Application of PIRS and fuzzy clustering on geometrical concept structure's analysis for first to third graders
| Autor: | Ssu-Ting Liu, 劉思玎 |
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| Rok vydání: | 2009 |
| Druh dokumentu: | 學位論文 ; thesis |
| Popis: | 97 Geometry plays an important role in mathematical field under Grade 1-9 Curriculum. The development of students in geometry is affected by pedagogy and being familiar with the concept structure of students is helpful for teachers to design geometrical curriculum and implement their instruction. The purpose of this study is to utilize the polytomous item relational structure (PIRS) and fuzzy clustering analysis on geometrical concept diagnosis. The subjects include 340, 363 and 362 students from first grade to third grade of elementary schools. Beyond the limitation of dichotomous scoring, the polytomous geometrical concept tests are designed according to annual details of Grade 1-9 Curriculum Guidelines. The researcher classifies the whole students into groups by fuzzy clustering analysis and then analyzes the differences between the concept structures of each group displayed by PIRS. From the result of this study, several findings are concluded as following: 1.Every grade is classified into two groups by fuzzy clustering analysis and mastery of all concepts in group 1 of every grade is higher than those in group 2. 2.The concept of “being able to describe or imitate simple plane figures” is the precondition of the concept of “being able to identify, describe and classify three-dimensional shapes and simple plane figures” in both groups on first grade. 3.Linkage from “being able to recognize objects around as angles, straight lines or planes” to “being able to recognize three- dimensional shapes and simple plane figures by the relation of sides” in group 1 is the only relationship on the concept structure of second graders. 4.There are many linkages in group 1 on the concept structure of third graders.Otherwise, the only linkage in group 2 is from “being able to recognize the interior, exterior and border of plane figures” to “being able to recognize and compare the size of angles”. 5. PIRS is feasible for cognition diagnosis. The features of each group and the precondition relationship among concepts are quite varied. Finally, some suggestions and recommendations are provided for teaching and future research. |
| Databáze: | Networked Digital Library of Theses & Dissertations |
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