| Summary: | 碩士 === 國立臺中教育大學 === 數學教育學系 === 102 === This study aims to investigate the intuitive rules usages about mathematics problems and their correlations with the performance of concepts of factor and multiple for fifth graders. Furthermore, fuzzy clustering is adopted to classify all students in order to analyze the respective intuitive rule usages and compare the differences on performance of concepts of factor and multiple among groups. The results are shown as follow:
1. Students’ belief that a larger number has more factors is revealed. It’s an example of application of the "More A-More B" intuitive rule. However, students tend to believe that a smaller number has more multiples. This result seems to support to the existence of the new "More A-Less B" intuitive rule.
2. The correlations between the intuitive rules usages and the performance of concepts of factor and multiple vary. "More A-More B" and "Habituation" have negative correlation with "factor", "multiple" ,"common factor" and "common multiple". "Same A-Same B" has positive correlation with "factor", "common factor" and "common multiple". "Everything comes to an end" has negative correlation with "multiple", "common factor" and "common multiple", but "Everything can be divided " has positive correlation with them.
3. According to the results of clustering, three clusters display their characteristics on intuitive rule usages. Each cluster has its own performance of concepts of factor and multiple.
The findings of this study could be as references for remedial instruction and curriculum design. And suggestions for future research are provided.
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