| Summary: | 碩士 === 國立屏東教育大學 === 教育心理與輔導學系碩士班 === 95 === Based on the theory of children’s development of the meaning of fraction phrase, the study tried to understand fifth graders and sixth graders’ performance on each sub-concept of equivalence fraction, made a comparison of 5th graders who had and hadn’t learned reduction and extent of a fraction to examine the difference of their performance on each sub-concept, and made a comparison between fifth graders who had learned reduction and extention of a fraction and sixth graders who had learned reduction of fractions to a common denominator to examine the difference of their performance on each sub-concept.
The study selected fifth and sixth graders in two different schools in Keelung City as a subject due to the different materials on math, one was Nenyi；the other Kangshuen. Through written evaluation, the study examined the performance the subject students on three sub-concepts, comparing the theory and the anticipant outcomes of the curriculum to investigate what students learned was either conceptual or operational understanding.
The study came to the following findings:
In the three parts of the questions, fractional unit, two level part-whole relationship of fraction and commensurate unit, the students who had not learned reduction and extention of a fraction scored the highest on fractional unit; the second highest on two level part-whole relationship of fraction and commensurate unit were the most difficult questions for the subject to answer. For those who had learned reduction and extention of a fraction in fifth grade, according to the performance on three sub-concepts, they scored the highest on commensurate unit ; the second highest on the questions of fractional unit, while two level part-whole relationship of fraction were the most difficult questions for the subject to answer. For those who had learned reduction of fractions to a common denominator in sixth grade, the performance on the evaluation of three sub-concepts was the same as that of the fifth graders who had learned reduction and extention of a fraction. Based on the performance of the three different subjects, only the performance of fifth graders who had not learned reduction and extention of a fraction met the anticipant model of the study, while the other two subjects didn’t. From the answers of the subject students with different learning experiences, the study found that when it came to learning equivalence fraction, the students were only in the operational stage instead of reaching the level of conceptual understanding.
According to the above-mentioned findings, the study proposed suggestions for teaching, evaluation and material designs as reference for teachers and editors.
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