Presented at the 1998 Gatlinburg Conference on Research and Theory in Mental Retardation and Developmental Disabilities in Charleston, South Carolina.

Mailing address: Department of Psychology and Civitan International Research Center, SC 313, University of Alabama at Birmingham, Birmingham, AL 35294. Phone: (205) 934-9768, FAX: (205) 975-6330. Send Internet email to: bray@cis.uab.edu

Addition is one academic task that has been frequently studied because it is universally learned by children with and without mild mental retardation in the elementary grades and because children can and do use a variety of strategies to solve addition problems. A microgenetic design, in which children's addition problem solving strategies are observed multiple times over an extended timeframe, permits delineation of developmental increases in the sophistication and usefulness of problem-solving strategies. Changes in strategy use over time (strategy evolution), can also be easily examined (Siegler & Jenkins, 1989).

The present microgenetic study examined how children with and without mental retardation use different strategies to solve simple addition problems. Participants were 9 children with mild mental retardation (M=8.9 years) and 14 children without mental retardation from kindergarten classrooms (M=6.4 years). Pretests showed the two intelligence groups were not significantly different from each other on addition accuracy or strategy use. Children were tested individually and given no strategy instruction. There were two sessions per week for 12 weeks with 12 addition problems per session. Addition problems appeared on a computer screen while the experimenter read them aloud (e.g., "How much is 3 + 5"?). After children answered, they were asked how they had arrived at the answer. Categorization of strategies was adopted from Siegler and Jenkins (1989). The sum strategy involved counting on fingers by first verifying each addend and then recounting all fingers from one. Short-cut sum involved counting fingers from one without first verifying each addend. Count-from-first involved counting from the first addend instead of from one. The min strategy involved counting from the larger of the two addends. Finger recognition involved holding up fingers to represent addends but then retrieving the answer without counting. Decomposition involved breaking down a difficult problem such as 5+3 into an easier one like 4+4. Retrieval was defined as answering without demonstrating any overt counting and explaining it by saying, "I just knew it."

Interestingly, each intelligence group dichotomously broke into low and high accuracy subgroups. The high accuracy group of nine children without mental retardation and four children with mental retardation achieved an average pretest accuracy of 89%. The low accuracy group of five children without mental retardation and five children with mental retardation achieved less than 30% pretest accuracy.

Overall, the two intelligence groups did not significantly differ on four of the six strategies observed: sum, count from first, finger recognition, and retrieval; they significantly differed with respect to frequency of the use of shortcut sum (t=1.63, p < .05) and min (t=-1.62, p < .05). The same general pattern held even when the two intelligence groups were broken into the high and low pretest accuracy groups. In the high pretest accuracy group, children with and without mental retardation differed significantly on the frequency of using shortcut sum (t=1.99, p <.05) and min (t=-1.65, p < .05). In the low pretest accuracy group, children with and without mental retardation only significantly differed on their use of shortcut sum (t=2.40, p < .05).

Strategy evolution is the change in strategy use over time from less to more sophisticated strategy use. Ten children without mental retardation showed strategy change while 4 did not. Of the 10 who showed strategy change, all used counting strategies; seven performed with high accuracy while three performed with low accuracy. Of the four who showed no strategy change, two used counting strategies, and two used retrieval only. Two performed with high accuracy, and two performed with low accuracy. Similarly, all 10 children with mental retardation used one of the six observed strategies. Six showed strategy change and four did not. As in the nonretarded sample, those six children used counting strategies; five performed with high accuracy, while one performed with low accuracy. The four who showed no change used only retrieval, and all performed with low accuracy. Children with and without mental retardation evolved from using less to more sophisticated strategies over a relatively brief period of time in the absence of direct instruction, and overall results indicate remarkable similarity in the types of simple addition strategies they devised.