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數學問題 解決過程에서 나타나는 誤謬에 관한 硏究

Title
數學問題 解決過程에서 나타나는 誤謬에 관한 硏究
Other Titles
(A) Study On The Errors Found In The Course of Solving The Problems of Mathematics : at the level of High - School students
Authors
崔在利
Issue Date
1988
Department/Major
교육대학원 수학교육전공
Keywords
수학문제해결과정오류수학
Publisher
이화여자대학교 교육대학원
Degree
Master
Abstract
Generally, the aim of the mathematical education is to cultivate the mathematical thinking ability. In connection with the mathematical thinking ability, how to drive students to think mathematically can be identified with how to cultivate the mathematical problem - solving ability. For this reason, it is necessary to investigate for the extension of the problem - solving ability. Thus, this thesis intends to analyze and synthesize the highschool students' errors in the process of solving verbal problems in logarithm, To examine closely, we set up research subject as follows: 1. When we observe the problem - solving procedure of the students, what are they showing in the aspect of the achievements? 2. If we divided the students errors which are shown in the precess of problem - solving into patterns, are there differences between the frequency classified by errors and their ability? 3. How did the four-step process presented by Polya apply to the students' problem - solving process? To solve the research subjects, the result of the tests of the verbal problems in logarithm intended for the first or second-year students are as follows: 1. The difference between the grades has not been emerged. In addition, the problems showing high achievement were those of the textual type and the problems showing low achievement were the applied ones related with the real life. 2. There were much correlation between the group of the achievement ability of study and the frequency classified by errors. And the latter showed the degree of the difficulty of each problem. 3. As a result of the analysis of the problem - solving procedure, we can conclude that the students have passed through the four-step process suggested by Polya. As proved above, the mathematics teachers should treat plenty of the applied problems connected with the practical life, develop the students' thinking ability and the logical ratiocinative power. Also they ought to give students a guidance to prevent the common errors which have come into existence in the process of problem -solving. Then the students will come to cultivate the mathematical problem - solving ability.;數學敎育의 目標는 한마디로 數學的으로 思考하는 能力을 기르는 것이다. 그런데 數學的으로 思考하도록 가르친다는 것은 數學的인 안목으로 問題를 解決하는 能力을 開發한다는 것과 동일시 되므로 問題解決能力 伸張을 위한 硏究가 필요하다. 本 論文에서는 대수분야의 文章制 問題를 解決하는 過程에서 高等學校 學生들이 보인 誤謬들을 分析·綜合하고자 한다. 이를 위해서 다음과 같은 硏究問題를 설정하였다. 1. 학생들의 問題에 대한 풀이過程을 살펴보고 일반적으로 成就度가 어떤 樣相을 보이는가? 2. 학생들이 풀이過程에서 보인 誤謬들을 類型別로 나누어 誤謬別 頻度數가 能力別로 다른가? 3. 학생들의 問題풀이 節次에 Polya가 提示한 4단계가 適用되었는가? 이러한 硏究問題를 위해 1 · 2학년을 대상으로 대수분야의 文章制 問題들로 테스트를 실시하였는데, 그 結果는 다음과 같았다. 1. 成就度에서 學年別 差異는 거의 나타나지 않았으며, 成就度가 높은 問題은 敎科書 類型의 問題였고 成就度가 낮은 問題은 實生活과 관련이 있는 應用問題였다. 2. 學業咸就能力別 集團과 誤謬別 頻度數 사이에 깊은 相關關係가 있었으며 誤謬別 頻度數가 各 問題의 困難度를 알 수 있게 해주었다. 3. 풀이過程을 分析해 본 結科, 학생들은 대체로 Polya가 提示한 4단계 過程을 거쳤음을 알 수 있었다. 이와같은 사실은 學校 數學敎育에서 實生活과 관련있는 應用問題를 많이 다루어 學生들의 思考力 및 論理的 推理力을 길러줘야 하며, 이러한 問題를 풀이하는 過程에서 범하기 쉬운 공통적인 誤謬에 대한 豫斷指導를 하여 學生들의 問題解決能力을 伸張시켜 줄 수 있어야 함을 示唆하고 있다.
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