| Summary: | 碩士 === 臺中師範學院 === 教育測驗統計研究所 === 91 === ABSTRACT
The purpose of this study is to discuss students’ geometric concept and meta-cognition of quadrilaterals by employing the geometric thinking model developed by Pierre van Hiele and the performance assessment. The Fuzzy Theory-oriented Cognition Structure Analysis will be integrated in the Item Response Theory, in an attempt to improve the analysis method of assessing learner cognition responses proposed by the original model.
The sample of this study is composed of students of 4th, 5th, and 6th grades from three elementary schools in Taichung City, totally 459 students from 12 classes. The Practice Evaluation of Quadrilateral Concept for Elementary School Students, a book designed by the researcher of this study, will be a tool in evaluating middle- and high-graders’ concept and degree of cognition about quadrilaterals. Besides, the Fuzzy Theory-oriented Cognition Structure Analysis will be adopted to reflect learner responses.
The results of the study are as follows
1.The book designed by the researcher has the feature of good test problems in the aspect of easiness, identifiability, credibility, and validity.
2.The performance of their geometric understanding varies greatly from different grades. The higher the grade, the more the students are in high level.
3.The reverse order phenomenon occurs when students pass the test of level n but fail the test of any previous level. In this study, 6.97% of the students show the reverse order phenomenon in their geometric understanding level.
4.The students of different van Hiele levels show significant differences in meta-cognition performance.
5.If the ability of the students in the order group is higher, accumulation is more obvious, the structure more complete. On the contrary, in the chart of students in the reverse order group, accumulation is not obvious and is in a less complete concept structure.
6.The students of low performances in the order group form an incomplete relation structure, and the relations among different concepts are not manifest; students of higher performances form an obvious structure in terms of relative concept problems, and hyponymy is also more evident. In the reverse order group, not only the relation structure is incomplete, hyponymy is also less regular, indicating the concept structure is more disarrayed.
7.The total original scores are fixed, but the cognition structure may vary. This serves as the evidence of the psychometric theories.
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