To Keep Alive The Sacred Spark

Grace M. BurtonDepartment of Education

University of North Carolina at WilmingtonWilmington, North Carolina 28406

John Dewey, in his seminal work How We Think, expressed well whatfocus the education of young children should take when he asserted thatthe teacher’s task is:

to keep alive the sacred spark of wonder and to fan the flame that already glows. Hisproblem is to protect the spirit of inquiry, to keep it from becoming blase from over-ex-citement, wooden from routine, fossilized through dogmatic instruction, or dissipatedby random exercise upon trivial things.’

These words argue for a systematic mathematics curriculum, but onewhich builds on the nature and the interests of the child.From their earliest years, children behave like scientists. At a level ap-

propriate to their mental development they practice all the skills that sci-entists use to advance the world of knowledge. These skills, fostered andencouraged in the schoolroom would help children acquire a commandof the mathematics with far less frustration on the part of teacher andstudent alike than is the norm in traditional mathematics instruction.What does a scientist do? A scientist observes, questions, forms hypo-

theses, collects data to test out these hypotheses, and draws conclusionsbased on the data collected. The child comes to school with a wide ex-perience in all of these areas.

Children seem to be born curious. Long before he can explore theworld with his hands he seeks it with his eyes. His immediate hungersatisfied, the screaming infant of a few minutes ago pulls his toothlessmouth from mother’s breast and gazes steadily at this new place to whichhe has come.Propped in her chair, the baby gurgles with delight as the shadow of

leaves dance on the wall. Two chubby pink objects wave, now in front ofher eyes, now out of sight. She pulls them to her mouth, gnaws on herknuckles and wonders at her control over these fascinating objects.The toddler wiggles on his belly to explore beneath the table, poking

and tasting any objects which lie in reach of his hand. Some taste goodand he smiles; those that don’t, he spits out without ceremony.

In the morning, a four-year-old watches with wonder as. a mixture ismade from powder and hot water. As if by magic, the sweet liquid be-comes a bouncy solid dessert for supper. When he tries the experimentwith baby powder, the miracle doesn’t happen.The five-year-old observes cars passing by his house and ponders what

John Dewey, How We Think (Boston: D.C. Heath, 1910), p. 34.

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would happen if wheels were not round. He makes up a song: "If wheelswere square, we wouldn’t get anywhere." And he sings it again andagain, delighting in his creation.The young child builds a high tower of blocks and calls to Dad to

"come and see." She cries out when it falls, and sheds a tear or two. Butthen she builds another tower, even taller. And another. And another.Then she goes to school, and then she is "taught." Suddenly the child

is not allowed to do, she must learn. She must not wonder^ she mustmemorize. To be curious is to be non-compliant; to experiment maymean a false prediction and, of course, errors are "bad" and must beavoided. Following the lead of curiosity "wastes time."What does the world gain from this elimination of wonder? Was any-

thing ever accomplished except by someone who dreamed and then testedthe dream against the reality of life? Especially in the years of the child’searliest school experience, shouldn’t we try to use, rather than eradicade,the child’s innate sense of wonder? Pencil and paper mathematics pro-grams, however expensive, however bright with cartoon characters, failyoungsters in a fundamental sense�they ignore the fact that childrenlearn by doing.We have all of us lost youth, some of us longer ago than others of us.

Many of us proclaim that the young don’t appreciate youth enough. Theshame of it is we adults don’t appreciate youth either. We pretend that ifadults can learn concepts in a certain way, kindergarteners can learnthem in the same way. If adults can sit quietly at office desks for hours ata stretch, a pigtailed first grader should be able to sit quietly at her deskfor the same amount of time. If adults can learn without talking to theirpeers, the six-year-old should be able to do so as well. For all we applyhis voluminous research on how the young child thinks, Piaget might aswell have saved his papers to start fires with.

It isn’t even as though it were harder, or more expensive, to teach mathin a humane and human way. It takes a little thought and, at first, a littletime. The rewards are tangible, however, if you accept as tangible thegoosebumps you feel as a child whispers,(’Guess what / found out!’’How is a math program which emphasizes the humanness of its young

clients detected? These are some of the distinguishing signs:

Each child has an opportunity to proceed at his/her own rate and, where possible, inhis/her own style.

The focus is on the development of meanings rather than on the memorization of num-ber facts and procedures.

Children drill only on the processes and number facts which they already understand.

Children set challenges for themselves and enjoy trying to meet them.

Children enthusiastically make their own number discoveries.

Children develop power in the use of the numerical processes and errors are acknowl-edged as a necessary part of these developmental processes.

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�iChildren show an awareness of the need for and can comfortably apply mathematics indaily life.

The teacher approaches math lessons in a cheerful frame of mind.

One who wishes to provide a mathematics program in kindergarten,grade one or two which is based on what we know about how childrenlearn will not be able to rely solely on standard textbook series. By theirvery nature, such materials are on the pictorial�if not the abstract�level and children need much experience with real objects before practicewith pictures and symbols is appropriate. A mathematics curriculum thatbuilds on the nature of the child will, therefore, differ from a traditionalprogram of studies in several ways. There will be a minimum of stress onpencil-and-paper activity and a maximum of involvement with real mate-rials both commercial and non-commercial. Instead of a headlong rushto fact memorization, a child-centered mathematics curriculum will placean emphasis on exploration of material and discovery of patterns and in-variants in number and in material.

At the very beginning of a mathematics program, before 2+3=5 iseven mentioned, there is much one can do to help the young child explorethe world of number and measurement. These activities, because they sonaturally occur in the life of the child, may be overlooked as important insetting the stage for mathematics. Some early experiences which help pre-prepare a child to deal with numbers are:

sorting toyssetting the tablewatching adults use money to pay for goods and serviceslistening to stories involving counting, such as The Three Bearssinging counting songs such as "This Old Man"counting out cookies for friendsplaying board namesnoticing the candles are on a birthday cakesharing candy with a friendtalking about how things are alike and how they are different

A child begins the exploration of the world of shape and size by:

stringing beads or buttonscrawling under thingsclimbing up treesrunning around a tablecurling up in a boxwalking up stairsmoving furniture in a roomputting toys awaycrayoning on a piece of paperunpacking groceriestrying on clothespouring sand or water from one container to anotherbalancing heavier and lighter objectsbeing weighed and measured at the doctor’s officebuilding with blocksmaking pudding or popsicles

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A child forms first notions about the meaning of symbols by such ex-periences as:

noticing common symbols such as traffic signs and barber polesidentifying TV station logsseeing letters addressed to the familyhaving clothers marked with his/her namediscussing road signs with a driveridentifying products at the grocery store

These are guides which will assist a teacher in designing and imple-menting a child-centered mathematics program. For the teacher inkindergarten, grade one or grade two Mathematics Their Way2 by MaryBarrata-Lorton will be a most valuable reference. For the teacher ingrades one to six an excellent program is described in Drill and Practiceon the Problem-Solving Level by Robert Wirtz.3 Both of these profes-sional references stress activity approaches designed to help childrenform a solid basis for mathematics learning and to build on early learn-ing in a systematic way. Both offer many suggestions to the teacher forrelated activities, reproductible pages to facilitate children’s record-keep-ing and individual exploration, and sample letters explaining the pro-gram which teachers may duplicate and send home to parents. (All stu-dent instruction in the Wirtz material appear in both Spanish and Eng-lish. Letters to parents are also available in both languages.) Both incor-porate planning guides but, respecting the professional judgment of theirreaders, encourage teachers to go beyond the material presented and/or

to adapt it to their own classroom conditions.Education is currently being shaken by a new force. "Back-to-the-

basics" is its rallying cry. Teachers of young children must assist othersto realize that there is nothing more basic to the intellectual developmentof the child than fostering the ability to solve problems. It is only whenthis has occurred a child can go on to acquire the needed competence andconfidence to apply mathematics to situations that make sense to them.How, then, shall one present mathematics to the young child? As if the

child were a thinking person. "The role of the adult in the classroom isthreefold: It is the role of a provider of material and stimuli as well as ofa ’climate’ which allows for individual and social growth, of a mediatorof experience who looks on every aspect of children’s living as a means oflearning, and of a teacher, whose professional knowledge and skills en-able her to teach at the moment of willingness and ability to learn."4 Theworld will be better for each of us who attempt humanizing mathematicsinstruction for young children, who sign boldly of that dream, and whodo whatever we can to bring it to reality.

2 Addison-Wesley Publishing Company, South Street, Reading, Massachusetts 01867

3 Curriculum Development Associates, Suite 414, 1211 Connecticut Avenue NW, Washington, DC 20036

4 Molly Brearley, The Teaching of Young Children: Some Applications of Piagef’s Learning Theory. New York:

Shocken Books,. 1970, p. 184.