On the Limited Evidence for the Effectiveness of Teaching General Problem-Solving Strategies.

Lawson (1990) summarizes well views that have had considerable currency in the recent past. As he indicates, the opinions he espouses have been held sufficiently widely to have resulted in revisions in some mathematics curricula. Owen and Sweller's (1989) purpose was to suggest that there may be alternative conceptualizations that have both greater theoretical coherence and, more importantly in the present context, vastly more empirical support. This reply will concentrate on the two major sections of Lawson's paper: the evidence concerning the influence of teaching general problem solving and work on transfer. Before discussing these issues, two preliminary points need to be addressed. Firstly, it needs to be pointed out that Lawson is using a definition of a domain-specific strategy that differs from mine. For instance, I would not class means-ends analysis or trying simple cases as examples of domain-specific strategies. These heuristics cover an enormous range of problem domains. A domainspecific strategy works in specific, clearly defined areas only. "If you need to isolate the first pro-numeral of an equation of the form (a + b)/c = d, first multiply out the denominator" is an example of a domain-specific strategy that mathematics students must learn. Readers should note that when I refer to domain-specific knowledge, I am not referring to heuristics such as means-ends analysis. I believe I can sensibly discuss Lawson's points despite differences in definitions. The second preliminary point that needs to be addressed concerns Lawson's indication that his comments are not intended as a critique of Owen and Sweller's analysis of expertise. I doubt that the nature of expertise and the issue of teaching general problem-solving techniques can be separated so easily. The work on expert-novice differences led directly to the hypothesis that expertise consisted of the accumulation of a large store of domain-specific knowledge and strategies (that is why it takes so long to become an expert) and that there were few differences between experts and novices in general strategies. Historically, until about 15 years ago, most cognitive researchers (including myself) assumed that expertise in problem solving resided largely in the acquisition of general problem-solving techniques. For example, early artificial intelligence programs were concerned almost solely with general strategies (e.g., Newell & Simon, 1972). It was the discovery that programs could only be made to perform more like humans by incorporating an enormous knowledge base rather than sophisticated general strategies that led to a reconsideration. (The discovery led also to expert systems.) This reappraisal was expedited by the early work on chess