中文摘要 許多文獻證實「More A─More B法則」、「Same A─Same B法則」、「無限細分法則」、「有限細分法則」等四種直覺法則(intuitive rules)的存在,會影響學童於數學、科學領域上的表現。然而,學童是否會同時擁有這四種直覺法則,或這四種直覺法則是各自獨立存在的,以及這些法則使用情形的分群,甚少見諸於文獻上探討。本研究係以國小五年級學童為對象,藉由SPSS軟體進行直覺法則之相關分析,統整出各直覺法則間的相關程度,並且透過SCM集群分析法(similarity-based robust clustering method),將受測學童於數學直覺法則的使用情形分群,分析結果輔助教師採取同質性分組及補救教學。 經相關分析及集群分析後,茲將研究結果摘述如下: 一、「無限細分法則」與「More A─More B法則」、「Same A─Same B法則」皆為負相關;「有限細分法則」與「More A─More B法則」、「Same A─Same B法則」皆為正相關。 二、藉由SCM演算法找出最佳群數為3群。 三、群組一的學童使用的直覺法則主要是「無限細分法則」;群組二的學童主要是使用「有限細分法則」;而群組三的學童並無主要使用的直覺法則,惟使用最多的是「有限細分法則」。
Abstract The intuitive rule on mathematics education is an important issue. Researches about intuitive rules have flourished the understanding of concept construction for pupils. However, the dependence and relationship of these four rules are rarely investigated. The purpose of this study is to investigate the clustering of rule usage and relationship on intuitive rules for pupils. In this study, the sample is fifth graders and the clustering method is SCM. Each clustered group displays its characteristics on intuitive rule usage. Moreover, the results of this study would provide suggestions and references for teachers on adaptive teaching and remedial instruction. Based on the correlation and clustering analysis, the results are as following: 1. The intuitive rule “Everything can be divided by two” has the negative correlation with “More A-More B” and “Same A-Same B”. And the intuitive rule “Everything comes to an end” has the positive correlation with “More A-More B” and “Same A-Same B”. 2. After finding the clustering by SCM, all the test-takers could be classified into three groups. 3. The primary intuitive rule used by students of groupⅠ is “Everything can be divided by two”. Group II students tend to use the intuitive rule “Everything comes to an end” for problem solving. Group III students, apart from the other two groups, do not use specific intuitive rule.