| Summary: | 碩士 === 國立臺南大學 === 數學教育學系教學碩士班 === 96 === The purpose of this study is to help students understand the concepts of fraction addition and subtraction by unit concept. The researcher believes that the best way to enhance mathematics concepts is to connect the new concept to the old relevant ones and to make the mathematics concepts form a whole connected net. Only learning metacognitvely can make it happen. To learn consistently is the human nature. We use unit concept to connect the new concept of fraction to the old one of whole numbers. By such way, students can understand the concept of fraction more easily and naturally.
In preview-work sheet, we help remind students’ relevant prior concepts, than ask them to solve the new concept problems. In classroom, we let students discuss the idea and the work in the preview-work sheet. After class, we ask the students to write down the journals in order to look back their concepts discussed in class. Postlesson journals help students to connect the concept of fraction to concept of whole numbers by unit concept.
The important findings of this study are as follows:
First: We find out when a student recognizes that all the addition and subtraction are units operation, it is easier for him to assimilate the operations of fractions to the operations of whole numbers. That means the fraction addition and subtraction are the unit operations, and the whole numbers operations are also the unit operations. His learning is consistent. Second: Through learning metacognitiovely, we find out that the students also use unit concept to manage the problems of different denominator fractions which is the mathematics content in fifth grade spontaneously. When they faced the problem 1/2+1/4, they naturally divided 1/2 into two 1/4 in paper in order to find the same unit for addition. They internalize the unit concept in addition and subtraction, so they can really understand the meaning of addition and subtraction both in whole numbers and fractions. Through this learning processes, students found out that one 1/2 equals to two 1/4, that means they made and understand the equivalent fraction 1/2=2/4 naturally. Third: In controlled classes, we find out that the students could do pretty good job in addition and subtraction of same denominators. But they didn’t sense how important role of the unit concept plays in fraction addition and subtraction and didn’t know that the unit of fraction comes from the denominator. As a result, they make wrong deduction
such as “ ＋ ＝ ＝ ”. On the contrary, such wrong deduction won’t happen
in the students of experimental class.
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