• Title/Summary/Keyword: mathematical problem solving

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

  • Kim, Min-Kyeong;Min, Sun-Hee;Kim, Hye-Won
    • The Mathematical Education
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    • v.50 no.2
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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.

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

  • Kim, Min-Kyeong;Heo, Ji-Yeon;Cho, Mi-Kyung;Park, Yun-Mi
    • The Mathematical Education
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    • v.51 no.2
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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.

Algebraic Problem Solving of the High School Students : An Analysis of Strategies and Errors (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))

  • Lee, Sang-Won;Jeon, Pyung-Kook
    • Communications of Mathematical Education
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    • v.2
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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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A comparative analysis of the MathThematics textbooks with Korean middle school mathematics textbooks - focused on mathematical communication - (현행 중학교 수학 교과서와 MathThematics 교과서의 비교 분석 - 수학적 의사소통 측면을 중심으로 -)

  • Han, Hye-Sook
    • The Mathematical Education
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    • v.49 no.4
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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.

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

  • Lee, Byung-Soo
    • Communications of Mathematical Education
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    • v.22 no.4
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    • pp.471-487
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    • 2008
  • Inventive mathematical thinking, original mathematical problem solving ability, mathematical invention and so on are core concepts, which must be emphasized in all branches of mathematical education. In particular, Polya(1981) insisted that inventive thinking must be emphasized in a suitable level of university mathematical courses. In this paper, the author considered two cases of inventive problem solving ability shown by his many students via real analysis courses. The first case is about the proof of the problem "what is the derived set of the integers Z?" Nearly all books on mathematical analysis sent the question without the proof but some books said that the answer is "empty". Only one book written by Noh, Y. S.(2006) showed the proof by using the definition of accumulation points. But the proof process has some mistakes. But our student Kang, D. S. showed the perfect proof by using The Completeness Axiom, which is very useful in mathematical analysis. The second case is to show the infinite countability of NxN, which is shown by informal proof in many mathematical analysis books with formal proofs. Some students who argued the informal proof as an unreasonable proof were asked to join with us in finding the one-to-one correspondences between NxN and N. Many students worked hard and find two singled-valued mappings and one set-valued mapping covering eight diagrams in the paper. The problems are not easy and the proofs are a little complicated. All the proofs shown in this paper are original and right, so the proofs are deserving of inventive mathematical thoughts, original mathematical problem solving abilities and mathematical inventions. From the inventive proofs of his students, the author confirmed that any students can develope their mathematical abilities by their professors' encouragements.

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

  • Lyou, Ik-Seung;Han, In-Ki
    • Communications of Mathematical Education
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    • v.24 no.3
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    • pp.793-806
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    • 2010
  • In this paper we study meaning and methods of analyzing problems related with equation of high school mathematics. By analyzing problem we can get two types of informations. Based on these informations we suggest some problem solving methods. Especially we try to extract second type information using analysis through synthesis. This second type information can help us to find new non-routine problem solving method.

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

  • Choi, Suyoung;Goo, A-Hyun;Ko, Ho Kyoung
    • East Asian mathematical journal
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    • v.37 no.4
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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.

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

  • Kim, Nam-Jun;Bae, Jong-Soo
    • Journal of Elementary Mathematics Education in Korea
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    • v.10 no.2
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    • pp.195-219
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    • 2006
  • This study was proposed to analyze mathematical communication activity and mathematical attitudes while students were solving project problem and to consider how the conclusions effects mathematics education. This study analyzed through qualitative research method. The questions for this study are following, First, how does the process of the mathematical communication activity proceed during solving project problem in a small group? Second, what reactions can be shown on mathematical attitudes during solving project problem in a small group? Four project problems sampled from pilot study in order to examine these questions were applied on two small groups consisting of four 5th grade students. It was recorded while each group was finding out the solution of the given problems. Afterward, consequences were analyzed according to each question after all contents were noted. Consequently, conclusions can be derived as follows. First, it was shown that each student used different elements of contents in mathematical communication activity. Second, during mathematical communication activity, most students preferred common languages to mathematical ones. Third, it was found that each student has their own mathematical attitude. Fourth, Students were more interested in the game project problem and the practical using project problem than others.

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

  • 이대현
    • The Mathematical Education
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    • v.42 no.5
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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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A case study on activating of high school student's metacognitive abilities in mathematical problem solving process using guidance material for metacognitive activities (문제해결 과정에서 메타인지적 활동 안내를 통한 고등학생의 메타인지 능력 활성화 가능성 탐색)

  • 이봉주
    • The Mathematical Education
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    • v.43 no.3
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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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