Lisa A. Grupe
Lisa F. Huffman
Laura Barnes
Carrie Robertson
Norman W. Bray, Ph.D.
University of Alabama at Birmingham

Presented at the 1999 Gatlinburg Conference on Research and Theory in Mental Retardation and Development 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) 934-0657, FAX: (205) 975-6330. Send Internet email to: bray@cis.uab.edu

The development of thinking and cognition is often studied by examining how children discover problem-solving strategies in the absence of direct instruction. The present research utilized a microgenetic design, with a high number of problem-solving sessions over a relatively long time period, to determine the exact point at which strategies are discovered by children with and without mental retardation faced with a simple addition task; addition marks the beginning of mathematical learning and provides an excellent context to observe how young children (who are still learning basic math facts) devise problem solving strategies.

While Siegler and Jenkins' (1989) study provided information about how children without mental retardation discover and use addition strategies, the present research extends their work by examining the discovery of addition strategies by children with and without mild mental retardation and provides an empirical base for an expanded view of strategy discovery. Two identical studies were conducted: one with children without mental retardation (N=14), for which data have been collected, analyzed, and are included herein, and one with children with mental retardation (N=9), for which data have been collected but are presently being analyzed in a parallel manner, thereby allowing an extremely detailed examination of strategy discovery between the two groups of children. Importantly, this research included addition and number competence pretests to ensure that the two groups of children had the same level of conceptual number knowledge, thus going beyond the standard mental age/chronological age comparison. After the pretests, children were videotaped individually in 2 sessions per week for 12 weeks with 12 addition problems per session. Addition problems appeared on a monitor while the experimenter read them aloud (e.g., "How much is 3 + 5"?). Once children answered, they were given accuracy feedback but no strategy instruction.

Strategy discovery results from the present research on children without mental retardation are consistent in many ways with the work of Siegler and Jenkins (1989), including their suggestion that strategy discovery may involve cognitive conflict indicated by long latencies on the trial immediately preceding discovery and/or on the discovery trial itself. Discovery of the relatively sophisticated Min strategy (counting from the larger of the two addends in an addition problem) was marked by an increase in solution time for 5 of the 14 children (36%) without mental retardation. While this demonstrates some consistency with Siegler and Jenkins' (1989) view of discovery, it necessarily implies an important inconsistency as well: for 9 of the 14 children (64%) without mental retardation, discovery of Min was not marked by a long latency and was sometimes accompanied by a very short latency. So, while Siegler and Jenkins' subjects presumably experienced conflict exhibited by long latencies around the Min discovery trial, many children without mental retardation in the present study showed no evidence of conflict indicated by a long latency around the discovery trial; in fact, the average latency on the Min discovery trial was only 10.9 sec, similar to the average overall latency of 10.0 sec and considerably less than Siegler and Jenkins' (1989) mean of 16.2 sec.

In exploring possible mechanisms of discovery in the children without mental retardation, we found that while the majority of Siegler and Jenkins' (1989) subjects discovered Min on a small addend problem (where both addends < 6), only 21% of the children in the present study did. These results support the idea that strategy discovery is not always impasse-driven; perhaps a general processing mechanism for discovery is at work on the familiar small addend problems which do not require all the child's available cognitive processing and consequently leave processing room left over to devise new ways to solve problems (Case, 1985). However, 79% discovered Min on a more difficult problem (where the sum exceeded 10), supporting the idea that some type of impasse is beneficial for discovery. Perhaps, in these cases, Belmont and Mitchell's (1987) inverted U-shaped function of task difficulty plays a role since easy or difficult problems did not tend to inspire discovery, but those in between did. Further exploration into possible mechanisms of discovery (e.g., insight , cognitive conflict, strategy transfer) is ongoing, and parallel analyses will be conducted on the children with mental retardation to determine if the same or different mechanisms underlie discovery.