The Mathematical Education (한국수학교육학회지시리즈A:수학교육)

Korean Society of Mathematical Education (한국수학교육학회)
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Study on recognition of the dependent generality in algebraic proofs and its transition to numerical cases

대수 증명에서 종속적 일반성의 인식 및 특정수 전이에 관한 연구

  • Received : 2013.10.21
  • Accepted : 2014.02.12
  • Published : 2014.02.28
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Abstract

Algebra deals with so general properties about number system that it is called as 'generalized arithmetic'. Observing students' activities in algebra classes, however, we can discover that recognition of the generality in algebraic proofs is not so easy. One of these difficulties seems to be caused by variables which play an important role in algebraic proofs. Many studies show that students have experienced some difficulties in recognizing the meaning and the role of variables in algebraic proofs. For example, the confusion between 2m+2n=2(m+n) and 2n+2n=4n means that students misunderstand independent/dependent variation of variables. This misunderstanding naturally has effects on understanding of the meaning of proofs. Furthermore, students also have a difficulty in making a transition from algebraic proof to numerical cases which have the same structure as the proof. This study investigates whether middle school students can recognize dependent generality and make a transition from proofs to numerical cases. The result shows that the participants of this study have a difficulty in both of them. Based on the result, this study also includes didactical implications for teaching the generality of algebraic proofs.

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References

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