Please read this chapter and write down one word, from every sentence ( I have uploaded for you)Please then make a word puzzle out of these words, intersecting them and crossing them, using letters as intersections.This word-puzzle won’t be a game to play so it doesn’t have to be perfect just try making it into a puzzle, but it will be a design and art piece to visually express the words that may have stayed with you from the reading.Please choose words that are interesting – or that you don’t know – or words that vibrate with meaning and richness for you.Please then scan or take a picture of this word-puzzle (please keep it all on one page) and it should be in hand written.THE PROCESS OF EDUCATION

inferred is the only known way of reducing the quick

rate of loss of human memory.

Designing curricula in a way that reflects the basic

structure of a field of knowledge requires the most

fundamental understanding of that field. It is a task that

cannot be carried out without the active participation

of the ablest scholars and scientists. The experience of

the past several years has shown that such scholars and

scientists, working in conjunction with experienced

teachers and students of child development, can prepare

curricula of the sort we have been considering. Much

more effort in the actual preparation of curriculum

materials, in teacher training, and in supporting research

will be necessary if improvements in our educational

practices are to be of an order that will meet the challenges of the scientific and social revolution through

which we are now living.

There are many problems of how to teach general

principles in a way that will be both effective and interesting, and several of the key issues have been passed

in review. What is abundantly clear is that much work

remains to be done by way of examining currently effective practices, fashioning curricula that may be tried out

on an experimental basis, and carrying out the kinds of

research that can give support and guidance to the general effort at improving teaching.

How may the kind of curriculum we have been discussing be brought within the intellectual reach of

children of different ages? To this problem we turn next.

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READINESS FOR LEARNING

W E begin with the hypothesis that any subj ect

can be taught effectively in some intellectually honest

form to any child at any stage of development. It is a

bold hypothesis and an essential one in thinking about

the nature of a curriculum. No evidence exists to contradict it; considerable evidence is being amassed that

supports it.

To make clear what is implied, let us examine three

general ideas. The first has to do with the process of

intellectual development in children, the second with

the aCt of learning, and the third with the notion of the

“spiral curriculum” introduced earlier.

Intellectual development. Research on the intellectual

development of the child highlights the fact that at each

stage of development the child has a characteristic way

of viewing the world and explaining it to himself. The

task of teaching a subject to a child at any particular

age is one of representing the structure of that subject in

terms of the child’s way of viewing things. The task can

be thought of as one of translation. The general hypothesis that has just been stated is premised on the considered

judgment that any idea can be represented honestly and

usefully in the thought forms of children of school age,

and that these first representations can later be made

more powerful and precise the more easily by virtue of

this early learning. To illustrate and support this view,

THE PROCESS OF EDUCATION

we present here a somewhat detailed picmre of the

course of intellectual development, along with some suggestions about teaching at different stages of it.

The work of Piaget and others suggests that, roughly

speaking, one may distinguish three stages in the intellecmal development of the child. The first stage need

not concern us in detail, for it is characteristic principally

of the pre-school child. In this stage, which ends (at

least for Swiss school children) around the fifth or sixth

year, the child’s mental work consists principally in

establishing relationships between experience and action;

his concern is with manipulating the world through

action. This stage corresponds roughly to the period

from the first development of language to the point at

which the child learns to manipulate symbols. In this

so-called preoperational stage, the principal symbolic

achievement is that the child learns how to represent the

external world through symbols established by simple

generalization; things are represented as equivalent in

terms of sharing some common property. But the child’s

symbolic world does not make a clear separation between

internal motives and feelings on the one hand and external reality on the other. The sun moves because God

pushes it, and the stars, like himself, have to go to bed.

The child is little able to separate his own goals from the

means for achieving them, and when he has to make

corrections in his activity after unsuccessful attempts at

manipulating reality, he does so by what are called intuitive regulations rather than by symbolic operations,

the former being of a crude trial-and-error nature rather

than the result of taking thought.

What is principally lacking at this stage of develop34

READINESS FOR LEARNING

ment is what the Geneva school has called the concept

of reversibility. When the shape of an object is changed,

as when one changes the shape of a ball of plasticene,

the preoperational child cannot grasp the idea that it

can be brought back readily to its original state. Because

of this fundamental lack the child cannot understand

cenain fundamental ideas that lie at the basis of mathematics and physics-the mathematical idea that one conserves quantity even when one partitions a set of things

into subgroups, or the physical idea that one conserves

mass and weight even though one transforms the shape

of an object. It goes without saying that teachers are

severely limited in transmitting concepts to a child at

this stage, even in a highly intuitive manner.

The second stage of development-and now the child

is in school-is called the stage of concrete operations.

This stage is operational in contrast to the preceding

stage, which is merely active. An operation is a type of

action: it can be carried out rather directly by the

manipulation of objects, or internally, as when one

manipulates the symbols that represent things and relations in one’s mind. Roughly, an operation is a means

of getting data about the real world into the mind and

there transforming them so that they can be organized

and used selectively in the solution of problems. Assume

a child is presented with a pinball machine which

bounces a ball off a wall at an angle. Let us find out what

he appreciates about the relation between the angle of

incidence and the angle of reflection. The young child

sees no problem: for him, the ball travels in an are,

touching the wall on the way. The somewhat older

child, say age ten, sees the two angles as roughly related

35

THE PROCESS OF EDUCATION

-as one changes so does the other. The still older child

begins to grasp that there is a fixed relation between the

two, and usually says it is a right angle. Finally, the

thirteen- or fourteen-year-old, often by pointing the

ejector directly at the wall and seeing the ball come back

at the ejector, gets the idea that the two angles are equal.

Each way of looking at the phenomenon represents the

result of an operation in this sense, and the child’s thinking is constrained by his way of pulling his observations

together.

An operation differs from simple action or goaldirected behavior in that it is internalized and reversible.

“Internalized” means that the child does not have to go

about his problem-solving any longer by overt trial and

error, but can actually carry out trial and error in his

head. Reversibiliry is present because operations are seen

as characterized where appropriate by what is called

“complete compensation”; that is to say, an operation

can be compensated for by an inverse operation. If

marbles, for example, are divided into subgroups, the

child can grasp intuitively that the original collection of

marbles can be restored by being added back together

again. The child tips a balance scale too far with a

weight and then searches systematically for a lighter

weight or for something with which to get the scale

rebalanced. He may carry reversibiliry too far by assuming that a piece of paper, once burned, can also be restored.

With the advent of concrete operations, the child

develops an internalized structure with which to operate. In the example of the balance scale, the structure is

a serial order of weights that the child has in his mind.

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READINESS FOR LEARNING

Such internal structures are of the essence. They are the

internalized symbolic systems by which the child represents the world, as in the example of the pinball machine

and the angles of incidence and reflection. It is into the

language of these internal structures that one must translate ideas if the child is to grasp them.

But concrete operations, though they are guided by

the logic of classes and the logic of relations, are means

for structuring only immediately present reality. The

child is able to give structure to the things he encounters,

but he is not yet readily able to deal with possibilities

not directly before him or not already experienced.

This is not to say that children operating concretely

are not able to anticipate things that are not present.

Rather, it is that they do not command the operations

for conjuring up systematically the full range of alternative possibilities that could exist at any given time. They

cannot go systematically beyond the infortnation given

them to a description of what else might occur. Somewhere between ten and fourteen years of age the child

passes into a third stage, which is called the stage of

“formal operations” by the Geneva school.

Now the child’s intellectual activity seems to be

based upon an ability to operate on hypothetical propositions rather than being constrained to what he has

experienced or what is before him. The child can now

think of possible variables and even deduce potential

relationships that can later be verified by experiment or

observation. Intellectual operations now appear to be

predicated upon the same kinds of logical operations

that are the stock in trade of the logician, the scientist,

or the abstract thinker. It is at this point that the child

37

THE PROCESS OF EDUCATION

is able to give formal or axiomatic expression to the concrete ideas that before guided his problem-solving but

could not be described or formally understood.

Earlier, while the child is in the stage of concrete

operations, he is capable of grasping intuitively and

concretely a great many of the basic ideas of mathematics,

the sciences, the humanities, and the social sciences.

But he can do so only in terms of concrete operations.

It can be demonstrated that fifth-grade children can

play mathematical games with rnIes modeled on highly

advanced mathematics; indeed, they can arrive at these

rules inductively and learn how to work with them.

They will flounder, however, if one attempts to force

upon them a formal mathematical description of what

they have been doing, though they are perfectly capable

of guiding their behavior by these rnIes. At the Woods

Hole Conference we were privileged to see a demonstration of teaching in which fifth-grade children very

rapidly grasped central ideas from the theory of functions, although had the teacher attempted to explain to

them what the theory of functions was, he would have

drawn a blank. Later, at the appropriate stage of development and given a certain amount of practice in concrete operations, the time would be ripe for introducing

them to the necessary formalism.

What is most important for teaching basic concepts

is that the child be helped to pass progressively from

concrete thinking to the utilization of more conceptually

adequate modes of thought. But it is futile to attem?t

this by resentin formal explanations based on a 10 IC

tfiat IS !Stant from t e c

s manner of t”

n

e in its implicanons for hlffi. Much teaching

38

READINESS FOR LEARNING

mathematics is 0 this sort. The child learns not to undermathematical order but rat er to apply certain

devices or reci es without understanding their significance and connecte ness.

ey are 0 trans ate mto

IUs way of thinking. Given this inappropriate start, he

is easily led to believe that the important thing is for him

to be “accurate”-though accuracy has less to do with

mathematics than with computation. Perhaps the most

striking example of this type of thing is to be found in

the manner in which the high school student meets

Euclidian geometry for the first time, as a set of axioms

and theorems, without having had some experience with

simple geometric configuratiQllS- and the intuitive means

whereby one deals with them. If the child were earlier

given the concepts and strategies in the form of intuitive

geometry at a level that he could easily follow, he might

be far better able to grasp deeply the meaning of the

theorems and axioms to which he is exposed later.

But the intellectual development of the child is no

clockwork sequence of events; it also responds to influences from the environment, notably the school environment. Thus instruction in scientific ideas, even at the

elementary level, need not follow slavishly the natural

course of cognitive development in the child. It can also

lead intellectual development by providing challenging

but usable opportunities for the child to forge ahead in

his development. Experience has shown that it is worth

the effort to provide the growing child with problems

that tempt him into next stages of development. As

David Page, one of the most experienced teachers of

elementary mathematics, has commented: “In teaching

I have been

from kindergarten to graduate

39

THE PROCESS OF EDUCATION

amazed at the intellectual similarity of human beings at

all ages, although children are perhaps more spontaneous,

creative, and energetic than adults. As far as I am concerned young children learn almost anything faster than

adults do if it can be given to them in terms they understand. Giving the material to them in terms they understand, interestingly enough, turns out to involve knowing the mathematics oneself, and the better one knows

it, the better it can be taught. It is appropriate that we

warn ourselves to be careful ·of assigning an absolute

level of difficulty to any particular topic. When I tell

mathematicians that fourth-grade students can go a

long way into ‘set theory’ a few of them reply: ‘Of

course.’ Most of them are startled. The latter ones are

completely wrong in assuming that ‘set theory’ is intrinsically difficult. Of course it may be that nothing is

intrinsically difficult. We JUSt have to Watt until the

proper point of view and corresponding TanguageTor

..

, ‘n (;jven particular subject matter

or a pamcular concept, It IS easy to ask trivial questions

or to lead the child to ask trivial questions. It is also easy

to ask impossibly difficult questions. The trick is to find

the medium questions that can be answered and that

rake you somewhere. This is the big job of teachers and

textbooks.” One leads the child by the well-wrought

“medium questions” to move more rapidly through the

stages of intellectual development, to a deeper understanding of mathematical, physical, and historical principles. We must know far more about the ways in which

this can be done.

Professor Inhelder of Geneva was asked to suggest

ways in which the child could be moved along faster

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READINESS FOR LEARNING

through the various stages of intellectual development

in mathematics and physics. What follows is part of a

memorandum she prepared for the Conference.

“The most elementary forms of reasoning-whether

logical, arithmetical, geometrical, or physical-rest on

the principle of the invariance of quantities: that the

whole remains, whatever may be the arrangement of its

parts, the change of its form, or its displacement in space

or time. The principle of invariance is no a priori datum

of the mind, nor is it the product of purely empirical

observation. The child discovers invariance in a manner

comparable to scientific discoveries generally. Grasping

the idea of invariance is beset with difficulties for the

child, often unsuspected by teachers. To the young

child, numerical wholes, spatial dimensions, and physical

quantities do not seem to remain constant but to dilate

or contraCt as they are operated upon. The total number

of beads in a box remains the same whether subdivided

into two, three, or ten piles. It is this that is so hard for

the child to understand. The young child perceives

changes as operating in one direction without being able

to grasp the idea that certain fundamental features of

things remain constant over change, or that if they

change the change is reversible.

“A few examples among many used in studying the

child’s concept of invariance will illustrate the kinds of

materials one could use to help him to learn the concept

more easily. The child transfers beads of a known quantity or liquids of a known volume from one receptacle

to another, one receptacle being tall and narrow, the

other flat and wide. The young child believes there is

more in the tall receptacle than the flat one. Now the

41

THE PROCESS OF EDUCATION

nt-“”>

.” -If…

(>G”

\t-G.)

child can be confronted concretely with the nature of

one-to-one correspondence between two versions of the

same quantity. For there is an easy technique of checking: the beads can be counted or the liquid measured in

some standard way. The same operations work for the

conservation of spatial quantity if one uses a set of sticks

for length or a set of tiles for surface, or by having the

child transform the shape of volumes made up of the

same number of blocks. In physics dissolving sugar or

transforming the shapes of balls of plasticene while conserving volume provides comparable instruction. If teaching fails to bring the child properly from his perceptual,

primitive notions to a proper intuition of the idea of

invariance, the result is that he will count without having

acquired the idea of the invariance of numerical quantities. Or he will use geometrical measures while remaining

ignorant of the operation of transitivity-that if A includes B, and B includes C, then A also includes C. In

physics he will apply calculations to imperfectly understood physical notions such as weight, volume, speed,

and time. A teaching method that takes into account the

natural thought processes will allow the child to discover

such principles of invariance by giving him an opportunity to progress beyond his own primitive mode of

thinking through confrontation by concrete data-as

when he notes that liquid that looks greater in volume

in a tall, thin receptacle is in fact the same as that quantity

in a flat, low vessel. Concrete activity that becomes

increasingly formal is what leads the child to the kind

of mental mobility that approaches the naturally reversible operations of mathematics and logic. The child

gradually comes to sense that any change may be men42

READINESS FOR LEARNING

tally cancelled out by the reverse operation-addition by

subtraction-or that a change may be counterbalanced

by a reciprocal change.

“A child often focuses on only one aspect of a phenomenon at a time, and this interferes with his understanding. We can set up little teaching experiments in

such a way that he is forced to pay attention to other

aspects. Thus, children up to about age seven estimate

the speed of two automobiles by assuming that the one

that gets there first is the faster, or that if one passes the

other it is faster. To overcome such errors, one can, by

using toy automobiles, show that two objects starting at

different distances from a finish line cannot be judged

by which one arrives first, or show that one car can pass

another by circling it and still not finish first. These are

simple exercises, but they speed the child toward attending to several features of a situation at once.

“In view of all this it seems highly arbitrary and very

likely incorrect to delay the teaching, for example, of

Euclidian or metric geometry until the end of the primary

grades, particularly when projective geometry has not

been given earlier. So too with the teaching of physics, ;

which has much in it that can be profitably taught at an

inductive or intuitive level much earlier. Basic notions in

these fields are perfectly accessible to children of seven

to ten years of age, provided that they are divorced from

their mathematical expression and studied through materials that the child can handle himself.

“Another matter relates particularly to the ordering

of a mathematics curriculum. Often the sequence of

psychological development follows more closely the

axiomatic order of a subject matter than it does the his-

‘1

43

…J7

S-V->L

T..>V.

….

THE PROCESS OF EDUCATION

torical order of development of concepts within the field.

One observes, for instance, that certain topological notions, such as connection, separation, being interior to,

and so forth, precede the formation of Euclidian and

projective notions in geometry, though the former ideas

are newer in their formalism in the history of mathematics than the latter. If any special justification were

needed for teaching the structure of a subject in its

proper logical or axiomatic order rather than its order

of historical development, this should provide it. This

is not to say that there may not be situations where the

historical order is important from the point of view of

its cultural or pedagogical relevance.

“As for teaching geometrical notions of perspective

and projection, again there is much that can be done by

the use of experiments and demonstrations that rest on

the child’s operational capaciry to analyze concrete experience. We have watched children work with an apparatus in which rings of different diameter are placed at

different positions between a candle and a screen with

a fixed distance between them so that the rings cast shadows of varying sizes on the screen. The child learns how

the cast shadow changes size as a function of the distance

of the ring from the light source. By bringing to the

child such concrete experience of light in revealing situations, we teach him maneuvers that in the end permit

him to understand the general ideas underlying projective geometry.

“These examples lead us to think that it is possible to

draw up methods of teaching the basic ideas in science

and mathematics to children considerably younger than

the traditional age. It is at this earlier age that systematic

44

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instruction can lay a groundwork in the fundamentals

that can be used later and with great profit at the secondary level.

“The teaching of probabilistic reasoning, so very common and important a feature of modem science, is hardly

developed in our educational system before college. The

omission is probably due to the fact that school syllabi

in nearly all countries follow scientific progress with a

near-disastrous time lag. But it may also be due to the

widespread belief that the understanding of random

phenomena depends on the leamer’s grasp of the meaning of the rarity or commonness of events. And admittedly, such ideas are hard to get across to the young. Our

research indicates that the understanding of random

phenomena requires, rather, the use of cenain concrete

logical operations well within the grasp of the young

child-provided these operations are free of awkward

mathematical expression. Principal among these logical

operations are disjunction (‘either A or B is true’) and

combination. Games in which lots are drawn, games of

roulette, and games involving a gaussian distribution of

outcomes are all ideal for giving the child a basic grasp

of the logical operation needed for thinking about probability. In such games, children first discover an entirely

qualitative notion of chance defined as an uncertain

event, contrasted with deductive certainty. The notion

of probability as a fraction of cenainty is discovered

only later. Each of these discoveries can be made before

the child ever learns the techniques of the calculus of

probabilities or the formal expressions that normally go

with probability theory. Interest in problems of a

probabilistic nature could easily be awakened and de-

45

THE PROCESS OF EDUCATION

veloped before the introduction of any statistical

processes or computation. Statistical manipulation and

computation are only tools to be used after intnitive

understanding has been established. If the array of computational paraphernalia is introduced first, then more

likely than not it will inhibit or kill the development of

probabilistic reasoning.

“One wonders in the light of all this whether it might

not be interesting to devote the first two years of school

to a series of exercises in manipulating, classifying, and

ordering objects in ways that highlight basic operations

of logical addition, multiplication, inclusion, serial ordering, and the like. For surely these logical operations are

the basis of more specific operations and concepts of all

mathematics and science. It may indeed be the case that

such an early science and mathematics ‘pre-curriculum’

might go a long way toward building up in the child

the kind of intnitive and more inductive understanding

that could be given embodiment later in formal courses

in mathematics and science. The effect of such an approach would be, we think, to put more continuity into

science and mathematics and also to give the child a

much better and firmer comprehension of the concepts

which, unless he has this early foundation, he will mouth

later without being able to use them in any effective

way.”

A comparable approach can surely be taken to the

teaching of social studies and literature. There has been

little research done on the kinds of concepts that a child

brings to these subjects, although there is a wealth of

observation and anecdote. Can one teach the struCture

of literary forms by presenting the child with the first

46

READINESS FOR LEARNING

part of a Story and then having him complete it in the

form of a comedy, a tragedy, or a farce-without ever

using such words? When, for example, does the idea of

“historical trend” develop, and what are its precursors

in the child? How does one make a child aware of literary style? Perhaps the child can discover the idea of style

through the presentation of the same content written in

drastically different styles, in the manner of Beerbohm’s

Christmas Garland. Again, there is no reason to believe

that any subject cannot be taught to any child at virtually any age in some form.

Here one is immediately faced with the question of

the economy of teaching. One can argue that it might

be better to wait until the child is thirteen or fourteen

before beginning geometry so that the projective and

intnitive first steps can immediately be followed up by

a full formal presentation of the subject. Is it worth

while to train the young inductively so that they may

discover the basic order of knowledge before they can

appreciate its formalism? In Professor Inhelder’s memorandum, it was suggested that the first two grades might

be given over to training the child in the basic logical

operations that underlie instruction in mathematics and

science. There is evidence to indicate that such rigorous

and relevant early training has the effect of making later

learning easier. Indeed the experiments on “learning set”

seem to indicate JUSt that-that one not only learns specifics but in so doing learns how to learn. So important

is training per se that monkeys who have been given

extensive training in problem solving suffer considerably

less loss and recover more qnickly after induced brain

damage than animals who had not been previously thus

47

THE PROCESS OF EDUCATION

educated. But the danger of such early training may be

that it has the effect of training out original but deviant

ideas. There is no evidence available on the subject, and

much is needed.

The act of learning. Learning a subject seems to involve three almost simultaneous processes. First there is

acquisition of new information-often information that

runs counter to or is a replacement for what the person

has previously known implicitly or explicitly. At the

very least it is a refinement of previous knowledge. Thus

one teaches a student Newton’s laws of motion, which

violate the testimony of the senses. Or in teaching a

student about wave mechanics, one violates the student’s

belief in mechanical impact as the sole source of real

energy transfer. Or one bucks the language and its builtin way of thinking in terms of “wasting energy” by introdncing the student to the conservation theorem in

physics which asserts that no energy is lost. More often

the situation is less drastic, as when one teaches the details of the circulatory system to a student who already

knows vaguely or intuitively that blood circulates.

A second aspect of learning may be called transformation-the process of manipulating knowledge to make it

fit new tasks. We learn to “unmask” or analyze information, to order it in a way that permits extrapolation or

interpolation or conversion into another form. Transformation comprises the ways we deal with information

in order to go beyond it.

A third aspect of learning is evaluation: checking

whether the way we have manipulated information is

adequate to the task. Is the generalization fitting, have

we extrapolated appropriately, are we operating proper48

READINESS FOR LEARNING

ly? Often a teacher is crucial in helping with evaluation,

but much of it takes place by judgments of plausibility

without our actually being able to check rigorously

whether we are correct in our efforts.

In the learning of any subject matter, there is usually

a series of episodes, each episode involving the three

processes. Photosynthesis might reasonably comprise

material for a learning episode in biology, fitted into a

more comprehensive learning experience such as learning

about the conversion of energy generally. At its best a

learning episode reflects what has gone before it and

permits one to generalize beyond it.

A learning episode can be brief or long, contain many

ideas or a few. How sustained an episode a learner is

willing to undergo depends upon what the person expects to get from his efforts, in the sense of such external

things as grades but also in the sense of a gain in understanding.

We usually tailor material to the capacities and needs

of students by manipulating learning episodes in several

ways: by shortening or lengthening the episode, by

piling on extrinsic rewards in the form of praise and

gold stars, or by dramatizing the shock of recognition

of what the material means when fully understood. The

unit in a curriculum is meant to be a recognition of the

importance of learning episodes, though many units drag

on with no climax in understanding. There is a surprising lack of research on how one most wisely devises

adequate learning episodes for children at different ages

and in different subject matters. There are many questions that need answers based on careful research, and

to some of these we turn now.

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THE PROCESS OF EDUCATION

‘v-

There is, to begin with, the question of the balance

between extrinsic rewards and intrinsic ones. There has

been much written on the role of reward and punishment in learning, but very little indeed on the role of

interest and curiosity and the lure of discovery. If it is

our intention as teachers to inure the child to longer and

longer episodes of learning, it may well be that intrinsic

rewards in the form of quickened awareness and understanding will have to be emphasized far more in the

detailed design of curricula. One of the least discussed

ways of carrying a student through a hard unit of

material is to challenge him with a chance to exercise

his full powers, so that he may discover the pleasure of

full and effective functioning. Good teachers know the

power of this lure. Students should know what it feels

like to be completely absorbed in a problem. They

seldom experience this feeling in school. Given enough

absorption in class, some students may be able to carry

over the feeling to work done on their own.

There is a range of problems that have to do with

how much emphasis should be placed on acquisition,

transformation, and evaluation in a learning episodegetting facts, manipulating them, and checking one’s

ideas. Is it the case, for example, that it is best to give

the young child a minimum set of facts first and then

encourage him to draw the fullest set of implications

possible from this knowledge? In short, should an episode for a young child contain little new information

but emphasize what can be done to go beyond that bit

on one’s own? One teacher of social studies has had

great success with fourth-graders through this approach:

he begins, for example, with the fact that civilizations

SO

READINESS FOR LEARt-lING

have most often begnn in fertile river valleys-the only

“fact.” The students are encouraged in class discussion

to fignre out why this is the case and why it wonld be

less likely for civilizations to start in mountainous country. The effect of this approach, essentially the technique of discovery, is that the child generates information on his own, which he can then check or evaluate

against the sources, getting more new information in

the process. This obviously is one kind of learning episode, and doubtless it has limited applicability. What

other kinds are there, and are some more appropriate

to certain topics and ages than others? It is not the case

that “to learn is to learn is to learn,” yet in the research

literature there appears to be little recognition of differences in learning episodes.

With respect to the optimum length of a learning

episode, there are a few commonsense things one can

say about it, and these are perhaps interesting enough

to suggest frnieful research possibilities. It seems fairly

obvious, for example, that the longer and more packed

the episode, the greater the pay-off must be in terms of

increased power and understanding if the person is to

be encouraged to move to a next episode with zest.

Where grades are used as a substitute for the reward

of understanding, it may well be that learning will cease

as soon as grades are no longer given-at graduation.

It also seems reasonable that the more one has a sense

of the structure of a subject, the more densely packed

and longer a learning episode one can get through without fatigne. Indeed, the amount of new’ information in

any learning episode is really the amount that we cannot

qnite fit into place at once. And there is a severe limit,

51

THE PROCESS OF EDUCATION

as we have already noted, on how much of such unassimilated information we can keep in mind. The estimate is that adults can handle about seven independent

items of information at a time. No norms are available

for children-a deplorable lack.

There are many details one can discuss concerning

the shaping of learning episodes for children, but the

problems that have been mentioned will suffice to give

their flavor. Inasmuch as the topic is central to an understanding of how one arranges a curriculum, it seems

obvious that here is an area of research that is of the

first importance.

The “spiral curriculum.” If one respects the ways of

thought of the growing child, if one is courteous

enough to translate material into his logical forms and

challenging enough to tempt him to advance, then it

is possible to introduce him at an early age to the ideas

and styles that in later life make an educated man. We

might ask, as a criterion for any subject taught in primary school, whether, when fully developed, it is worth

an adult’s knowing, and whether having known it as a

child makes a person a better adult. If the answer to

both questions is negative or ambiguous, then the material is cluttering the curriculum.

If the hypothesis with which this section was introducedis true-that any subject can be taught to any

child in some honest form-then it should follow that

a curriculum ought to be built around the great issues,

principles, and values that a society deems worthy of

the continual concern of its members. Consider two

examples-the teaching of literarure and of science. If

it is granted, for example, that it is desirable to give

S2

READINESS FOR LEARNING

children an awareness of the meaning of human tragedy

and a sense of compassion for it, is it not possible at the

earliest appropriate age to teach the literarure of tragedy

in a manner that illuminates but does not threaten?

There are many possible ways to begin: through a retelling of the great myths, through the use of children’s

classics, through presentation of and commentary on

selected films that have proved themselves. Precisely

what kinds of materials should be used at what age with

what effect is a subject for research-research of several

kinds. We may ask first about the child’s conception of 41.,. “••.1

tragic. and here one might proceed in mucn tne same 1;’, …. Or

“”ay that Piaget and his colleagues have proceeded In

srudying the child’s conception of physical causality, . tcH”1

of morality, of number, and the rest. It is only when ‘of

we are e ui ed with such knowledge that we wdl be eJ.Jc..

inaositio

wtec’

ever we present to him into his own su Jectlve terms.

Nor need we wait for all the research findings to be in

before proceeding, for a skillful teacher can also experiment by attempting to teach what seems to be inruitively

right for children of different ages, correcting as he

goes. In time, one goes beyond to more complex versions

of the same kind of literarure or simply revisits some of

the same books used earlier. What matters is that later

teaching build upon earlier reactions to literarure, that

it seek to create an ever more explicit and marure understanding of the literarure of tragedy. Any of the great

literary forms can be handled in the same way, or any

of the great themes-be it the form of comedy or the

theme of identity, personal loyalty, or what not.

So too in science. If the understanding of number,

53

THE PROCESS OF EDUCATION

measure, and probability is judged crucial in the pursuit

of science, then instruction in these subjects should begin

as intellectually honestly and as early as possible in a

manner consistent with the child’s forms of thought. Let

the topics be developed and redeveloped in later grades.

Thus, if most children are to take a tenth-grade unit in

biology, need they approach the subject cold? Is it not

possible, with a minimum of formal laboratory work if

necessary, to introduce them to some of the major biological ideas earlier, in a spirit perhaps less exact and more

intuitive?

Many curricula are originally planned with a guiding

idea much like the one set forth here. But as curricula

are actually executed, as they grow and change, they

often lose their original form and suffer a relapse into

a certain shapelessness. It is not amiss to urge that acmal

curricula be reexamined with an eye to the issues of

continuity and development referred to in the preceding

pages. One cannot predict the exact forms that revision

might take; indeed, it is plain that there is now available

too little research to provide adequate answers. One can

only propose that appropriate research be undertaken

with the greatest vigor and as soon as possible.

54

4

INTUITIVE AND ANALYTIC THINKING

MUCH has been said in the preceding chapters

about the importance of a student’s intuitive, in contrast

to his formal, understanding of the subjects he encounters. The emphasis in much of school learning and student examining is upon explicit formulations, upon the

ability of the student to reproduce verbal or numerical

formulae. It is not clear, in the absence of research,

whether this emphasis is inimical to the later development of good intuitive understanding-indeed, it is even

unclear what constitutes intuitive understanding. Yet we

can distinguish between inarticulate genius and articulate

idiocy-the first represented by the student who, by his

operations and conclusions, reveals a deep grasp of a subject but not much ability to “say how it goes,” in contrast

to the student who is full of seemingly appropriate words

but has no matching ability to use the ideas for which

the words presumably stand. A careful examination of

the nature of intuitive thinking might be of great aid to

charged with curriculum construction and teachmg.

Mathematicians, physicists, biologists, and others stress

the value of intuitive thinking in their respective areas.

In mathematics, for example, intuition is used with two

rather different meanings. On the one hand, an individual is said to think intuitively when, having worked for

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