Acta Psychologica Sinica

Abstract

Mathematical problem solving as a complex cognitive function requires the interplay of a number of effect factors. That involves: firs, mathematical problem solving is a cognitive function, which means, from the point of view of the information-processing system, it can’t be studied by simple S-R theory. On the contrary, it is the product of an information-processing system, which can be represented as R = f (S × M), where M represents mental representation. Second, the information-processing of mathematical problem solving is effected by a number of factors. Third, procedure knowledge as well as declarative knowledge determines what interpretation will be given of the context of the problem. Finally, Each effect factor such as worked examples and Exercise time interactively develops the ability of problem solving.

However, psychologists seldom understand the respective contribution of each effect factor and their interaction. So we carried out an experiment in which we used mathematical problem to investigate the effects of worked examples and exercise time on skill learning and transfer. The subjects were 96 seventh grade students from a junior middle school. There were eight groups of 12 subjects each. They were part of a complete factorial experimental design based on the three independent variables of ability (high vs. low), practice (short vs. long exercise time), and teaching method (worked examples vs. conventional problem solving during acquisition). The experiment concludes four phases: acquisition phase, similar test phase, transfer test and post-test phase.

The result indicated that errors on each phase problems were almost significant lower for each of the worked-example groups over the equivalent conventional-problem groups; But the differences between the long exercise time groups and the short exercise time groups varied according to the ability of the subjects, the teaching method and the type of errors.

Based on the results, we can conclude that subject trained with worked examples were better able to solve both similar and transfer problems than those subjects trained without worked examples. Exercise time did not ensure to facilitate the skill acquisition and transfer. There were at least three factors effecting its efficiency: guide or feedback; the nature of the task; the IQ and cognitive ability of the subjects.

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