• 제목/요약/키워드: mathematical problem solving

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수학 교과에서의 상황맥락적 문제에 대한 교사의 인식 (A study of the elementary teachers' perception about the situation-contextual problem in mathematics education)

  • 김민경;민선희;김혜원
    • 한국수학교육학회지시리즈A:수학교육
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    • 제50권2호
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    • pp.149-164
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    • 2011
  • The purpose of this study was to analyze the perception of elementary school teachers about situation-contextual problem and to show efforts on order to enable students to improve their problem solving ability and thinking skills. In this research, two hundred elementary school teachers in Seoul were surveyed and three elementary school teachers were interviewed to determine their perception and the status about situation-contextual problem. As a result, most of teachers replied that situation-contextual problem would be useful and applicable to improve students' problem solving and creative thinking skill.

초등학교 4학년 학생들의 비구조화된 문제에서 나타난 해결 과정 및 추론 분석 (An Analysis on the 4th Graders' Ill-Structured Problem Solving and Reasoning)

  • 김민경;허지연;조미경;박윤미
    • 한국수학교육학회지시리즈A:수학교육
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    • 제51권2호
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    • pp.95-114
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    • 2012
  • This study examines the use of ill-structured problem to help the 4th graders' problem solving and reasoning. It appears that children with good understanding of problem situation tend to accept the situation as itself rather than just as texts and produce various results with extraction of meaningful variables from situation. In addition, children with better understanding of problem situation show AR (algorithmic reasoning) and CR (creative reasoning) while children with poor understanding of problem situation show just AR (algorithmic reasoning) on their reasoning type.

고등학교(高等學校) 학생(學生)의 대수(代數) 문제(問題) 해결(解決) : 전략(戰略)과 오류(誤謬) 분석(分析) (Algebraic Problem Solving of the High School Students : An Analysis of Strategies and Errors)

  • 이상원;전평국
    • 한국수학교육학회지시리즈E:수학교육논문집
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    • 제2권
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    • pp.181-191
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    • 1997
  • The purpose of this study is to provide the primary sources to improve the problem solving performance by analyzing the errors and the strategies selection of the high school students when solving given algebraic problems. To attain the purpose of this study, the questions for investigation in this study are : 1. What are the differences / similarities in the patterns of errors committed by successful and unsuccessful problem-solvers when solving particular algebraic problems ? 2. What are the error types chosen by unsuccessful problem-solvers when solving particular algebraic problems? 3. Do students utilize checking, either locally or globally, when solving particular algebraic problems? Twenty students were drawn out of 10th grade students in J girls' high school in Yengi -gun, Chung-Nam, for this study. The problem-solving test was used as a test instrument. From the data, the verbal protocols and the written protocols were analyzed by the patterns. The conclusions drawn from the results obtained in the present study are as follows: First, in solving particular algebraic problems, when the problems were solved with one strategy, most students didn't give any consideration to other strategies. So mathematics teachers should teach them to use the various strategies, and should develop the problems to be used the various strategies. Second, in solving particular algebraic problems, errors on notions or transformations of equations were found. Thus, the basic knowledges related to equation should be taught. In addition, most unsuccessful students seleted the strategies inadequately to solve the problems because of misunderstanding the problems. So, to improve the problem solving performance the processes of 'understanding problem' should be emphasized to students. Third, although the unsuccesful students used the 'checking' processes when solving the problems, most of them did not find the errors because of misconceptions related to the problems, carelessness, and unskillfulness of checking. Thus, students must be taught more carefully and encouraged to use the checking.

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현행 중학교 수학 교과서와 MathThematics 교과서의 비교 분석 - 수학적 의사소통 측면을 중심으로 - (A comparative analysis of the MathThematics textbooks with Korean middle school mathematics textbooks - focused on mathematical communication -)

  • 한혜숙
    • 한국수학교육학회지시리즈A:수학교육
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    • 제49권4호
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    • pp.523-540
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    • 2010
  • The purpose of the study were to analyze MathThematics textbooks and Korean middle school mathematics and to investigate the difference among the textbooks in the view of mathematical communication. According to the results, the textbook developers made a variety of efforts to develope students' mathematical communication ability. Students were encouraged to communicate with others about their mathematical ideas or problem solving processes in words or writing by means of discussion, oral report, presentation, journal, etc. MathThematics textbooks provided student self-assessment opportunity to improve student performance in problem solving, reasoning, and communication. In communication assessment, students can assess their use of mathematical vocabulary, notation, and symbols, the use of graphs, tables, models, diagrams and equation to solve problem and their presentation skills. The assessment activities would make a positive impact on the development of students' mathematical communication ability. MathThematics textbooks provided a variety of problem situation including history, science, sports, culture, art, and real world as a topic for communication, however, the researcher found that some of Korean textbooks depends heavily on mathematical problem situations.

대학교의 해석학 강좌에서 학생들의 수학적 발명에 관한 연구 (A research on Mathematical Invention via Real Analysis Course in University)

  • 이병수
    • 한국수학교육학회지시리즈E:수학교육논문집
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    • 제22권4호
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    • pp.471-487
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    • 2008
  • 본 연구에서는 해석학 강좌를 운영하는 과정에서 얻어진 학생들의 수학적 발명의 사례를 제시하고 분석하여, 수학적 발명과 관련된 구체적인 교수-학습 과정, 얻어진 수학적 산출물들, 이들의 수학적 의의를 기술하였다.

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고등학교 수학의 방정식에 관련된 문제의 분석 및 해결에 관한 연구 (A Study on Analyzing and Solving Problems Related with Equation of High School Mathematics)

  • 유익승;한인기
    • 한국수학교육학회지시리즈E:수학교육논문집
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    • 제24권3호
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    • pp.793-806
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    • 2010
  • 본 연구는 2007개정 교육과정에서 강조하는 창의적인 탐구, 문제해결에 관련된 문헌연구로, 본 연구에서는 문제의 이해 단계에서 수행하는 분석의 본질 및 유형을 문헌연구를 통해 고찰하였으며, 구체적인 방정식 문제들에 대한 분석을 제시하였고, 분석을 통해 얻어진 정보들을 활용한 다양하고 비정형적인 문제해결의 방법들을 제시하였다. 이를 통해, 고등학교의 수학교실에서 방정식 단원의 다양한 해법찾기 활동에 관련된 기초자료를 제공할 수 있을 것으로 기대된다.

집단지성을 활용한 폴리매스(Polymath) 활동 사례 (The Case of Polymath Activities Using Collective Intelligence)

  • 최수영;구아현;고호경
    • East Asian mathematical journal
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    • 제37권4호
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    • pp.523-541
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    • 2021
  • Education for the future society should emphasize the experience of sharing, coexisting, and solving problems in cooperation with each other in the community. Accordingly, in addition to the problem-solving capability, which is the ultimate goal of mathematics education, it is necessary to strengthen the capability to solve unstructured problems through collaboration. This study attempted to suggest that solving complex problems through collaboration is used in school classes or gifted education by introducing polymath that solves problems using collective intelligence. Accordingly, a target problem was set and an example of polymath in which community members exert each other's intelligence to solve the problem. In addition, by investigating the perceptions of students who have experienced polymath, positive aspects and improvements of polymath were suggested. Through this, this study can contribute to revitalization of mathematics teaching and learning methods using collective intelligence.

서술형 평가가 초등학생의 수학적 성향에 미치는 영향 연구 (Effect on Mathematical Inclination of Elementary School Students Using the Description Style Assessment)

  • 김남준;배종수
    • 한국초등수학교육학회지
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    • 제10권2호
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    • pp.195-219
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    • 2006
  • 서술형 평가가 실시됨에 따라 학생들의 수학적 성향이 어떻게 변화되었는지 살펴보았다. 학생들이 서술형 평가를 처음 접하였을 때 어렵게 생각하고 부담을 느끼고 있었으며, 풀이과정을 쓴다는 것이 불필요하다고 여기는 학생들도 있었다. 하지만 연구를 진행하는 동안 학생들은 곧 서술형 평가에 익숙해졌다. 서술형 평가를 통해 학생들은 수학을 자신의 글로 표현하는 경험을 하게 되었고. 수학적 개념이나 원리에 관심을 가지고 되었다. 또 풀이과정을 논리적으로 전개하려는 경향이 나타났다. 또 서술형 평가를 통해 학생들은 문제에 대한 자신의 생각을 논리적으로 서술하는 경험을 하게 되었고, 자신이 푼 문제에 대하여 반성하는 과정을 거칠 수 있었다. 또한 학생들은 새로운 형태의 서술형 문항을 접하면서 서술형 평가에 대한 호기심도 나타내었다. 그러나 어려운 문제를 풀어야 하는 경우에는 부담스러워 했으며, 자신만의 방법으로 문제를 풀기보다 교과서에 제시되었거나 교사가 알려 준 방법대로 풀려는 경향이 강하여 수학적 융통성은 다소 떨어지는 것을 알 수 있었다.

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수학교육에서 시각적 표현에 관한 소고 (A Study on the Visual Representation in Mathematics Education)

  • 이대현
    • 한국수학교육학회지시리즈A:수학교육
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    • 제42권5호
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    • pp.637-646
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    • 2003
  • Visual representation is very important topic in Mathematics Education since it fosters understanding of Mathematical concepts, principles and rules and helps to solve the problem. So, the purpose of this paper is to analyze and clarify the various meaning and roles about the visual representation. For this purpose, I examine the status of the visual representation. Since the visual representation has the roles of creatively mathematical activity, we emphasize the using of the visual representation in teaching and learning. Next, I examine the errors in relation to the visual representation which come from limitation of the visual representation. It suggests that students have to know conceptual meaning of the visual representation when they use the visual representation. Finally, I suggest some examples of problem solving via the visual representation. This examples clarify that the visual representation gives the clues and solution of problem solving. Students can apprehend intuitively and easily the mathematical concepts, principles and rules using the visual representation because of its properties of finiteness and concreteness. So, mathematics teachers create the various visual representations and show students them. Moreover, mathematics teachers ask students to design the visual representation and teach students to understand the conceptual meaning of the visual representation.

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문제해결 과정에서 메타인지적 활동 안내를 통한 고등학생의 메타인지 능력 활성화 가능성 탐색 (A case study on activating of high school student's metacognitive abilities in mathematical problem solving process using guidance material for metacognitive activities)

  • 이봉주
    • 한국수학교육학회지시리즈A:수학교육
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    • 제43권3호
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    • pp.217-231
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    • 2004
  • The purpose of this paper is to investigate a new method for activating the metacognitive abilities that play a key role in the Mathematical Problem Solving Process (MPSP). The proposed research question is as follows: Can the MPSP activate metacognitive abilities of high school students in the pencil-and-paper environment using guidance material for metacognitive activities\ulcorner To solve this question, two case studies have been carried out. Two students for the study were selected via informal interview. They voluntarily took part in 13 experimental lectures. The activating paths of their metacognitive abilities in the MPSP were chronically described and analyzed. All the activating processes of the students focusing on the aspects of metacognitive behaviors were analyzed by means of interview, observation, self-report, and activity data. The two high school students participating in the MPSP voluntarily recognized and reflected their deficiencies in metacognitive abilities, and therefore maximized their own performance. They made quite significant progress in the course of activating their metacognitive abilities through voluntary participation and gained greater confidence in the MPSP. Hence they have become good problem solvers. They expressed not only the factors influencing their behavior but also their self-awareness during the metacognitive activities. In the long run, this experiment will increase possibilities for the internalization of the metacognitive process.

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