[논문]동적 기하 환경의 문제 해결 과정에서 연속 스펙트럼 활용에 대한 소고

허남구

doi:10.7468/mathedu.2021.60.4.543

동적 기하 환경의 문제 해결 과정에서 연속 스펙트럼 활용에 대한 소고
A study on the use of continuous spectrum in problem solving in a dynamic geometry environment 원문보기

Journal of the Korean Society of Mathematical Education. Series A. The Mathematical Education, v.60 no.4, 2021년, pp.543 - 554

허남구 (순천대학교)

초록
AI-Helper

동적 기하 환경은 학생들의 기하 문제 해결에 긍정적인 역할을 한다. 학생들은 드래깅을 통해 변화 속에서 불변성을 추측할 수 있으며, 분석법은 기하 문제를 해결하는 데 도움을 준다. 하지만 드래깅 활동과 분석법을 활용한 문제 해결은 제한점이 있으며, 연속 스펙트럼은 대안이 될 수 있다. 학생들은 코딩이 결합된 동적 기하 환경에서 프로그래밍을 통해 연속 스펙트럼을 구현할 수 있다. 이에 본 연구에서는 동적 기하 환경의 문제 해결에서 연속 스펙트럼을 활용하는 방안을 제시하였다. 학생들은 문제 해결의 이해 단계에서 시각적으로 표현된 문제 상황을 통해 즉각적으로 이해하고, 계획 단계에서 해결 전략을 수립하고, 반성 단계에서 결과의 점검 및 일반화하는 데 도움을 줄 수 있다.

Abstract ▼ AI-Helper

The dynamic geometric environment plays a positive role in solving students' geometric problems. Students can infer invariance in change through dragging, and help solve geometric problems through the analysis method. In this study, the continuous spectrum of the dynamic geometric environment can be used to solve problems of students. The continuous spectrum can be used in the 'Understand the problem' of Polya(1957)'s problem solving stage. Visually representation using continuous spectrum allows students to immediately understand the problem. The continuous spectrum can be used in the 'Devise a plan' stage. Students can define a function and explore changes visually in function values in a continuous range through continuous spectrum. Students can guess the solution of the optimization problem based on the results of their visual exploration, guess common properties through exploration activities on solutions optimized in dynamic geometries, and establish problem solving strategies based on this hypothesis. The continuous spectrum can be used in the 'Review/Extend' stage. Students can check whether their solution is equal to the solution in question through a continuous spectrum. Through this, students can look back on their thinking process. In addition, the continuous spectrum can help students guess and justify the generalized nature of a given problem. Continuous spectrum are likely to help students problem solving, so it is necessary to apply and analysis of educational effects using continuous spectrum in students' geometric learning.

주제어

표/그림 (16)

그림 [Fig. 1] Activity sheet (Heo, 2021, p. 363)
그림 [Fig. 3] Spectrum in Earth ScienceⅠ(Lee et al., 2018, p. 125)
그림 [Fig. 2] Spectrum in PhysicsⅠ(Kim et al., 2018, p. 104)
$[Fig. 5] Plot of f(z)=<TEX>$\frac{(z-1)(z+1)^2}{(z+i)(z-i)^2}$</TEX> (Poelke & Polthier, 2009, p. 737)$ 그림 [Fig. 5] Plot of f(z)=$\frac{(z-1)(z+1)^2}{(z+i)(z-i)^2}$ (Poelke & Polthier, 2009, p. 737)
그림 [Fig. 4] Line Spectrum in Calculus (Stewart, Clegg, & Watson, 2021, p. 940[Left], p. 1020[Right])
그림 [Fig. 6] Steepest Descent Method (Jeong et al., 2018, p. 71)
그림 [Fig. 7] Continuous Spectrum of Viviani's Theorem
그림 [Fig. 8] Exploration Activity (Heo, 2021, p. 360)
그림 [Fig. 9] Exploration Activity using GSP
그림 [Fig. 10] Continuous Spectrum using GSP
그림 [Fig. 11] Hypothesis : P is a circumcenter of ABC
그림 [Fig. 12] Solution of the task
그림 [Fig. 13] Idea and solution
그림 [Fig. 14] Continuous Spectrum of the task
그림 [Fig. 15] Continuous Spectrum f(P)-d(P,l)-d(P,F)
$[Fig. 16] Continuous Spectrum f(P)=<TEX>$\frac{d(P,F)}{d(P,l)}$</TEX>$ 그림 [Fig. 16] Continuous Spectrum f(P)=$\frac{d(P,F)}{d(P,l)}$

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