| Summary: | 碩士 === 國立台北師範學院 === 數學暨資訊教育學系(含數學教育碩士班) === 93 === The purpose of this study is to integrate 2 —parameter Item Response Theory and Fuzzy Theory to propose another analytical methodology(IFM) associating with van Hiele Levels of Geometric Thought in triangle , and conduct comparisons with traditional classification method (TCM)based on statistical item passing rate of 2/3,3/4,4/5 . The distribution of students’ levels and the students’ misconceptions in triangle were also investigated。All subjects from North Taiwan were elementary school fourth, fifth, and sixth grade students ; Based on the results, the findings are showed as follows:
1. IFM is better than TCM，The former gives more each student’s developmental information than the later。 IFM shows that all students are classified into 3 categories, students in category III and with high competency are in van Hiele Second Level(V2) of Geometric Thought, students in category II and with medium competency are in van Hiele First Level (V1)of Geometric Thought, and students in category I and with low competency are in van Hiele Zero Level (V0)of Geometric Thought. Most fourth graders are in categories I and II, most fifth and sixth graders are in categories II and III. The results show that most middle grade students are in the medium and low levels, and most senior students are in the medium and high levels.
2. Using item passing rates of 2/3,3/4 ,4/5 as the criteria of classification respectively to show that there are significant differences in the levels of Geometric Thought for fourth, fifth, and sixth graders.
3. There is no significant difference in the performance of triangle for gender. Sixth graders show better performance than fourth graders, fifth graders show better performance than fourth graders, but there is no difference between fifth and sixth graders.
4. The results show that the highest passing rate is in visual recognition items, and the lowest passing rate is in including relationship items and reverse thinking items. Students could be easily affected by figure paradigms when answering.
5. There is no significant difference in errors type of misconceptions for gender, but shows significant difference in grade.
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