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An Analysis of Example Spaces Constructed by Students in Learning the Area of a Trapezoid based on Dienes' Theory of Learning Mathematics (Dienes의 수학학습이론에 따른 사다리꼴의 넓이 학습에서 학생들이 구성한 예 공간 분석)

Oh, Min Young;Kim, Nam Gyun
- Education of Primary School Mathematics
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- v.24 no.4
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- pp.247-264
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- 2021
The area of a trapezoid is an important concept to develop mathematical thinking and competency, but many students tend to understand the formula for the area of a trapezoid instrumentally. A clue to solving these problems could be found in Dienes' theory of learning mathematics and Watson and Mason' concept of example spaces. The purpose of this study is to obtain implications for the teaching and learning of the area of the trapezoid. This study analyzed the example spaces constructed by students in learning the area of a trapezoid based on Dienes' theory of learning mathematics. As a result of the analysis, the example spaces for each stage of math learning constructed by the students were a trapezoidal variation example spaces in the play stage, a common representation example spaces in the comparison-representation stage, and a trapezoidal area formula example spaces in the symbolization-formalization stage. The type, generation, extent, and relevance of examples constituting example spaces were analyzed, and the structure of the example spaces was presented as a map. This study also analyzed general examples, special examples, conventional examples of example spaces, and discussed how to utilize examples and example spaces in teaching and learning the area of a trapezoid. Through this study, it was found that it is appropriate to apply Dienes' theory of learning mathematics to learning the are of a trapezoid, and this study can be a model for learning the area of the trapezoid.
https://doi.org/10.7468/jksmec.2021.24.4.247 인용 PDF KSCI