Lisa A. Grupe
Norman W. Bray, Ph.D.
University of Alabama at Birmingham

Presented at the 1999 Biennial Meeting of the Society for Research in Child Development in Albuquerque, New Mexico.

Mailing address: Department of Psychology and Civitan International Research Center, SC 313, University of Alabama at Birmingham, Birmingham, AL 35294. Phone: (205) 934-0657, FAX: (205) 975-6330. Send Internet email to: bray@cis.uab.edu

This poster investigates the effects of manipulatives on kindergartner's strategy discovery and use in a simple addition problem solving task.

The subjects were 27 kindergartners (mean age = 6.1 years) in public schools randomly assigned to one of two conditions: the manipulative condition (N=13) where forty small, plastic bears were available and the no manipulative condition (N=14) where no bears were available. Based on a similar microgenetic study conducted by Siegler and Jenkins (1989) and Bray, Huffman, Ward, and Hawk (1994), subjects attended two sessions per week for 12 weeks; there were 12 addition problems in each session (6 small addend, 3 large addend, 3 challenge). Subjects were given no direct strategy instruction. Sessions were videotaped, and a detailed trial-by-trial analysis was conducted.

There was no difference between manipulative conditions on overall accuracy; children without manipulatives were 72% accurate, while children with manipulatives were 80% accurate. Neither was there a difference between manipulative condition on the discovery of five particular strategies (see Table 1) examined in detail: count without verification, successive count, count aloud, count from first addend, and min. Further, children ceased to use the manipulatives approximately halfway through the 12-week study.

Interestingly, children with and without manipulatives used some kind of external aid, whether manipulatives or fingers, with about the same frequency. Children without manipulatives used their fingers on 30% of all trials, while children with manipulatives used the bears on 9% of the trials but used their fingers on 19% of trials for a combined total of 28%. Children in both conditions showed no difference in frequency of strategy use for strategies which require no representation (e.g., count aloud, versions of min and count from first addend where children verbalize the strategy without using fingers or bears); children without manipulatives used these strategies on 19% of all trials, while children with manipulatives used them on 23% of all trials. Too, patterns of strategy use were similar across manipulative condition with children showing decreasing use of the less sophisticated strategies and increasing use of the more advanced strategies as time progressed. Thus educational concerns over whether manipulatives might actually hinder development of strategies seem without merit. Also, manipulatives may provide only a transient counting aid since children chose to stop using them halfway through the study once they had developed sophisticated strategies such as min and retrieval to solve problems.

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STRATEGY	DESCRIPTION OF STRATEGY FOR "HOW MUCH IS 3 + 5?"
Counting Strategies
Count without Verification	Put out 3 fingers/bears, count "1,2,3". Put out 5 fingers/bears, count "1,2,3,4,5". Begin counting again at 1, "1,2,3,4,5,6,7,8".
Successive Count	Count fingers/bears successively by holding them out one-by-one while counting, "1,2,3,4,5,6,7,8"
Count Aloud	Count out loud from 1; no representation.
Count from First Addend	Say "3,4,5,6,7,8" or "4,5,6,7,8", perhaps while putting out one finger/bear for each count.
Min	Count from larger addend by saying, "5,6,7,8" or "6,7,8", perhaps while putting out one finger/bear for each count.

Bray, N. B., Huffman, L. F., Ward, J. L., & Hawk, T. M. (1994). A microgenetic study of addition strategies in young children with and without mental retardation. Paper presented at Gatlinburg Conference on Research and Theory in Mental Retardation and Developmental Disabilities, Gatlinburg, TN.

Siegler, R. S., & Jenkins, E. (1989). How children discover new strategies. Hillsdale, NJ: Erlbaum.