Critique of the Thornton Study

Abstract

Most mathematics educators agree on the importance of formal thinking strategies. Brownell (1935) regards such strategies as essential components underlying a meaningful program of instruction. Still, questions exist as to when such strategies should be introduced. Recently, Rathmell (1978) and Thornton (1978) have advocated teaching thinking strategies before drilling on the basic facts. The Thornton study, Emphasizing Thinking Strategies in Basic Fact Instruction (1978), is of prime interest since it represents one of the few empirical studies examining this important issue. Thornton's article would seem to provide strong research evidence that thinking strategies facilitate the learning of basic facts. Indeed, the study cites overwhelming evidence supporting such a claim. However, on closer examination of the Thornton study, several questions arise that threaten its validity. In addition, the written report of the study suffers from lack of clarity, thus minimizing the usefulness of the report (i.e., more information must be provided before replications can be attempted). The first problem one encounters in reading the report is Thornton's discussion of the subjects used in the study. The population for the study consisted of secondand fourth-grade pupils. An experimental and a traditional group were formed within each grade. It is reported that random selection of pupils for groups was not possible. Since complete randomization was not possible one would expect a careful description of the sampling procedures. Yet, Thornton fails to give a clear account of the sampling. Justification is needed to explain how the groups were formed (i.e., Why was a pooling scheme employed? Was there reason to question the equality of the classes?). The facts are further clouded by the use of ambiguous phrases (e.g., For the sample it was necessary to pool intact groups from multilevel classes . etc.). This pervading lack of clarity takes on added significance as one reads further. Analysis of the results raises other questions about the nature of the treatments. The results reflect an overwhelming superiority of the experimental groups over the traditional groups. However, this apparent evidence