关键信息对正确解决数学应用问题的影响研究

The Effect of Key Information on Mathematics Problem Solving

本研究主要探讨问题中包含的关键信息和解题所需要的相关公式信息对正确解决数学应用问题的影响。八年级(初二)学生按班级分成三组:在实验1组中,明显标示出问题所包含的关键信息;在实验2组中,除了明显标示出问题所包含的关键信息以外,还给出解决问题所需要的相关公式信息;在控制组中,未给出任何信息。要求被试正确列出方程式。结果发现,在两个题目上,实验2组成绩高于实验1组,实验1组又高于控制组,且三组存在显著性差异;然而,在题目1上,实验1组和实验2组无显著性差异;在题目2上,控制组和实验1组无显著性差异。结果表明,虽然关键信息和相关公式信息均对被试正确解决数学应用问题起着重要作用,但是公式信息对题目1的作用较小,关键信息对题目2的作用较小。基于研究结果,对数学教师提出一些教学建议。

This study investigated to what extent the key information in a math problem and the information of relevant formulas essential for solving the problem had an effect on solving it correctly. Three classes of students in Grade 8 participated in the study and were divided into three experimental groups by class. All groups were asked to do two math problems. In Group 1, the key information of the problems was clearly marked. In Group 2, the key information was clearly marked, and the relevant formulas needed to solve the problems were also given. In the control group, no information was given. The subjects were asked to correctly list the equations. The results showed that the scores of the two problems of Group 2 were significantly higher than those of Group 1, and the scores of Group 1 were significantly higher than those of the control group. However, there was no significant difference between the scores of Group 1 and Group 2 in solving Problem 1, and no significant difference between the scores of Group 1 and the control group in solving Problem 2. The results suggested that although both the key information and the information of related formulas played a significant role in correctly solving the math problems, the formula information did not play a significant role in solving Problem 1, and the key information did not play a significant role in solving Problem 2. Implications for mathematics teaching were discussed.