연속적으로 공변하는 두 양에 대한 추론의 차이가 문제 해결에 미치는 영향
How does the middle school students’ covariational reasoning affect their problem solving?
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There are many studies on ‘how’ students solve mathematical problems, but few of them sufficiently explained ‘why’ they have to solve the problems in their own different ways. As quantitative reasoning is the basis for algebraic reasoning, to scrutinize a student‘s way of dealing with quantities in a problem situation is critical for understanding why the student has to solve it in such a way. From our teaching experiments with two ninth-grade students, we found that emergences of a certain level of covariational reasoning were highly consistent across different types of problems within each participating student. They conceived the given problem situations at different levels of covariation and constructed their own quantity-structures. It led them to solve the problems with the resources accessible to their structures only, and never reconciled with the other’s solving strategies even after having reflection and discussion on their solutions. It indicates that their own structure of quantities constrained the whole process of problem solving and they could not discard the structures. Based on the results, we argue that teachers, in order to provide practical supports for students’ problem solving, need to focus on the students’ way of covariational reasoning of problem situations.
Abstract
There are many studies on ‘how’ students solve mathematical problems, but few of them sufficiently explained ‘why’ they have to solve the problems in their own different ways. As quantitative reasoning is the basis for algebraic reasoning, to scrutinize a student‘s way of dealing with quantities in a problem situation is critical for understanding why the student has to solve it in such a way. From our teaching experiments with two ninth-grade students, we found that emergences of a certain level of covariational reasoning were highly consistent across different types of problems within each participating student. They conceived the given problem situations at different levels of covariation and constructed their own quantity-structures. It led them to solve the problems with the resources accessible to their structures only, and never reconciled with the other’s solving strategies even after having reflection and discussion on their solutions. It indicates that their own structure of quantities constrained the whole process of problem solving and they could not discard the structures. Based on the results, we argue that teachers, in order to provide practical supports for students’ problem solving, need to focus on the students’ way of covariational reasoning of problem situations.
참고문헌 (35)
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