How do representative materials increase effi-ciency in learning and knowledge of the represen-tative ideas of the disciplines?

chapter 26 representative ideas from ways of knowing through the realms of meaning by william allan...

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distinctively human goal

fairly advanced stage

mizing learning effort

achieve comprehensive understanding

comprehensive ideas

main features

expand rapidly

good teachers