| 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 === A study on structure analysis of elementary school fifth graders’ concept of fraction subtraction
Abstract
This study is to create test items on fraction subtraction, and to analyze the test outcome through the related structure figures that are drawn in the Item Relational Structure (IRS) analysis. The expectation is to explore the construction process of elementary school students when they form their equivalent fraction concepts.
The researcher has made references to the present math curriculum of elementary school and foreign studies, In the part of the same denominators, including four subclasses. In the part of different denominators, including three subclasses. According to the above seven subclasses, the researcher creates a test item for the perspective numerator.
The study was done on a class of fifth graders of an elementary school in Taichung city. After the students took the test, the outcome was analyzed with IRSP, which was designed based on IRS with the expectation of getting information through the item relational structure analysis figure. According to the structure figure, several findings are concluded:
In the part of the same denominators, the researcher has found the cognition development of the students has the following orders:
1. Concepts of numerator subtraction,--> concepts of reduction-how to get highest submultiples --> the concepts of numerator subtraction, borrowing, reduction through integral working with subtracting fractions.
2. Concepts of numerator borrowing -->concepts of reduction-how to get highest submultiples --> the concepts of numerator subtraction, borrowing, reduction through integral working with subtracting fractions.
3. The concepts of reduction- the denominator and the numerator related in multiples --> the concepts of numerator subtraction, borrowing, reduction through integral working with subtracting fractions.
In the part of different denominators, the cognition development of the students has the following orders:
The two denominators are the prime numbers --> the two denominators are multiple relative --> the two different denominators have to get a lowest common multiple.
With the findings and the conclusion, the researcher has made some suggestions that teachers and future studies can draw references to.
Keywords: fraction subtraction, Item Relational Structure Analysis
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