Teaching Problem-Solving Heuristics: A Critique of Two Studies

Abstract

The mathematics curriculum innovations of the sixties generated a great deal of research comparing discovery with other teaching methods. It soon became evident that there was widespread disagreement about the definition of discovery and that results were difficult to interpret because many research reports did not make clear what the discovery treatment had been. Further, it was often impossible to learn from the studies the effects of discovery on anything other than overall achievement. Although the absence of consistent and clear research results was not the only reason, there was doubt that discovery teaching ever gained wide classroom acceptance (NACOME, 1975). Are we destined to repeat these same errors, with similar implications for classroom acceptance, in research on the teaching of methods of problem solving? Renewed interest in methods has generated research on comparisons of these with other approaches to teaching problem solving. The parallels with discovery research are already evident, beginning with the lack of a clear or consistent meaning of heuristic and the failure of research reports to define treatments operationally. Two recently reported studies (Bassler, Beers, & Richardson, 1975; Post & Brennan, 1976) illustrate these and other serious problems in doing research on the teaching of heuristics. In neither study were the authors able to establish a sound rationale for the comparison of the methods used. Both seemed to be based on a feeling or intuition that one method ought to be better than the other. The absence of theoretical or empirical bases for hypotheses about treatments raised questions about the application of controlled experimental designs that both studies were so careful to use (although neither study was careful enough to include a true control group in the design). It is interesting that both studies attempted to remove the teacher effect as completely as possible by using written instructional packages. This solution to the difficulties of experimental control has the disadvantage that