Peer-reviewed
Effects of schema acquisition and rule automation on mathematical problem solving transfer
We carried out a series of experiments in which we used algebra transformation and algebra word problems to investigate relations between schema acquisition and rule automation on learning and transfer. We hypothesised that schema acquisition would precede rule automation and that it would have a strong effect on problems similar to initial acquisition problems. We further hypothesised that rule automation would have its primary effect on transfer and that the use of worked examples could facilitate both transfer and performance on similar problems. Experiments 1 and 2 contained simple algebra transformation problems involving the changing of the subject of an equation. The results indicated that subjects whose training included a heavy emphasis on worked examples or an extended acquisition period were better able to solve both similar and transfer problems than were those subjects trained with conventional problems. In Experiment 3, the use of verbal protocols gave some support to the hypotheses. Experiment 4, using algebra word problems, yielded data supporting the hypotheses. We concluded that in mathematical problem solving, schemas and rule automation may facilitate problem solving on different categories of problems, that schema acquisition occurs before rule automation, and that the use of worked examples facilitates the development of both
Downloadable Article, 1987