A Study on Student's Processes of Problem Solving Using Open-ended Geometric Problems in the Middle School

중학교 기하단원의 개방형문제에서 학생의 문제해결과정의 사고 특성에 관한 연구

This study is to investigate student's processes of problem solving using open-ended Geometric problems to understand student's thinking and behavior. One 8th grader participated in performing her learning in 5 lessons for June in 2006. The result of the study was documented according to Polya's four problem solving stages as follows: First, the student tended to neglect the stage of "understanding" a problem in the beginning. However, the student was observed to make it simplify and relate to what she had teamed previously Second, "devising a plan" was not simply done. She attempted to solve the open-ended problems with more various ways and became to have the metacognitive knowledge, leading her to think back and correct her errors of solving a problem. Third, in process of "carrying out" the plan she controled her solving a problem to become a better solver based on failure of solving a problem. Fourth, she recognized the necessity of "looking back" stage through the open ended problems which led her to apply and generalize mathematical problems to the real life. In conclusion, it was found that the student enjoyed her solving with enthusiasm, building mathematical belief systems with challenging spirit and developing mathematical power.

교과서에서 사용되는 문제는 주로 정형화된 폐쇄형의 문제로 학생의 문제해결력을 육성하거나 학생의 자주적인 학습을 촉구하는데 제한적이다. 본 연구는 문제해결력을 육성하기 위해 개방형 문제를 해결해가는 과정을 폴리아의 문제해결단계를 따라 학생에게 나타나는 학습변화를 관찰하였다. 학생은 문제를 더욱 신중히 읽고 이해하는 과정에서 단순화하였고 계획수립과정에선 처음엔 익숙하지 않았지만 다양한 방법으로 해결하려는 시도와 체계적으로 되돌아보는 인지과정을 나타냈으며, 실행과정에서는 오류를 통한 계획수립의 재시도가 일어나 통제가 향상되는 과정을 보였다. 반성단계는 점검만하는 수준을 벗어나 다른 해결방법을 무엇인지 등의 반성단계의 필요성을 인식하였고 개방형문제의 실생활 적용과 일반화하는 과정을 통해 문제 해결력이 더욱 향상됨을 알 수 있었다.