the bane of traditional educational practice and flies in the face of the child's natural
modes of learning.
Horizontal elaboration precedes vertical integration. When children, or adults for that
matter, are learning a particular skill or subject matter, there is a spontaneous tendency to
practice these new acquisitions in as wide an array of situations as possible (cf. Chapter
V1). Children who are learning to read, for example, will practice the "left to right" visual
swing on a wide range of materials including their examination of pictures. Likewise an
adult who is learning a foreign language will practice it on every possible occasion.
When we learn, we want to substantiate our new skills and knowledge by applying them
to as wide a range of new and different situations as we possibly can. This is horizontal
elaboration.
The tendency, indeed necessity, for individual's to elaborate their abilities in the
horizontal direction is sometimes forgotten in education. It often appears as if vertical
acceleration is regarded as more important than horizontal elaboration. Children are
encouraged to move continually to harder and harder problems without ensuring that they
have fully elaborated their abilities at a particular level of difficulty. As a consequence
they may move ahead too rapidly before they have fully consolidated their cognitive
gains.
It is much more natural, however, for children to apply their skills in a wide variety of
domains at the same level. At about the age of seven and eight, children have learned to
classify and order materials. What they need at this point is the opportunity to classify
and order materials of many different kinds. They can begin to distinguish the many
different kinds of leaves, fern patterns, geological formations, and fossil forms. They can
arrange forms of housing and clothing in rough order from ancient to most modern, and
they can order materials according to hardness, softness, durability, and the like. Such
orderings need not be, indeed should not be, numerical but rather ordered according to
qualitative properties.
Exercises of this sort not only expand the child's realm of experience and
representation, they also strengthen his cognitive skills and make further cognitive
growth more easy and substantial. Such activities prepare the child for the quantification
of experience, which, in the absence of such quantification, might be empty and devoid
of real meaning. Once a child has classified and ordered many different kinds of natural
elements, quantification of the physical world follows naturally and is a meaningful next
step in the way of re-presenting experience. But, as we said earlier, qualitative
representation precedes quantitative re-presentation.
As the child elaborates his abilities on many different materials and re-presents his
experience in many different modes, he prepares himself for the vertical integration of his
knowledge. A child who has learned geometric forms, such as circle and square, can
elaborate these skills by looking for circles and squares in all spheres of his experience.
He can discover that coins, wheels, and doughnuts all are circles. Through this
elaboration of his experience he arrives at a general concept of circles that, combined
with general concepts of squares and triangles, will lead naturally to the more general
concept of geometrical forms. The horizontal elaboration of experience multiplies the
variety of the child's encounters with a concept and renders it at once more general and
more susceptible to vertical integration within a broader more abstract conceptualization.
The absolute precedes the relative. In the spontaneous learning of children, the
understanding of relations is always later than the understanding of absolute properties.
The young child first believes that "right" and "left," "up" and "down" are absolute
properties of things. Likewise, a five-year-old who knows that he has a brother
nonetheless argues that his brother does not have a brother. At this stage "having a
brother" is not a reciprocal relation that implies "being a brother." Rather it is like having
blue eyes or brown hair, a "property" of the individual. It is only in late childhood that
most children understand the relational nature of kinship terms.
It is important to say that these absolute ideas are not "wrong" in the same sense that 4
+ 4 = 9 is wrong. The child's absolute ideas of brother and sister are necessary steps in his
construction of relationistic kinship concepts. They are stages along the way to a correct
concept in a way that 4 + 4 = 9 is not. An arithmetic error can be produced by accident,
by inattention, or by incorrect understanding, but an absolutist notion is simply a stage in
a progression toward a more advanced concept.
Attempts to correct such relational errors merely enlarge the child's fears and inhibit
further growth. Relations are hard to learn, and if a child knows that he has a brother,
even in an absolute way, then that is an achievement worthy of praise in and for itself,
PRINCIPLES OF CONNOTATIVE LEARNING
Proximal experience precedes distal experience. Recently I visited a school in which
six- and seven-year-old children were doing a unit on the San Francisco earthquake of
1906. Most of the compositions were little more than copies of the story as it was told by
the teacher. In other schools I have seen children of six or seven doing units on the
planets or on maps of the United States. The problem of all these units, from a
developmental point of view, is that they are far too distant from the child's experience
and level of conceptualization to be comprehended. In order to re-present an experience
meaning- fully, the experience must be within the child's realm of comprehension. But
the San Francisco earthquake, the planets, and the geography of the United States are
beyond the realm of the early elementary school child's understanding. Indeed the
experience itself must be introduced symbolically, and the child's only alternative is
a secondhand representation of what was given him. Not surprisingly, material re-
presented in this way is seldom retained for any length of time and rarely becomes a
useful component of the child's fund of information.
Connotative learning, particularly in children of preschool and elementary school age,
begins with proximal or near experiences. Children attempt to re-present objects, vistas,
animals, plants, and buildings that they can see, feel, touch, smell, and manipulate. They
will learn more connotatively from a trip to a bakery than from hearing about a trip to the
moon. They will learn more from observing a live guinea pig than they will from a story
about dinosaurs. And they will learn more from making a map of their room than they
will from coloring a map of the United States. The most meaningful experiences children
have are those which they can encounter firsthand.
This is not to say, of course, that the child's experiences must be limited to the
proximal, but only that they should begin there. If children are to understand a map of the
United States, they must first understand a map of their immediate environment. After
making maps of the school room, of their homes, of the neighborhood that surrounds
school and home, children have a better sense of the nature of maps and what they
represent, Maps of larger and more distant regions can be presented after the children
have comprehended maps of their immediate environment. The principle that proximal
precedes distal experience is a procedural and sequential one and does not mean that
proximal experience is to be used to the exclusion of distal experience. Rather, it means
that children should learn what is near at hand before they venture to learn what is far a
field.
Interest precedes involvement.
By chance I happened to be in England visiting schools
at the time of Princess Anne's wedding. The schools were closed for the day and the
wedding was at the forefront of newspaper and television discussion. The next day I
visited several schools and found the children to be very much involved in writing,
drawing, and talking about the wedding. Young children liked the Queen and the
carriages, whereas somewhat older children were enthralled by the gowns and uniforms.
What was more natural than to capitalize upon this interest to involve children in a
variety of activities in which they could re-present their exciting memories of the
wedding.
Clearly, children become involved in activities that enable them to pursue and develop
their spontaneous interests. Sometimes these interests derive from the development of
new abilities. The interest of four- and five-year-old children in quantity comparisons of
all sorts (*'who has more") reflects the development of concrete operations during this
age period (cf. Chapter, VI on motivation). It is easy to involve children at this age in
quantity-related activities such as counting and size estimation. Sometimes children's
interests derive from upcoming holidays such as Thanksgiving, Christmas, or Easter.
These can be the occasion for excursions such' as visiting a turkey farm, which can then
be represented in words, graphically, and in movements (imitation of the turkeys). The
child's spontaneous interests are thus guides to experiences that children will attend to
and wish to represent in various ways.
In addition to the spontaneous interests that grow out of events common to all children,
interests develop out of the experiences of particular children or groups of children. If the
children in a particular class visit a railroad yard, doughnut factory, or museum, the
experience will generate spontaneous interest. The interest may not always be what the
teacher expects. Sometimes children at a museum may be more interested in the snack
shop than they are in the museum displays. Sometimes a worm outside the museum may
be more interesting than what the children saw inside. The teacher has to be alert to the
spontaneous interests of children and allow them to. become involved in re-presenting
what is important and significant to them.
Occasionally spontaneous interests emerge out of the child's individual life
circumstances. Perhaps a new baby has arrived, a trip is to be taken, a new car has been
purchased, a new house is to be moved into, or grandparents are to visit. The child has a
genuine need to involve herself in these experiences and to re-present and assimilate
them. In this process she can expand and elaborate many different skills such as writing
and drawing.
Accordingly, whether the spontaneous interests of children come out of their
developing mental abilities, out of upcoming events of general interest, from class
excursions, or from individual circum- stances, they are the prerequisite to the child's
active involvement in connotative activities of many different kinds. Children practice
and extend their vocabulary, reading, and mathematical skills in the process of re-
presenting experiences which elaborate their spontaneous interests.
Fluency precedes accuracy.
When I was learning French, I was petrified to speak it for
fear of making a fool of myself. Fortunately we were living in Switzerland at the time
and I was forced to speak French if I wanted to ask questions and learn anything. I
gathered up my courage and began speaking without worrying too much about grammar
and pronunciation. To my amazement I was able to communicate-there were, to be sure,
grimaces on the part of my French-speaking companions--and this gave me the
confidence to continue speaking. I became fluent and gradually cleaned up my grammar,
syntax, and pronunciation. This is not an unusual experience, but is in the very nature of
connotative learning. Whether we are talking about motor skills such as swimming or
skills of the intellect such as reading, fluency precedes accuracy. In learning to swim, the
most important thing for a child to overcome is his fear of the water, of having his head
in the water. Once he feels comfortable in the water and overcomes his fear of having his
head in the water, he will learn several strokes, such as the dog paddle, and be susceptible
to instruction. He needs to overcome his fear of the water, to be fluent in it, before he can
develop accuracy in swimming. The same is true for many other skills such as bike
riding, skiing, and water skiing.
In academic learning the same holds true. In reading, the child needs to develop a sense
of acquiring meaning before he attains complete accuracy in letter recognition and
pronunciation. The situation is not really that different from learning to speak a foreign
language. The child who is learning to read is afraid he is going to make mistakes and
embarrass himself. Once he gets the courage to read, his errors should be overlooked and
his courage in reading out loud should be applauded. Later, when he feels comfortable in
reading aloud, he can be helped to be more accurate. But initially, while he is gaining the
courage to read out loud, it is much more important to reward his fluency than to be
concerned with his accuracy.
The same principle holds for a child's writing. In the Bush of creating, the child cannot
and should not be bothered by spelling and grammar. What is important are getting his
thoughts down on paper as they tumble out and experiencing writing as a natural mode of
expressing his thoughts. There is plenty of time later to clean up the grammar, spelling,
and syntax. This is the way most writers work, anyway. Getting it down on paper is the
hard part, while "polishing" the rough spots is the finishing touch.
It should be clear from the foregoing remarks that a too early insistence upon accuracy
can inhibit and block connotative learning. Accuracy in any creative endeavor is the
luxury of the last or terminal stage of the effort. To insist on accuracy too soon magnifies
the child's fears about his competence and thus undermines the learning process. In
helping children construct meaning our main task is not to correct errors but to encourage
fluency in communication and expression. Once we do this, children will want to correct
their own spelling and grammar to improve the appearance of their work. Eliminating
errors should be the fun part of expressive work.
Please understand, however, that the principle of fluency preceding accuracy holds true
for connotative learning but not necessarily for operative or figurative learning.
PRINCIPLES OF FIGURATIVE LEARNING
Quality of practice is more important than quantity.
In traditional discussions of
learning much space was devoted to the advantages and to the disadvantages of massed
versus distributed practice in learning. Is it better, for example, for the student to study
regularly all semester long or can he or she do equally well by studying for long hours
several days before the exam) The question presupposes that the kind of knowledge
required by the exam is figurative and that the studying involves memorizing facts,
names, and dates. If this is the case, the question is whether massed or distributed practice
most facilitates memorization. Contemporary opinion, however, suggests that the issue is
more complicated than that because other variables, such as motivation, enter the
equation regarding the effects of practices.
Indeed, it is now recognized that one of the most crucial variables in figurative learning
is motivation and attention. If someone engages in distributed practice but is not really
concentrating, then the practice is not going to be worth much. On the other hand,
intense, highly concentrated practice can be quite effective because it is highly motivated.
But there is a danger here as well. A certain amount of anxiety is healthy to figurative
learning, but too much or too little can interfere with it. In studying regularly for the
exam, there may not be enough anxiety to make studying very profitable. On the other
hand, waiting to the last minute may make the anxiety too high for the studying to be of
much value. Figurative leaning, then, is not necessarily improved by massing or
distributing practice. Such learning is enhanced by attaching sufficient motivation to it to
make it interesting but not so much as to make it emotionally debilitating. One technique
for providing motivation is to provide individual attention. At the Mt. Hope School the
children may spend only about an hour and a half a day in reading, less perhaps than is
spent in the public school. But if they are reading with a student, they are spending the
whole hour and a half on motivated reading, really practicing the task.
In a large classroom, where children cannot be conveniently worked with individually,
children can effectively avoid practice even though they are spending two or three hours
on "reading." The only way to overcome this inefficient practice is through social
motivation and, if possible, individual attention--at least in the beginning. The use of
older children, of teacher aids, of small groups among which the teacher can circulate, are
all means of improving the quality of practice. The improvement comes about as a result
of enhanced social motivation. Once a child acquires attentional skills less individual
attention is required.
Present the skill at the child's level of competency
. Artistic and musical skills, no less
than many academic skills, must often be taught in a figurative way. What is crucial in
introducing such tasks is that the skill being taught is within the limits of the child's
competence. A nice example is the Suzuki music method. Young children are taught to
play the violin and other instruments by ear and in the company of one or both parents,
who must take lessons at the same time. (This method makes use of the attachment
dynamism to be described in the following chapter.) What the Suzuki method builds upon
is the fact that young children can coordinate hand and ear much better than they can
coordinate hand and eye. By building upon this coordination ability, the child is able to
acquire a skill which brings enjoyment to himself and to others. Reading music, on the
other hand, is not taught until much later when children are far along in concrete
operations.
Drawing can also be taught in ways that capitalize on the skills which children do have.
Too often children begin with material that is much too advanced and they attempt to
draw houses, trees, people, and so on. The results are, for the most part, rather
stereotyped and quite unsatisfactory. On the other hand, a program that begins where the
children are, developmentally, can produce quite lovely work. One art teacher I know
starts children out by having them draw straight lines coming up from the bottom of the
page in various directions--a kind of fireworks' display. The effect, particularly with the
use of a colored pencil or two, is quite pleasant. It is a task well within the child's
competence. But one child whom I was observing could not resist putting in the grass and
flowers at the bottom and the blue sky at the top!
Printing is one figurative skill on which children do not usually spend enough time and
which is well within their competence. By the age of five children can begin printing
letters if they demonstrate the necessary motor coordination. Such printing is an excellent
pre-reading exercise and facilitates letter discrimination. Printing also has another
function--it helps the child to recognize the symbolic nature of letters and helps to lessen
some of the strangeness and mysteriousness young children often experience with respect
to printed symbols. When the child discovers that she can make those lines, some of their
mystery and frightening quality is lost.
Overcoming the child's fears and apprehensions about a task is, by the way, one of the
more important reasons for teaching figurative tasks at the level the child can cope with.
When a task is taught which is beyond the child's capabilities, at best the results are
innocuous, like drawings of grass and sky. But at the worst, children can experience so
much frustration and anger that any possible interest in the skill being taught is destroyed.
This often happens when children are given formal instruction in reading before they
have attained concrete operations. Many children in this situation cannot understand what
it is they are being asked to do and some convince themselves that they, not the task, are
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