The Mathematical Education (한국수학교육학회지시리즈A:수학교육)

Korean Society of Mathematical Education (한국수학교육학회)
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An Analysis of Teachers' Knowledge on the Strategies for Understanding and Solving Equations by Fourth Graders

초등학교 4학년 학생들의 등식 이해 및 해결 전략에 대한 교사의 지식 분석

  • Pang, JeongSuk (Department of Elementary Education (Mathematics Education), Korea National University of Education) ;
  • Lee, Yujin (Daejeon Heungryong Elementary School)
  • Received : 2022.01.22
  • Accepted : 2022.02.11
  • Published : 2022.02.28
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Abstract

The purpose of this study is to explore how well teachers anticipate students to understand and solve equations. For this purpose, a questionnaire of the equal sign was developed, and 20 fourth-grade classes were selected as research participants. Teachers in each class were asked to predict various strategies on how their own students would respond to the questionnaire, and a total of 450 students from the 20 classes solved the questionnaire. As a result of the analysis, the teachers could predict students' computational strategies and relational strategies easily but did not fully understand that some students used both strategies or employed incorrect computational or relational strategies. The students tended to use relational strategies better than the teachers expected. They also employed operational strategies more often than the teachers expected. The teachers predicted that students' strategies would be influenced by the types of the problems such as equation-structure items and equation-solving items, whereas the students were more influenced by the forms of equations in the problems. Based on these results, several implications for the knowledge to which teachers needed to attend were discussed so that elementary school students could enhance the relational understanding of the equal sign.

본 연구의 목적은 학생들의 등식 이해 및 해결 전략에 대해서 교사가 얼마나 잘 예상하는지 탐색하는 것이다. 이를 위해 등호 이해 검사지를 개발하였고, 4학년 20개 학급을 연구대상으로 선정하였다. 각 학급의 교사에게 담당 학생들이 검사지 문항을 어떻게 해결할 것인지 다양한 전략을 예상하게 하고, 실제 학생 전략과 비교·분석하였다. 그 결과 교사들은 전반적으로 학생들의 계산적 전략과 관계적 전략에 대해서는 비교적 쉽게 예상할 수 있었던 반면, 학생들이 계산적 전략과 관계적 전략을 함께 사용하기도 한다는 점, 틀린 계산적 전략이나 틀린 관계적 전략을 사용하기도 한다는 점 등에 대해서는 충분히 이해하지 못하는 것으로 드러났다. 또한, 교사들이 예상한 것보다 학생들은 관계적 전략을 더 잘 사용할 수 있었고, 등식의 형태에 좀 더 영향을 많이 받는 것으로 나타났다. 이와 같은 연구 결과를 토대로 초등학교 학생들이 등호에 대한 관계적 이해를 진작할 수 있도록 교사에게 필요한 지식에 대하여 시사점을 논의하였다.

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