| Summary: | 碩士 === 國立臺中教育大學 === 數學教育學系在職進修教學碩士學位班 === 96 === The purpose of this study is to apply latent class analysis in analyzing the data of longitudinal study on four fundamental operation of arithmetic concept. The researcher designs pre-test and post-test for fifth graders. This sample includes 391 students, who are from Taichung city, Taichung county and Changhua county. The self-design tool is “the four fundamental operations of arithmetic test” which consists of three components. These components are bracket, rule of operation and rule of left-to-right. Besides, each compomnet includes two parts, which are word problem and calculation problem. According to the results of latent class analysis, it displays the characteristics of changing situation on cognitive structure of four fundamental operations of arithmetic. The research results are as follows.
1. From the results of longitudinal study, it shows that studnets’ performances are better on arithemetic problems than those of word problems.
2. Based on the results of pre-test and post-test, students are not so familiar with using bracket on word problem. It should be also improved on operation rule of computational problems.
3. There are no significant differences between pre-test and post-test, except to rule of left-to-right on world problems.
4. According to the results of latent class, the number groups for pre-test and post-test vary. It also shows that studnets of different groups own different cognitive structures.
5. On comparison with the rule of operation for pre-test and post-test, one can find that students have dissimilar cognitive structures.
The result of this study can provide teachers referencec on remedial teaching and pedagogy for students. Finally, sufggestions and for research are also discussed in this study.
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