| Summary: | 碩士 === 國立新竹教育大學 === 應用數學系碩士班 === 96 === Abstract
The goal of this study is to discuss not only the mathematical reasoning norms of the fifth-grade students in the mathematical discussion class ,but also the relation-
ships between the reasoning norms and the concept of the fractions. We gathered data by taking part in the classroom activities ,and described the results in the following parts.
First, we described the mathematical reasoning norms formed in the class.They can be divided into eight parts : problem clarified、solving strategy、conjecture、
explain、rationality、disproof、proof、and generalization. We obtained three norms in “problem clarified”, four norms in” solving strategy”, five norms in “conjecture”, eight norms in” explain”, four norms in “rationality”, four norms in” disproof”, five norms in” proof”, and four norms in” generalization”.
Second, we discuss the relationships between the concept of the fractions and the mathematical reasoning norms. We divided the concept of the fractions into eight parts : equivalent Fractions、expansion of a fraction、reduction of a fraction、unlike denominator fraction addition、unlike denominator fraction subtraction、the fraction multiply by an integer、and the fraction divided by integers .Then we discuss the relation-
ships between the fractions and the mathematical reasoning norms based on these data.
Finally, we found that the forms of the mathematical reasoning norms are similar to the social norms and socialmathematical norms.While the mathematical reasoning norms are only to develop ,they are quite varied. Therefore, we suggest the teachers can build a reasoning discussing-classroom about the mathematical reasoning norms in order to further promote the reasoning ability of the students involved.
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