대한수학교육학회지:수학교육학연구 (Journal of Educational Research in Mathematics)

  • 제26권4호
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  • Pages.635-662
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  • 2016
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  • 2288-7733(pISSN)
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  • 2288-8357(eISSN)
대한수학교육학회 (The Korea Society of Educational Studies in Mathematics)
권호 표지

순열 조합 이해 과제에서의 안구 운동 추적 연구

Eye Movements in Understanding Combinatorial Problems

  • 투고 : 2016.08.09
  • 심사 : 2016.11.11
  • 발행 : 2016.11.30
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초록

조합(combinatorics)은 확률적 사고의 기초가 되며 정보, 과학 등 타교과와 연계성이 높은 중요한 영역이지만, 학교 수학에서 학생들이 가장 어려워하는 단원 중 하나이다. 본 연구는 순열 조합 문제의 구조를 나타낼 수 있는 표현식을 도입하여, 문제를 표현식으로 변환하는 대학원생의 안구 운동을 분석함으로써 순열 조합 문장제의 이해 과정과 의미 구조에 따른 난이도 차이를 조사하였다. 연구 결과, 연구참여자들의 순열 조합 문장제 이해 전략은 문제에 대한 수학적 모델을 내적으로 직접 표상하는 전략과 보기에 주어진 표현식과 문제를 비교하여 답을 찾는 전략으로 분류할 수 있었다. 전문가 집단인 연구참여자들은 대상들의 구별성, 중복가능성, 의미 구조에 관한 단어나 수치 정보 등 문제의 핵심정보를 빠르게 파악하고 주의를 기울였다. 의미 구조의 변환이 필요한 문제를 풀 때 학생들은 문제의 핵심정보를 더 많이 보고, 보기의 표현식을 더 오래 응시하며, 문제와 보기 사이의 비교를 더 많이 하는 등 복잡한 인지 처리와 연관된 안구운동 지표가 나타났다. 안구 운동 데이터는 문제 이해 과정에서 연구참여자의 수학적 인지를 분석하는데 유의미한 정보를 제공하였다.

Combinatorics, the basis of probabilistic thinking, is an important area of mathematics and closely linked with other subjects such as informatics and STEAM areas. But combinatorics is one of the most difficult units in school mathematics for leaning and teaching. This study, using the designed combinatorial models and executable expression, aims to analyzes the eye movement of graduate students when they translate the written combinatorial problems to the corresponding executable expression, and examines not only the understanding process of the written combinatorial sentences but also the degree of difficulties depending on the combinatorial semantic structures. The result of the study shows that there are two types of solving process the participants take when they solve the problems : one is to choose the right executable expression by comparing the sentence and the executable expression frequently. The other approach is to find the corresponding executable expression after they derive the suitable mental model by translating the combinatorial sentence. We found the cognitive processing patterns of the participants how they pay attention to words and numbers related to the essential informations hidden in the sentence. Also we found that the student's eyes rest upon the essential combinatorial sentences and executable expressions longer and they perform the complicated cognitive handling process such as comparing the written sentence with executable expressions when they try the problems whose meaning structure is rarely used in the school mathematics. The data of eye movement provide meaningful information for analyzing the cognitive process related to the solving process of the participants.

키워드

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