| Summary: | 碩士 === 國立臺南大學 === 數學教育學系碩士班 === 98 === The purpose of the study is to explore the learning processes and efficacy when the second grade students learned the concepts of four types problems of multiplication and division almost at the same time. The researcher believes that the best way to learn mathematics is to connect the new concepts to the old relevant ones, and also to make the mathematics concepts form a whole constructed, connected net. Multiplication and division are mutually negative concepts in mathematics. If we can make the students learns those concepts in the same problems, we can let students see their connections and relationships. Therefore, the students can understand and combine the concepts. In this study, we use experience, observation, induction and metacognitive teaching approaches to help students learn and understand four types problems of multiplication and division.
In actual teaching, we use metacognitive way to help students learning. First, before teaching we use pre-class learning sheet to remind students’ relevant concepts, and also ask them try to solve the new concept problems. Then in the class, we guide the students to discuss and clarify the concepts in the pre-class sheet. At last, after class we ask students to look back their learning concepts by solving the similar problems and answering the questions in the after-class sheet. Through these three steps learning processes, the students use relevant concepts to solve, to connect new concept problems; clarify their misconceptions through classroom discussing; and consolidate their new concepts by looking back.
The important findings of this study are as follows:
1.Finding the patterns in four types problems helps students abstract the concepts about multiplication and division.
2.Letting the students learn multiplication and division concepts in the same problem helps students see their connections and relationships.
3.The connective learning about multiplication and division concepts helps concepts generalized, and can make students use different, accurate approaches to solve problems.
4. Metacognitive approach learning can make the concepts about multiplication and division connected, generalized, and really understood. Through pre-class sheet, classroom discussion and post-class sheet students look back their learning, their concepts, and then know how to use.
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