One Point of View: Mathematics for the Young Child—Not ArithmeticAuthor(s): Donna M. WolfingerSource: The Arithmetic Teacher, Vol. 35, No. 6, FOCUS ISSUE: Early Childhood Mathematics(February 1988), p. 4Published by: National Council of Teachers of MathematicsStable URL: http://www.jstor.org/stable/41193341 .

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One Point oF X7ÍGCD

Mathematics for the Young Child- Not Arithmetic By Donna M. Wolfinger

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For young children, those in pre- school through first grade, the world is a stage complete with props and scenery, a world to be manipulated and discovered. But because of the emphasis on standardized curriculum and testing, this discovery through manipulation has been seriously cur- tailed in many mathematics programs for young children. Instruction is fo- cusing on correct answers to compu- tational problems. First graders are frequently taught material once cov- ered in the second or third grade, and they learn through paper-and-pencil exercises and memorization that are too abstract for them. Young children are being presented with a mathemat- ics program in which the computa-

■ tions of arithmetic are excluding the I conceptualizations of mathematics. I Because the terms "mathematics" I and "arithmetic" are so often used I interchangeably outside the realm of I early childhood education, a distinc- I tion between these two aspects of a I quantitative program needs to be I made. On the one hand, Baratta- I Lorton (1976) defines arithmetic as I being oriented toward skill develop- 1 ment and mastery, requiring the

I Donna Wolfinger is an associate professor of I science and mathematics education at Auburn I University, Montgomery, AL 36193-0401. Her I major area of interest is the application of I developmental psychology to teaching and cur- ■ riculum development at the preschool and ele- I mentary school levels.

I Readers are encouraged to react to these edi- I torials by writing to the author, with copies to I the Arithmetic Teacher for consideration in I "Readers' Dialogue." Please double-space all I letters that are to be considered for publication. I Editorials from readers are welcomed.

W4Í: W ff 1 teacher to act as a diagnostician and including such topics as symbol rec- ognition, sums and differences, place value, and regrouping. This collection may be viewed as the computation component of the curriculum from a more traditional perspective. Arith- metic may be approached in the early childhood setting through materials and through memorization, but the outcome is the same: a particular an- swer to a particular problem using a structured approach.

On the other hand, Baratta-Lorton defines mathematics as being oriented toward concept development, as hav- ing no pressure for mastery, and as allowing the teacher to act as an ob- server and guide. The mathematics aspect of the curriculum includes ex- ploration of materials, patterning, comparing, graphing, sorting, and classifying. This collection includes far more than the simple manipulation of materials to determine correct an- swers to computational problems. Mathematics is concerned with the development of concepts.

Unfortunately, the trend in many early childhood education settings is toward the inclusion of more and

more arithmetic. This trend needs to be reversed. A sound program dealing with the quantitative aspect of the school program for young children should emphasize mathematics rather than arithmetic, should develop un- derstanding rather than answers, and should generate concepts rather than folders of completed worksheets. Guidance toward understanding through activity rather than pushing toward computational mastery is ap- propriate for young children. Our un- derstanding of the cognitive develop- ment of children as described by Piaget, Kamii, Ginsburg, Copeland, and others requires that we take this approach.

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References Baratta-Lorton, Mary. Mathematics Their

Way. Menlo Park, Calif.: Addison- Wesley Publishing Co., 1976.

Copeland, Richard W. How Children Learn Mathematics. 4th ed. New York: MacMillan Publishing Co., 1984.

Ginsburg, Herbert. Children's Arithmetic: The Learning Process. New York: Van Nostrand Reinhold Co., 1977.

Kamii, Constance. Young Children Reinvent Arithmetic, New York: Teacher's College Press, 1985.

Piaget, Jean. The Child's Conception of Number. New York: W. W. Norton & Co., 1965. W

I 4 Arithmetic Teacher

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