최적화 문제해결 활동에서 “CAS의 도구화”가 교육과정 내용제시 순서에 미치는 영향 = The Influence of Instrumentalization of Computer Algebra System(CAS) on the Sequence of Mathematics Curriculum in the Optimization Problem Solving Activities of CAS

다국어 초록 (Multilingual Abstract)

This study was designed to investigate the possibility that the optimization problem solving activities based on the instrumented CAS can have an influence on the sequence of mathematics curriculum in secondary mathematics education.
Some optimization problem solving activities based on CAS were constructed and executed to eleventh grade(the penultimate year of Korean high school) 7 students for nine class hours.
They have experienced using CAS in mathematics class for three months, but never learned calculus.
The data which consists of classroom observations(audio and video taped) and post-unit interviews with students were analyzed.
In the analysis, with CAS, students can highly deal with the applied optimization problems made up of calculus, cubic equation, solution of radical equation, and graph analysis which never learned. This result shows CAS may have an influence on the sequence of mathematics curriculum in secondary mathematics education.

국문 초록 (Abstract)

본 연구는 중등수학교육에서 도구화된 CAS에 기반한 최적화 문제해결 활동을 통해 CAS가 교육과정 내용제시 순서에 영향을 줄 수 있는지를 분석하기 위해 설계되었다. 이를 위하여 본 연구자는 CAS를 활용한 최적화 문제해결 활동을 구안하였으며 3개월간의 CAS 활용 수업 경험이 있으나 아직 미적분학을 접해 본 적이 없는 고등학교 2학년 7명을 선정하여 총 9차시의 수업을 실시하고, 수업녹화자료와 면담을 통해 학생들의 활동을 분석하였다. 분석 결과, 학생들은 CAS를 이용하여 미 학습된 교육내용인 미분과 삼차방정식, 무리방정식의 해구하기와 그래프 분석이 포함된 최적화 문제해결활동을 수준 높게 다룰 수 있는 것으로 나타나 CAS가 교육과정 내용제시 순서에 영향을 줄 수 있음을 확인할 수 있었다.

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