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Kenneth R. Conklin, "Wholes and Parts in Teaching," THE ELEMENTARY SCHOOL JOURNAL, LXXIV, 3 (December, 1973), pp. 165-171.
Reprinted from THE ELEMENTARY SCHOOL JOURNAL Volume 74, Number 3,
December 1973 Published by the University of Chicago Press with the
Department of Education of the University of Chicago ©1973 by the
University of Chicago. All rights reserved. Printed in U.S.A.
Wholes and Parts in Teaching
by Kenneth R. Conklin
Boston University,
Boston, Massachusetts
Teachers are utterly dependent on their pupils for
success. No matter how knowledgeable and skillful a teacher may be, he
can impart knowledge to a pupil only if the pupil cooperates.
Knowledge is produced by the knower's private, free, and active
exercise of intelligence: knowledge cannot be delivered in finished
form by someone else. The phrase "learning by discovery" is redundant,
because learning comes only through discovery. Plato, St. Augustine,
and St. Thomas Aquinas demonstrated the use of this principle in
teaching adults knowledge of absolutes. Here we are more concerned
with the use of this principle in teaching children ordinary
understandings, skills, and attitudes. Most teachers may agree that
they need their pupils' active cooperation. Yet, certain teaching
methods that are now gaining widespread popularity conflict with the
idea that pupils are intelligent creatures whose active cooperation is
necessary to the success of teaching, while some valid methods based
on this premise are ignored or misused.
Wholes and parts
Why is it that knowledge cannot be delivered from teacher to pupil in finished
form? Because what can be delivered is
[end page 165 / start page 166]
always one level below what is intended. The explanation is
the same whether we are talking about skills, understandings, or
attitudes: a teacher must communicate by breaking down his subject
matter into smaller pieces and conveying the pieces to the pupil. The
teacher depends on the pupil to put the pieces back together for
himself in the correct manner. Let's take some examples (1).
To teach the skill of writing, we have pupils practice subskills. Pupils learn
to hold a pencil, to shape individual letters, and to make
connections between letters. We depend on the pupil to integrate
these subskills into the smooth performance of the skill of writing.
If a pupil has trouble writing, we point out the things he is doing
wrong and have him practice doing them correctly one by one. Then we
can only hope that he will be able to work these particulars properly
into the total task.
All skills are taught by breaking them into
subskills. Swimming is broken down into floating, breathing,
arm-stroking, and leg-kicking. Reading is broken into recognizing
letters, diphthongs, syllables, and small words. For every skill,
teachers require pupils to practice subskills, but depend on pupils
to integrate subskills into the smooth performance of the total
skill.
To help a pupil understand a generalization ("red"), we deliver
some particulars (stoplight, apple, rose). To convey the notion of an
abstract concept ("money"), we deliver some concrete examples,
(pennies, quarters, dollar bills). To teach the attitude of "respect
for the flag," we instruct pupils to keep the flag from touching the
ground, we teach them to say the Pledge of Allegiance, and we teach
them to sing "The Star-Spangled Banner."
These examples demonstrate a general principle: all skills, under-standings, and attitudes are
taught by breaking a whole into its parts and having pupils master the
parts. In every case the pupil alone can integrate the parts into a
single whole. This act of integration is private and cannot be forced
or guaranteed by anyone but the pupil himself.
Thus, a whole is greater than the sum of its parts. The whole is not merely the
collection of its parts, but also the properly organized integration
of them. The whole gives meaning to the parts, and it is the intuitive
grasping of this meaning that enables a pupil to integrate the parts.
Teacher and pupil have reverse roles: a teacher breaks a whole into
deliverable parts and presents them to the pupil, whose task is then
to accept the parts, internalize them, and integrate them.
Excessive concentration on the parts can block the internalizing and integrating
processes. For this reason rote memorization and recitation must stop
before deeper understanding can begin. When we concentrate on the
parts we block the view of the whole; likewise, when we focus on the
whole we temporarily forget about the parts. Pupils studying a
foreign language must memorize vocabulary and grammatical rules. But
as long as a pupil must refer consciously to what he has memorized,
he will not read or speak
[end page 166 / start page 167]
fluently. The breakthrough to fluency (understanding without translation) occurs
when the pupil stops paying attention to the subsidiary elements of
grammar and vocabulary, and starts paying attention to his
internalized sense of meaning. Smooth performance is always crippled
by worrying about subsidiary elements in skills, understandings, and
attitudes. Analysis and piecemeal mastery of parts can be helpful, but
only if the separate masteries are reintegrated into the whole.
A whole can be broken into parts, each of which can be broken into
subparts, ad infinitum. Likewise, anything regarded as a whole may
later turn out to be only part of a still greater whole. A teacher's
task, then, is not only to break a whole into parts for delivery to a
pupil, but also to decide which level of the analysis is best for the
pupil being taught. More mature pupils are able to understand concepts
at a higher level of abstraction and are distracted and frustrated if
a teacher requires close attention to particulars at too low a level.
Likewise, immature pupils are unable to comprehend subject matter
that is presented at too high a level.
Fallacies in favorite methods
We have seen why rote memorization and recitation may be detrimental
to a pupil's progress if continued for too long. The pupil's attention
remains focused on the parts, and he is prevented from integrating
them into awareness of the whole, which is the object of instruction.
Almost everyone today agrees that rote learning can be useless or even
harmful if carried to excess. But some recent fads in teaching methods
depend on rote learning. Large numbers of new teachers have apparently
learned by rote that rote learning is bad, without understanding why
it is bad and how these popular methods are derived from it.
One populartechnique is called "small-step learning." The idea is to break
up subject matter into the smallest conceivable bits and feed them to
pupils bit by bit. Even the most dull pupil can understand these bits;
and so, we reason, we can feed a child all the bits, thereby making
him understand the big idea.
What happens at best is that the pupil
memorizes all the bits and gives them back to us on demand. The real
test of understanding is to see whether a pupil can tell us a bit that
was not told to him. That would demonstrate that he had integrated the
bits we gave him into a greater whole and had generated the new bit
out of that whole. But if we give the pupil all conceivable bits in
the first place, we cannot rely on the fact that he gives us one back
as proof that he understands the whole.
Programmed materials,
teaching machines, and other forms of small-step learning are based
on rote learning. As already noted, excessive concentration on the
parts can cripple the process of integration, while analysis that is
too simple for a pupil will bore, frustrate, and mislead him.
Small-step learning can help slow learners and may occasionally
improve the efficiency of bright pupils who get stuck at some point,
but small-step
[end page 167 / start page 168]
learning can help only if the size of the steps and the level of delivery are carefully
selected for the individual.
Behavior modification is another
popular technique that can block higher-level understanding. In using
this method, teachers give unruly or inattentive pupils praise,
tokens, or pieces of candy for doing small tasks or parts of tasks
correctly. Pupils can be rewarded for keeping silent for five
minutes, or raising their hands in response to a teacher's question,
or getting to class on time.
There are ethical questions about
behavior modification that go beyond the scope of this paper. For
example, we may criticize behavior modification as a form of
materialistic bribery that leads to brain-washing. What concerns us
here, however, is that the behavior that is rewarded must be
short-term, physically observable, and precisely specified. Thus,
behavior modification is a form of small-step learning and is subject
to the criticisms developed earlier. Pupils have their attention
focused on little pieces instead of what is important, so that
integration to a higher level of awareness is blocked.
The same criticisms apply to some current efforts to improve the overall
effectiveness of schools. In the arrangement known as "performance
contracting," a corporation signs a contract with a school
guaranteeing that by the end of a specified period every pupil will
achieve a promised level on a standardized test. The corporation
receives school-tax money for each child who succeeds, but must
refund the money for each child who fails. The profit motive operates
to create extra effort and efficiency in teaching. However, all the
effort goes into achieving the goals written into the contract.
In performance contracting or in any form of performance-based education,
the goals must be stated as specific, observable, short-range
behaviors. Performance-based education is the newest version of
teaching for the test. The chief flaw is that teachers and pupils are
distracted from large-scale, important, general goals when their
attention is focused on a list of nitty-gritties that only partially
define the goals. The growing new fad called "performance-based
teacher education" is especially hazardous to the profession of
teaching. Professors who educate teachers are under increasing
pressure to focus instruction on the least important, least
generalizable elements of teaching. The long-term result of
performance-based teacher education will be the production of a
generation of teachers who lack professional judgment and
flexibility. Instead of professionals who understand the complexities
of educational problems, we shall have semiskilled craftsmen who can
only reproduce a limited set of behaviors.
Some good methods overlooked
We have seen that the teacher's task is to break a whole
into its parts and deliver the parts, while a pupil's task is to
receive the parts and integrate them. The teacher depends on the pupil
to do the integrating, which is of necessity a private act of creative
intelligence. No teacher can do the
[end page 168 / start page 169]
integrating for a pupil. But teachers can sometimes prod pupils or
lead them toward integration.
One way of promoting integration is to
shock the pupil by doing or saying something unexpected. For example,
pupils who have carefully practiced each procedure to be followed in
case of fire may understand and integrate those procedures when the
bell rings for an unannounced fire drill. Seventh-grade pupils
studying rules of etiquette may suddenly discover how to follow those
rules when attending their first school dance.
A less traumatic way of
fostering integration is to have the pupil witness the correct
performance of the whole, in the hope that he can model or imitate
that performance. Thus, a pupil who is practicing pronunciation of
foreign phrases begins by paying attention to specific movements of
his own lips and tongue, but then watches and listens to a native
speaker.
Since integration is internal and private, the best a teacher
can do is to prod or lead a pupil toward his own discovery. But shock
and modeling are not the only techniques available. We have seen that
correct selection of the teacher's level of delivery is important:
focusing attention at too low a level cripples integration. Can
focusing attention at a level slightly too high promote integration?
The answer is yes, but the explanation is complex.
Wholes have parts, which have subparts, and so on. The phenomenon called "plateau
learning" can now be accounted for. When pupils are learning how to
type, they make steady gains in speed for a while but then make almost
no further gains in speed despite much additional practice. At this
point pupils are at a plateau: they must integrate subsidiary skills
to a new level of wholeness before additional practice will improve
speed. Then, once again speed improves with practice for a while until
another plateau is reached. Plateau learning occurs in reading,
mathematics, and other areas where skills are involved. The
developmental stages described by Freud for personality, by Piaget for
cognition, and by Kohlberg for moral reasoning might be regarded as
plateaus.
When a pupil has reached a plateau, shock and modeling are
two ways of hastening a break-through. Another way is to encourage
pupils to "play around" with the whole above the plateau even though
they have not completely mastered its parts. There is some evidence to
suggest that when a pupil plays with a whole, its parts draw together.
The reason is that a part derives its significance or meaning from
belonging in the whole. Unmastered parts become more understandable
when they are viewed in context.
Three paradoxical but useful
principles of teaching may now be stated as applications of what has
been said here:
1. A skill or a concept of moderate difficulty may be
learned more easily when studied only tangentially, as part of a more
difficult skill or concept, than when studied directly. For example,
pupils who are having difficulty with arithmetic may learn it
painlessly when they study mechanical drawing or modern algebra in
some of the "new
[end page 169 / start page 170]
math" programs. Pupils who have difficulty
learning the grammar of a foreign language, or even the standard form
of their native language, may improve their scores on grammar tests
by stopping the direct study of grammar and learning some
conversations by means of audiolingual methods. Pupils or employees
can carry out instructions more effectively when told the purposes
they serve.
2. Intuitive notation systems can facilitate faster
learning of organized subject matter than standard notation systems,
even counting the time required for pupils to transfer from the
intuitive system to the standard system. For example, pupils learn to
read English faster when the phonetically appealing initial teaching
alphabet is used than when the ordinary alphabet is used, even
counting the time needed later to change from the initial teaching
alphabet to the standard one. As another example, pupils can learn how
to program computers by writing programs for a while In the code
system that is most intuitively appealing to them: ordinary English
(that is, their native language); then, having mastered the general
skill of programming, pupils can easily learn and apply new code
systems such as FORTRAN and COBOL.
3. Pupils whose basic ideas are
mistaken sometimes learn high-level correct ideas faster if
encouraged to build a false system based on their mistaken ideas than
if the pupils are shown their mistakes and required to start all over
with correct ideas. This principle is obviously a corollary of the
previous one, since the pupil's mistaken
basic ideas are probably intuitively appealing to him. The point is
that if a pupil is to gain a sense of depth or logical hierarchy, he
will have to master the skill of moving from one plateau of parts to
the integration of those parts into a whole at the next plateau. This
skill may be mastered more easily if the pupil starts with ideas, even
though mistaken, that seem natural to him. For example, in mathematics
it is important to know how to reason from axioms to more complex
theorems; once this skill is mastered pupils may make rapid progress
regardless of which axioms are chosen as starting points. Pupils can
learn to construct grammatically correct sentences even if their
spelling is incorrect. Indeed, nonsense words can be used as in
'Twas brillig, and the slithy toves
Did gyre and gimble in the wabe [2].
Teachers are utterly dependent on their pupils for success in teaching
skills, understandings, and attitudes. Teachers deliver parts, but
only pupils can integrate the parts to achieve personal knowledge of
the whole, which is the object of instruction. A whole may be only
part of a still greater whole. At any level, focusing on parts for too
long may cripple the process of integrating them into their whole.
Small-step learning, behavior modification, and performance-based
education can therefore be detrimental to a pupil's deeper
achieve-ment. Shock, modeling, and teaching slightly above a pupil's
level can help him master difficult parts and rise to higher plateaus.
[end page 170 / start page 171]
Notes
-----------
1. The discussion of wholes and
parts, personal knowledge, and the manner in which focusing on parts
can hinder their integration into a whole is based on Michael
Polanyi's theory of knowing, found in his books The Tacit Dimension
(Garden City, New York: Doubleday, 1966) and Personal Knowledge
(London: Routledge and Kegan Paul, 1958). Gestalt psychology also
supports what is said here: see Gestalt Psychology by George W.
Hartmann (New York: Ronald Press, 1935). For a more thorough
explanation of how knowledge is communicated, and why a teacher
cannot deliver knowledge to a pupil in finished form, see "Knowledge,
Proof, and Ineffability in Teaching," by Kenneth R. Conklin in
Educational Theory, forthcoming.
2. Lewis Carroll. Through the
Looking-Glass. "The Jabberwocky Poem." In The Annotated Alice, chap.
1, pp. 191-97. Edited by Martin Gardner. New York, New York: Bramhall
House, 1960.
[end of article]
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