Sfard의 구상화(Reification) 이론에 근거한 중·고등학생의 이차방정식 근의 공식 개념 형성 수준 분석
An analysis on the secondary students’ conceptualization level of the formula of quadratic equation based on Sfard's reification theory
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In this paper, we applied Sfard's reification theory to analyze the secondary students’ level of conceptualization with regard to the formula of quadratic equation. Through the generation and development of mathematical concepts from a historical perspective, Sfard classified the formulation process into three stages of interiorization, condensation, and reification, and proposed levels of formulation. Based on this theory, we constructed a test tool reflecting the reversibility of the nature of manipulation of Piaget’s theory as a criterion of content judgement in order to grasp students’ conceptualization level of the formula of quadratic equation. By applying this tool, we analyzed the conceptualization level of the formula of quadratic equation of the 9th and 10th graders. The main results are as follows. First, approximately 45% of 9th graders can not memorize the formula of quadratic equation, or even if they memorize, they do not have the ability of accurate calculation to apply for it. Second, high school curriculum requires for students to use the formula of the quadratic equation, but about 60% of 10th graders have not reached at the level of reification that they can use the formula of quadratic equation. Third, as a result of imaginarily correcting the error of the previous concept, there was a change in the levels of 9th graders, and there was no change in 10th graders.
Abstract
In this paper, we applied Sfard's reification theory to analyze the secondary students’ level of conceptualization with regard to the formula of quadratic equation. Through the generation and development of mathematical concepts from a historical perspective, Sfard classified the formulation process into three stages of interiorization, condensation, and reification, and proposed levels of formulation. Based on this theory, we constructed a test tool reflecting the reversibility of the nature of manipulation of Piaget’s theory as a criterion of content judgement in order to grasp students’ conceptualization level of the formula of quadratic equation. By applying this tool, we analyzed the conceptualization level of the formula of quadratic equation of the 9th and 10th graders. The main results are as follows. First, approximately 45% of 9th graders can not memorize the formula of quadratic equation, or even if they memorize, they do not have the ability of accurate calculation to apply for it. Second, high school curriculum requires for students to use the formula of the quadratic equation, but about 60% of 10th graders have not reached at the level of reification that they can use the formula of quadratic equation. Third, as a result of imaginarily correcting the error of the previous concept, there was a change in the levels of 9th graders, and there was no change in 10th graders.
참고문헌 (21)
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