• 제목/요약/키워드: mathematical problem solving

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수학적 모델링 적용을 위한 문제상황 개발 및 적용 (A Study on Development of Problem Contexts for an Application to Mathematical Modeling)

  • 김민경;홍지연;김혜원
    • 한국수학교육학회지시리즈A:수학교육
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    • 제49권3호
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    • pp.313-328
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    • 2010
  • Mathematical modeling has been observed in the way of a possibility to contribute in improving students' problem solving abilities. One of the important views of real life problem context could be described such as a useful ways to interpret the real life leading to children's abstraction process. The problem contexts for the grade 6 with mathematical modeling perspectives were developed by reviewing the current 7th National Mathematics Curriculum of Korea. Those include the 5 content areas such as number & operation, geometry, measurement, probability & statistics, and pattern & problem solving. One of problem contexts, "Space", specially designed for pattern & problem solving area, was applied to the grade 6 students and analyzed in detail to understand student's mathematical modeling progress.

초등학교 고학년 아동의 정의적 특성, 수학적 문제 해결력, 추론 능력간의 관계 (A Study on Correlations among Affective Characteristics, Mathematical Problem-Solving, and Reasoning Ability of 6th Graders in Elementary School)

  • 이영주;전평국
    • 한국수학교육학회지시리즈C:초등수학교육
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    • 제2권2호
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    • pp.113-131
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    • 1998
  • The purpose of this study is to investigate the relationships among affective characteristics, mathematical problem-solving abilities, and reasoning abilities of the 6th graders for mathematics, and to analyze whether the relationships have any differences according to the regions, which the subjects live. The results are as follows: First, self-awareness is the most important factor which is related mathematical problem-solving abilities and reasoning abilities, and learning habit and deductive reasoning ability have the most strong relationships. Second, for the relationships between problem-solving abilities and reasoning abilities, inductive reasoning ability is more related to problem-solving ability than deductive reasoning ability Third, for the regions, there is a significant difference between mathematical abilities and deductive reasoning abilities of the subjects.

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유사성 구성과 어포던스(affordance)에 대한 사례 연구 -대수 문장제 해결 과정에서- (The Case Study for The Construction of Similarities and Affordance)

  • 박현정
    • 한국수학교육학회지시리즈A:수학교육
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    • 제46권4호
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    • pp.371-388
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    • 2007
  • This is a case study trying to understand from the view of affordance which certain three middle school students perceive an activation of previous knowledge in the course of problem solving when they solve algebra word problems with a previous knowledge. The results of this study showed that at first, every subjects perceived the text as affordance which explaining superficial similarities, that is, a working(painting)situation rather than problem structure and then activated the related solution knowledge on the ground of the experience of previous problem solving which is similar to current situation. The subject's applying process for solving knowledge could be arranged largely into two types. The first type is a numeral information connected with the described problem situation or a symbolic representation of mathematical meaning which are the transformed solution applied process with a suitable solution formula to the current problem. This process achieved by constructing a virtual mental model that indicating mathematical situation about the problem when the solver read the problem integrating symbolized information from the described text. The second type is a case that those subjects symbolizing a formal mathematical concept which is not connected with the problem situation about the described numeral information from the applied problem or the text of mathematical meaning, which process is the case to perceive superficial phrases or words that described from the problem as affordance and then applied previously used algorithmatical formula as it was. In conclusion, on the ground of the results of this case study, it is guessed that many students put only algorithmatical knowledge in their memories through previous experiences of problem solving, and the memories are connected with the particular phrases described from the problems. And it is also recognizable when the reflection process which is the last step of problem solving carried out in the process of understanding the problem and making a plan showed the most successful in problem solving.

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수학적 모델링과 수학화 및 문제해결 비교 분석 (Comparison and Analysis among Mathematical Modeling, Mathematization, and Problem Solving)

  • 김인경
    • 한국수학사학회지
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    • 제25권2호
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    • pp.71-95
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    • 2012
  • 현재 수학교육에서 큰 흐름을 이루고 있는 수학적 모델링, 수학화, 문제해결을 살펴보았다. 먼저, 1990년대 이후 수학교육에서 활발히 연구되기 시작한 수학적 모델과 수학적 모델링을 살펴보았다. 그리고 1970년대 Freudenthal가 주장한 수학화를 분석하여 수학적 모델링과 비교분석하였다. 또한, 1980년대 이후 수학교육의 중심이 된 문제해결도 살펴보고, 이를 수학적 모델링과 비교분석하였다.

한국과 미국 6학년 학생들의 직관적 사고에 의한 수학 문제해결 분석 (An Analysis on the Mathematical Problem Solving via Intuitive Thinking of the Korean and American 6th Grade Students)

  • 이대현
    • 한국수학교육학회지시리즈A:수학교육
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    • 제55권1호
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    • pp.21-39
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    • 2016
  • This research examined the Korean and American $6^{th}$ grade students' mathematical problem solving ability and methods via an intuitive thinking. For this, the survey research was used. The researcher developed the questionnaire which consists of problems with intuitive and algorithmic problem solving in number and operation, figure and measurement areas. 57 Korean $6^{th}$ grade students and 60 American $6^{th}$ grade students participated. The result of the analysis showed that Korean students revealed a higher percentage than American students in correct answers. But it was higher in the rate of Korean students attempted to use the algorithm. Two countries' students revealed higher rates in that they tried to solve the problems using intuitive thinking in geometry and measurement areas. Students in both countries showed the lower percentages of correct answer in problem solving to identify the impact of counterintuitive thinking. They were affected by potential infinity concept and the character of intuition in the problem solving process regardless of the educational environments and cultures.

반성적 문제 만들기 활동이 초등학생들의 문제해결력 및 수학적 태도에 미치는 영향 (The Effects of Reflective Problem Posing Activities on Students' Problem Solving Ability and Attitudes toward Mathematics)

  • 배준환;박만구
    • 한국초등수학교육학회지
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    • 제20권2호
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    • pp.311-331
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    • 2016
  • 본 연구는 학습자 스스로 수학적 오류를 분석하고 반성적 문제 만들기 활동을 하도록 한 것이 문제해결력과 수학적 태도에 미치는 영향을 알아보기 위한 것이다. 본 연구를 위하여 서울특별시 강서구에 소재한 초등학교 5학년 2개 반(62명)을 대상으로 실험집단과 비교집단을 선정하였다. 연구 결과 반성적 문제 만들기 활동은 학생들로 하여금 구하고자 하는 것을 파악하는 능력과 문제를 해결하는데 필요한 조건을 선별하여 활용하는 능력을 향상시켜 학생들의 문제해결력 향상에 효과적이었다. 또한, 학습자가 가지고 있었던 수학적 오개념을 수정하고 올바른 수학적 개념을 정립하는데 도움을 주었다. 그리고 반성적 문제 만들기 활동은 학생들의 수학적 의지를 향상시키고 반성적 사고를 촉진시키며, 반성의 과정에서 자연스럽게 스스로 자신의 문제를 풀이 과정을 점검하는 습관을 갖도록 하는데 도움을 주었다. 학습자는 반성적 문제가 올바르게 만들어졌는지 점검하고 이것을 바르게 해결하기 위해, 토의 활동에서 타인과의 수학적 의사소통에 적극적으로 참여하는 모습과 함께 끝까지 스스로 문제를 해결하고자 하는 과제집착력을 강하게 나타냈다.

교사.학생이 수학문제 해결에서 사용하는 전략에 관한 연구 (A Study on the Strategies in Mathematical Problem Solving used by Teachers and Students)

  • 성인서
    • 한국수학교육학회지시리즈A:수학교육
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    • 제26권1호
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    • pp.11-19
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    • 1987
  • The purpose of this research is to investigate the strategies for problem solving used by teachers and students and obtain some information which would be useful to enhance the ability of problem solving of the students. For this purpose we apply the thinking aloud method to study 6 graders and 6 teachers who were asked to solve 5 word problems. And we create a coding system to analyze those strategies. Using this coding system, we code the examinees and problems. we come up with the following facts from our study. (1) The number of strategies used by teachers is less than that used by students. (2) The characteristic of the strategies used by students is to set up an equation. (3) There is deep relationship between understanding the question and choosing the successful strategies for problem solving. (4) The students use the inductive argument more often than the teachers in the case of nonroutine mathematical problem. (5) The student of high success rate have fewer strategies than the others. From the above facts. it proposes the following conclusion for the enhancement of the ability of problem solving: So far the teachers usually use a few typical strategies for problem solving. But they need to create various strategies for pqoblem solving. It makes it possible for the students to choose proper strategies according to their ability. The students need to be given nicely constructed problem with enough time.

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수학적 문제 해결 연구에 있어서 미래 연구 주제: 델파이 기법 (Future Research Topics in the Field of Mathematical Problem Solving: Using Delphi Method)

  • 김진호;김인경
    • 한국수학교육학회지시리즈C:초등수학교육
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    • 제14권2호
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    • pp.187-206
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    • 2011
  • 1980년대 이후로 현재까지 수학적 문제해결은 수학교육학의 주요 연구 주제 중의 하나로 자리매김하고 있다. 초창기에는 문제 그 자체에 대한 연구, 학습자들이 문제를 해결하는 방법 및 메타인지에 대한 연구, 교수학습 방법에 대한 연구 등 다양한 방법에서 연구가 진행되었으며, 최근 들어서는 문제해결을 통한 수학교육 및 모델링을 통한 문제해결이 연구자들의 관심을 끌고 있다. 이처럼 문제해결과 관련된 연구주제들은 변하면서도 지속적으로 연구자들의 관심을 끌고 있다. 따라서, 수학적 문제해결 영역에서 미래에 어떤 주제들이 더 연구될 필요가 있는지를 델파이를 기법을 통해서 알아보았다.

창의적인 문제해결과정에서의 직관과 논리의 역할 (The Role of Intuition and Logic in Creative Problem Solving Process)

  • 이대현
    • 한국수학교육학회지시리즈A:수학교육
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    • 제38권2호
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    • pp.159-164
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    • 1999
  • The purpose of this paper is to find role of in and logic in creative problem solving process. Intuition and logic have played an important role in creative problem solving process. Nevertheless, Intuition has been treated less importantly than logic. Therefore, I intend to review the role of intuition, and then the relationship of intuition and logic, and the role of intuition and logic in creative problem solving process. Although intuition gives an important clue in problem solving process, it may sometimes cause an error. This fact gives an idea that intuition and logic have to be harmoniously cultivated. In fact, Intuition and logic have been playing a complementary role in creative problem solving process. A creative learner is regarded as a mathematician of his age. It must be through intuition and logic that he/she solves the problem creatively, just as a mathematician invents the new mathematical fact through unconscious and conscious process. In this respective, teachers also should make every effort to cultivate intuition and logic themselves.

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수학 문제 해결의 역사와 모델링 관점 (The History of Mathematical Problem Solving and the Modeling Perspective)

  • 이대현;서관석
    • 한국수학사학회지
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    • 제17권4호
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    • pp.123-132
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    • 2004
  • 이 글에서는 20세기의 문제 해결의 역사에 대하여 개관하고, 21세기에 새로운 경향으로 주목받고 있는 모델링 관점에서의 수학 문제 해결에 대하여 알아보았다. 전통적인 문제 해결에서는 상황과 분리되어 있는 문제의 조건을 수학적 표현으로 바꾸는 번안 기술의 습득을 주요 관심사로 다루었다. 반면에, 모델링 관점에서 문제 해결은 해결할 필요가 있는 현실적인 문제 상황에서 출발하여 수학적인 정리 수단으로 재조직하고, 수학적 상황에서 문제를 해결하여 다시 실제 현상에 적용하는 과정을 따른다. 따라서, 학생들은 문제를 해결해 가는 과정에서 수학화를 경험하게 되고, 수학을 배우게 되는 이점이 있다.

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