AN ADDITIONAL EXPLANATION FOR PRODUCTION DEFICIENCIES

Jesse L. M. Wilkins

Virginia Polytechnic Institute and State University

wilkins@vt.edu

Arthur J. Baroody

University of Illinois at Urbana-Champaign

baroody@uiuc.edu

Counting out or producing a specified number of objects is a relatively difficult counting task. A common error among young children is a failure to stop the counting process after reaching the specified number (the target). Such no-stop errors have been attributed to two types of memory failures, namely a failure (a) to register or remember the target or (b) to stop counting at the designated target because of a working-memory overload (Resnick & Ford, 1981). However, Baroody (1987) found that production errors occurred even when children could remember the target and hypothesized that a conceptual deficit might be a cause of such errors. Specifically, he argued that production requires what Fuson (1992) calls the “cardinal-count concept” (e.g., understanding that the cardinal term “five” predicts or is equivalent to the outcome of counting a set of five objects).

A case study (Madison, age 2 years, 11 months) was conducted to examine the possibility that production errors are also due to a conceptual deficit. Production errors made by Madison did not appear to be the result of memory failures. That is, testing indicated that he could both register and retain the target and use it to stop a verbal count. However, he exhibited--at best--a shaky understanding of the cardinal-count concept.

References

Baroody, A. J. (1987). Children’s mathematical thinking. NY: Teachers College Press.

Fuson, K. C. (1992). Research on whole number addition and subtraction. In D. Grouws (Ed.). Handbook of research on mathematics teaching and learning (pp. 243-275). NY: Macmillan.

Resnick, L. B., & Ford, W. W. (1981). The psychology of mathematics for instruction. Hillsdale, NJ: Erlbaum.