• Title/Summary/Keyword: mathematical problem solving

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A Study on Social Intuitionist Model of Haidt in Mathematical Problem Solving (수학문제해결 측면에서의 Haidt의 사회적 직관주의 모델에 관한 고찰)

  • Choi, Kyounga;Kang, Moonbong
    • Journal of Educational Research in Mathematics
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    • v.26 no.3
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    • pp.565-581
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    • 2016
  • Intuition in the mathematical problem solving has been stressed the importance with the logic because intuition is the cognition that give significant clue or idea to problem solving. Fischbein classified intuition by the origin; primary intuition and secondary intuition And he said the role of the personal experience and school education. Through these precedent research, we can understand the social influence. This study attempt to investigate social intuition model of Haidt, moral psychologist that has surfaced social property of intuition in terms of the mathematical problem solving. The major suggestions in problem solving and the education of intuition are followed. First, I can find the social property of intuition in the mathematical problem solving. Second, It is possible to make the mathematical problem solving model by transforming the social intuitionist model. Third, the role of teacher is important to give the meaningful experience for intuition to their students. Fourth, for reducing the errors caused by the coerciveness and globality of intuition, we need the education of checking their own intuition. In other words, we need intuition education emphasized on metacognition.

Enhancing Student Beliefs about Mathematical Problem Solving: Effects of a Problem-Solving based Intervention

  • Deng, Feng;Tay, Eng Guan;Toh, Tin Lam;Leong, Yew Hoong;Quek, Khiok Seng;Toh, Pee Choon;Dindyal, Jaguthsing;Ho, Foo Him
    • Research in Mathematical Education
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    • v.19 no.1
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    • pp.19-41
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    • 2015
  • Previous studies indicated that students tended to hold less satisfactory beliefs about the discipline of mathematics, beliefs about themselves as learners of mathematics, and beliefs about mathematics teaching and learning. However, only a few studies had developed curricular interventions to change students' beliefs. This study aimed to examine the effect of a problem-solving curriculum (i.e., Mathematical Problem Solving for Everyone, MProSE) on Singaporean Grade 7 students' beliefs about mathematical problem solving (MPS). Four classes (n =142) were engaged in ten lessons with each comprising four stages: understand the problem, devise a plan, carry out the plan, and look back. Heuristics and metacognitive control were emphasized during students' problem solving activities. Results indicated that the MProSE curriculum enabled some students to develop more satisfactory beliefs about MPS. Further path analysis showed that students' attitudes towards the MProSE curriculum are important predictors for their beliefs.

Difference between Gifted and Regular Students in Mathematical Problem Solving Ability (중학교 1학년 수학 영재학생과 일반 학생의 수학 문제해결과 문제설정 능력의 차이 비교)

  • Hwang, Dong-Jou
    • Journal of the Korean School Mathematics Society
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    • v.9 no.3
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    • pp.287-308
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    • 2006
  • In this study, an instrument of mathematical problem solving ability test was considered, and the difference between gifted and regular students in the ability were investigated by the test. The instrument consists of 10 items, and verified its quality due to reliability, validity and discrimination. Participants were 168 regular students and 150 gifted from seventh grade. As a result, not only problem solving but also problem finding and problem posing could be the characteristics of the giftedness.

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Intuition and metacognition in Mathematical Problem Solving Process (수학 문제해결 과정에서의 직관과 메타인지)

  • 이대현;이봉주
    • Journal of Educational Research in Mathematics
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    • v.12 no.2
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    • pp.265-274
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    • 2002
  • The purpose of the paper is to provide the importance of matacognition as a factor to correct the errors generated by the intuition. For this, first of all, we examine not only the role of metacognition in mathematics education but also the errors generated by the intuition in the mathematical problem solving process. Next, we research the possibility of using metacognition as a factor to correct the errors in the mathematical problem solving process via both the related theories about the metacognition and an example. In particular, we are able to acknowledge the importance of the role of metacognition throughout the example in the process of the problem solving It is not difficult to conclude from the study that emphasis on problem solving will enhance the development of problem solving ability via not only the activity of metacognition but also intuitive thinking. For this, it is essential to provide an environment that the students can experience intuitive thinking and metacognitive activity in mathematics education .

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A Study of Mathematical Problem Solving in Korea (우리나라에서의 수학적 문제해결연구)

  • 김부윤;이영숙
    • The Mathematical Education
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    • v.42 no.2
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    • pp.137-157
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    • 2003
  • Mathematical Problem solving has had the largest focus in the spread of mathematical topics since 1980. In Korea, most of the articles on problem solving appeared 1980s and 1990s, during which there were special concerns on this issue. And there is general acceptance of the idea that the famous statement "Problem solving must be the focus of school mathematics"(NCTM, 1980, p.1) in Agenda for Action, reflected in the curriculum of Korea. In a historical review focusing on the problem solving in the National Curriculum of Mathematics, we can infer that the primary goal of mathematics instruction should be to have students become competence problem solver. However, the practices of mathematics classroom and the trends of research in mathematical problem solving have oriented to ′teaching about problem solving′ and ′teaching for problem solving′. The issue of teaching via problem solving′ remain unsolved in the community of mathematics education and we need much more attention to this issue.

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The Effect of Picture Book Based Mathematical Activities on Mathematical Problem-Solving Performance in children (그림책에 의한 수학활동이 유아의 수학적 문제해결력에 미치는 영향)

  • Park, Seok Youn;Choi, Kyoung Sook
    • Korean Journal of Child Studies
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    • v.21 no.4
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    • pp.227-241
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    • 2000
  • This study investigated the effectiveness of mathematical activities based on picture books for the development of children's problem-solving performance. Subjects were 72 children divided in two groups of 36 each; one group had mathematical activities based on picture books and the other group had of pencil-and-paper tasks. The problem-solving performance was measured in terms of the test by Ward(1993) with a few modification for pretest and posttest. Mathematical activities were performed 12 times over a 6 week period. The data was analyzed by Analysis of Covariance(ANCOVA). The group taught by picture books significantly improved mathematical problem-solving performance.

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A Survey on the Teachers' Belief about Teaching Mathematical Problem Solving and Teaching Practice (수학적 문제 해결 지도에 대한 교사의 인식과 지도의 실제 조사)

  • 조완영;김남균
    • Education of Primary School Mathematics
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    • v.4 no.1
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    • pp.51-61
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    • 2000
  • Mathematical Problem solving has been the focus of a considerable amount of research over past 30 years. But nowadays problem solving is being beginning to be of less interest to mathematics education researchers. Moreover, mathematics teachers have an urgent need to be provided with well-documented informations about "teaching of(expecially, via) problem solving" though following research issues :ⅰ) the role of the teacher in a problem-centered classroom, ⅱ) what actually takes place in problem-centered classrooms, and iii) groups and whole classes' problem solving rather than individuals. This paper intends to give some informations about practice of teaching mathematical problem solving in elementary school.ry school.

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

  • 이영주;전평국
    • Education of Primary School Mathematics
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    • v.2 no.2
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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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An Analysis of Intuitive Thinking of Elementary Students in Mathematical Problem Solving Process (수학 문제해결 과정에 나타난 초등학생들의 직관적 사고 분석)

  • You, Dae-Hyun;Kang, Wan
    • Education of Primary School Mathematics
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    • v.12 no.1
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    • pp.1-20
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    • 2009
  • The purposes of this study are to analyze elementary school student's intuitive thinking in the process of mathematical problem solving and to analyze elementary school student's errors of intuitive thinking in the process of mathematical problem solving. According to these purposes, the research questions can be set up as followings. (1) How is the state of illumination of the elementary school student's intuitive thinking in the process of mathematical problem solving? (2) What are origins of errors by elementary school student's intuitive thinking in the process of mathematical problem solving? In this study, Bogdan & Biklen's qualitative research method were used. The subjects in this study were 4 students who were attending the elementary school. The data in this study were 'Intuitine Thinking Test', records of observation and interview. In the interview, the discourses were recorded by sound and video recording. These were later transcribed and analyzed in detail. The findings of this study were as follows: First, If Elementary school student Knows the algorithm of problem, they rely on solving by algorithm rather than solving by intuitive thinking. Second, their problem solving ability by intuitive model are low. What is more they solve the problem by Intuitive model, their Self- Evidence is low. Third, in the process of solving the problem, intuitive thinking can complement logical thinking. Last, in the concept of probability and problem of probability, they are led into cognitive conflict cause of subjective interpretation.

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Ability to Shift a Viewpoint and Insight into Invariance in Stage of Mathematical Problem Solving Process (수학 문제 해결 과정에서 사고(발상)의 전환과 불변성의 인식)

  • Do, Jong-Hoon
    • The Mathematical Education
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    • v.48 no.2
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    • pp.183-190
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    • 2009
  • This is a following study of the preceding study, Flexibility of mind and divergent thinking in problem solving process that was performed by Choi & Do in 2005. In this paper, we discuss the relationship between ability to shift a viewpoint and insight into invariance, another major consideration in mathematical creativity, in the process of mathematical problem solving.

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