| 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 === 99 === The purpose of this research is to edit a good measurement for “circle and complex graph areas” concept in order to study the reaction and misconception the sixth graders may have while doing the test. The study result will be used as a reference for teaching and a remedy instruction at school. Based on the results of this study, several findings have been concluded as below：
I. The analysis of the test and items：
1. The average item difficulty index of the items is .597, which categorizes this test as the middle slanting simple items.
2. The average item discrimination index of the items is .426, which shows this item with an excellent discrimination.
3. The reliability coefficient of of the Cronbach α of the test is .776, which ensures the test with a greater reliability.
4. The content validity and expert validity of the test are good.
II. The features of the item option characteristic curve of the test：
1. According to the shapes of the correct item option characteristic curve ,there are six different types of the test.
2. According to the item option characteristic curve of each question ,there are three different types of the test.
III. The understanding conditions of the sixth grade students on the circle area and complex graph area concept：
1. Standard measurement of area concept :
About 50 percents of the students must be more careful while they are counting points of figures including non-integral gridded areas.
2. Straight line measurement of area concept :
Most students are familiar with circle and sector area formulas. However, most of them have difficulties in converting the measurement units of circle areas.
3. Based on this research, the score performances of students with foreign
parents and non-foreign parents have no significant difference. As to the
students with different genders, their score performances on “calculating the areas of irregular shapes through counting and composing activities within given squared grids” and “circle area formula” have a significant difference, but not to the rest.
Keywords: area, circle area and complex graph area concept,
item option characteristic curve.
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