One Point of View: Pressing Problems in Primary Mathematics Programs: Time, Texts, andTestsAuthor(s): Leroy G. CallahanSource: The Arithmetic Teacher, Vol. 33, No. 2 (October 1985), p. 2Published by: National Council of Teachers of MathematicsStable URL: http://www.jstor.org/stable/41192697 .

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One Point OF X7ÍGCO Pressing Problems in Primary Mathematics

Programs: Time, Texts, and Tests

By Leroy G. Callahan

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1985 It is my point of view that the

desired cognitive outcomes of an effective primary mathematics pro- gram are an integral blending of pro- cesses and products. Observable mathematics performance (products) and the thinking strategies construct- ed by children that influence their performance (processes) are mutually inclusive aspects of a balanced pri- mary mathematics program. I would like to consider three forces that can cause some disequilibrium in this blend and balance: time, texts, and tests.

Just as the connoisseur of wines insists that "no wine shall be sold before its time," some of those in early childhood education argue that no mathematics should be taught be- fore its time. They argue that since intellectual development must pre- cede instruction in mathematics, we should delay our teaching of mathe- matics until "it is time." Yet evidence from research is persuasive that in- struction and development are inter- active and mutually influential. Knowledge of children's developmen- tal tendencies should influence our instruction ; appropriate instruction will influence development. The rela- tion between development and in- struction is not linear and unidirec- tional but interactive. We must guard against programs that encourage teachers not to serve any stimulating

Leroy Callahan teaches graduate courses in the psychology and instruction of elementary school mathematics at State University of New York at Buffalo, Buffalo, NY 14260, and serves as a consultant to schools in the improvement of instruction in mathematics.

mathematics before its time. Another problem in our mathemat-

ics programs is quite different; it con- cerns societal pressures to have all children conform to a normative clock. Pressed for time, teachers must often sacrifice activities that encour- age thinking processes. Carefully paced instruction that nurtures under- standing, a rich variety of applications that give sense to the study of mathe- matics, the weaving of mathematics through other subjects, and the posing of probing problems that require time to explore and that give students a glimpse of the power of mathematics are all restricted. Instead children are moved quickly through the shallower aspects of mathematics where per- formance can quickly be influenced. This push for performance can be a bad bargain for our young students over the long haul.

Textbooks are also a force to be reckoned with in primary mathemat- ics programs. Their content tends to be dominated by paper-pencil com- puting skills. Such abilities as rapid mental approximations of sums or re- mainders are increasingly valued, yet texts give little priority to such topics. After the facts of addition and sub- traction have been learned, estima- tions and approximations with larger numbers should be presented prior to work with paper-pencil algorithms. Aside from their direct value, well- designed estimating and approximat- ing activities can help students focus on the holistic character of numbers and operations and curtail "syntac- tic" errors in subsequent work on paper-pencil computing. Current tex- tual development tends to focus stu-

dents' attention on the trees (digit-by- digit processing) before they are aware of the forest (holistic ideas of numbers and operations). Whitehead suggested that curricular experiences should be cyclical in design and move from romance to precision to general- ization. Primary mathematics text- books are not very romantic, move too quickly to precision, and offer little opportunity for generalization.

Tests play an important role in our primary mathematics program, but the tail of the test often wags the body of the program. An overreliance on tests sacrifices some of the important goals of the primary mathematics pro- gram. In the push for excellence and accountability, more tests are being imposed on schools at all levels. The primary grades are not immune. Cre- ative teachers are finding it necessary to teach to the test - often trading cognitive treasures for test trivia.

Just as disturbing are the test-di- rected instructional management sys- tems. Coupled with the computer, these systems bring a gleam to the eye of the accounting-oriented bureau- crat. Security is being able to point to seventy-nine behavioral objectives accomplished at an 80-percent mas- tery level. The critical problem is that these systems reduce the learning process to a single mode of perform- ance. They redefine education from a quest for knowledge and understand- ing to a quest for the one best answer to predetermined tasks. Many of the valuable process outcomes of primary programs are under siege from con- tent easily measured by tests. And this is a pressing problem in primary mathematics, w

2 Arithmetic Teacher

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