| Summary: | 碩士 === 國立新竹教育大學 === 數理教育研究所 === 98 === This study is to compare the differentiation between Greatest Common Factor ( GCF) and Least Common Multiple (LCM) by Item Response Theory(IRT). Our study subject is the 1st grade students from one of the junior high schools in Taipei. The number of valid samples is 317. “The questionnaire survey of GCF and LCM “ was used as our study tool. The questions in this survey include calculation and application.
According to the result of the study, we have the following findings: (1) The students’ ability of direct calculating is better than the ability of contrary calculating when it comes to calculation. The ability of finding GCF is better than LCM; the ability of direct figure solving is better than integer factorization. (2) Students’ ability of solving GCF is better than LCM when it comes to application ability. (3) The degree of difficulty of different scenarios for students from the lowest to the highest is listed in sequence as following: Length, the number of times, volume and insufficiency.
The ability of calculating GCF is significantly better than LCM; however, ability for solving GCF or LCM shows no difference in the scenario of volume. (4) Solving standard question is easier than comparison question when it comes to the ability of using keywords; it indicates that key words do affect students’ judgment on questions; the ability of calculating GCF is better than LCM for both standard questions and comparison questions.
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