解决几何问题的思惟过程

THOUGHT PROCESSES IN SOLVING GEOMETRICAL PROBLEMS

本研究探讨了初中学生解几何题的思惟过程。所用的方法是要求被试证题时出声想,收集他们证题时的口语材料,并对这些材料作了初步的分析。 结果表明: 一、几何问题解决过程往往包含有假设验证的过程。其中,被试如果能从问题的情境中正确地辨认出某种模式,就能唤起与解题有关的知识。 二、两组被试在解题的时间和过程方面有一些差异。甲组被试(解题经验较多)解题的平均时间是乙组被试的三分之一。甲组被试能很快地把他原来熟悉的模式辨认出来。乙组被试(相当于初学者)多半要作一些无效的尝试才有可能正确地认出模式。甲组被试比乙组被试善于交替运用逆推和顺推的搜索策略以及其他有效的策略和办法。

In our experiment we collected protocols from subjects who were solvinggeometrical problem and analyzed them from the point of view of cognitivepsychology. The result shows that:correct and quick recognition of the patterns whichaccesses the necessary knowledge in permanent memory is the key in solvinggeometrical problems. The difference between the students with more experience and those withless experience is that the former recognized patterns more quickly andcorrectly than the latter whose activity showed more trial and error approaches;the former could,in some cases,keep away from interferences,while thelatter suffered from them easily;the former were able to combine variousrelated information for their reasoning while the latter utilized the informa-tion in isolation;the former could trade-off between backward and forwardsearches,while the latter were poor at using backward search.