| Summary: | 碩士 === 國立新竹教育大學 === 教育與學習科技學系 === 103 === The purpose of this study was to draw up examination questions with two-tier diagnostic test items of addition and subtraction of fraction with different denominators in fifth graders in elementary school. Through statistical analysis from software of SPSS and TestGraf98 to examine the examination papers and examination questions and from answering situations of each option in examination questions of subjects to explore the real reasons that students choose wrong answers. In addition to helping teachers interpret students’ answering mode, understand the obvious meanings behind test scores, the most important thing is to achieve diagnose students with learning difficulties effectively which can be a reference in remedial teaching for teachers in the future. The results of the study are as follow:
I. The analysis results of coefficient of stability for diagnostic test items reached .000 which had significant level. It meant that there is a significant positive correlation between the first and the second test. Independent-sample t-test of examination papers is significant in statistics which meant that there is a significant difference in answering situations of each examination questions between subjects from high and low score groups. From characteristic curve of analyzing options of examination questions, it found that expect question 1, characteristic curve of options of examination questions of all the other 9 questions shown that it has identification on fifth-grade subjects whose ability are between 25%~75%.
II. Error Type: There are many error patterns in conceptual understanding of addition and subtraction of fraction with different denominators in fifth graders in elementary school (results of this study are coincide with results of related studies proposed by scholars). The findings are listed as follows:
1. The ability of “explaining composing (decomposing) results by using equal amount ” is insufficient.
2. The ability of “explaining composing (decomposing) results of test representation by using per unit quantity” is insufficient.
3. The ability of “illustrating composing (decomposing) by using graphical representation” is insufficient.
4. Conceptual misconception and procedural misconception in calculating (ignoring per unit quantity; integer subtracting integer, denominator subtracting denominator, numerator subtracting numerator directly; integer adding integer, denominator adding denominator, numerator adding numerator directly; big number subtracting small number- subtrahend subtracting minuend; denominator multiplying with each other, numerator subtracting with each other; denominator multiplying with each other, numerator multiplying with each other; denominator multiplying with each other, integer subtracting with each other, numerator subtracting with each other).
5. There is no clear understanding of semantics of word questions and casually using “keyword” to solve problem; however, there is a concept of unit conversion of fraction and correctly finding a common denominator.
6. There is no clear understanding of semantics of word questions and conversion of mixed fraction and improper fraction is wrong (do not understand the meaning of mixed fraction and multiply integer with numerator); however, there is a clear concept of unit of fraction and correctly finding a common denominator.
7. There is no clear understanding of semantics of word questions and conversion of mixed fraction and improper fraction is wrong (adding integer with numerator and then numerator subtracting with each other and denominator subtracting with each other); however, there is a clear concept of unit of fraction.
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