部总知识在解决加法文字题中的作用

THE ROLE OF PART-WHOLE KNOWLEDGE IN SOLVING ADDITION WORD PROBLEMS

探讨的问题是部总知识是否制约着算术文字题的解答过程。小学 4年级学生 (192人 )和大学生 (178人 )被要求解答一步加法文字题。实验结果发现 ,正确列式方式受到已知客体集合具体特征的系统性影响 ,尤其是随着年龄的提高和练习程度的深入 ,这种影响越来越明显。这是部总知识作用假设所不能解释的。现根据集合在心理表征中的位置和表征强度解释结果 。

In previous research on addition and subtraction word problems, people argued th at part-whole knowledge plays a crucially important role, which is called part -whole hypothesis. However, there has been little convincing evidence to show t he substantial influence of part-whole knowledge on children's performance. The present experiment was to test the hypothesis. Children in the forth grade of p rimary school and undergraduates were asked to solve one-step addition word prob lems (correct answer is ”a+b”, ”a” referring to the first quantity occurred in p roblem text, ”b” to the second quantity). If the part-whole knowledge that is a type of abstract logic-mathematical knowledge discarding the concrete features of object sets, mediate children's thinking, it could be predicted that the corr ect answer was unanimously ”a+b” or ”b+a” without regard to the concrete fea ture s of object sets and the trend was more pronounced for undergraduates. The resul ts showed that the concrete features of known object sets systematically influen ced the surface of the correct answer, and especially the influence became more and more salient with age and practice, which was called hypothesis of problem f amiliarity on the surface of correct answer. The results were totally inconsiste nt with predictions. Therefore, it is necessary to doubt the part-whole hypothe sis. The present research accounted for the results based on the position of obj ect set in mental representation and representational strength. The instructiona l implication was discussed at the end of this paper.