• Title/Summary/Keyword: mathematical problem solving

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Establishing a Theoretical Rationale for Mathematical Problem Solving in Early Childhood Education (유아 수학에서의 문제해결에 대한 이론적 고찰)

  • Kim, Eun-Jung;Lee, Jeongwuk
    • Korean Journal of Child Studies
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    • v.28 no.4
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    • pp.319-331
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    • 2007
  • This review of literature establishes a contemporary meaning of mathematical problem solving including young children's mathematical problem solving processes/assessments and teaching strategies. The contemporary meaning of mathematical problem solving involves complicated higher thinking processes. Explanations of the mathematical problem solving processes of young children include the four steps suggested by $P{\acute{o}}lya$(1957) : understand the problem, devise a plan, carry out the plan, and review/extend the plan. Assessments of children's mathematical problem solving include both the process and the product of problem solving. Teaching strategies to support children's mathematical problem solving include mathematical problems built upon children's daily activities, interests, and questions and helping children to generate new approaches to solve problems.

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An Analysis on Teachers′ Role in Teaching Mathematical Problem Solving (수학적 문제해결 지도에서 교사의 역할에 대한 분석)

  • 전평국;정인수
    • Education of Primary School Mathematics
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    • v.7 no.1
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    • pp.1-14
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    • 2003
  • The purpose of this research is to explore teachers' role actions in teaching mathematical problem solving and to analyze the influences of the teachers'role actions on their students' activities and beliefs about problem solving. The results obtained in this study suggested that the teachers' role actions brought qualitative differences to students' activities, and students' beliefs about mathematical problem solving were consistent with the perspective held by their teachers. Therefore, teachers should help students build up desirable beliefs about problem solving. They should understand teaching mathematical problem solving and play proper roles in various situations of teaching mathematical problem solving.

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A Case Study of Procedural and Conceptual Knowledge Construction in the Computer Environments

  • Lee, Joong-Kwoen
    • Research in Mathematical Education
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    • v.8 no.2
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    • pp.81-93
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    • 2004
  • This study investigated three preservice teachers' mathematical problem solving among hand-in-write-ups and final projects for each subject. All participants' activities and computer explorations were observed and video taped. If it was possible, an open-ended individual interview was performed before, during, and after each exploration. The method of data collection was observation, interviewing, field notes, students' written assignments, computer works, and audio and videotapes of preservice teachers' mathematical problem solving activities. At the beginning of the mathematical problem solving activities, all participants did not have strong procedural and conceptual knowledge of the graph, making a model by using data, and general concept of a sine function, but they built strong procedural and conceptual knowledge and connected them appropriately through mathematical problem solving activities by using the computer technology.

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Effect of Children's Mathematical Problem Solving Ability and Their Self-Esteem through Havruta Method Using Math Storybooks (수학동화를 활용한 하브루타 수업이 유아의 수학적 문제 해결력 및 자아존중감에 미치는 영향)

  • Lim, Kyeong Mi;Ahn, Hyojin
    • Family and Environment Research
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    • v.55 no.2
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    • pp.193-204
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    • 2017
  • This study examines the effect of 5-year-old children's mathematical problem solving ability and their self-esteem based on the Havruta method using math storybooks. The subjects of this study were 40 5-year-old students attending a kindergarten in the Incheon area: 20 students comprised the treatment group and 20 students comprised the control group. An instrument originally created by Ward (1993) but adapted by Hwang (1997) and later modified by Ryu (2003) was used to test the children's mathematical problem solving abilities. A modified version (Kim, 1997) of an instrument developed by Harter and Pike (1984) was used to measure children's self-esteem. Test results were analyzed using SPSS ver. 18.0 for Windows. The findings are as follows. First, the treatment group that had Havruta classes utilizing math story books was found to improve significantly more than the control group in their mathematical problem solving ability. Havruta classes had positive effects on children's mathematical problem solving abilities. Second, there was no significant difference found between the two groups in terms of self-esteem when the children's self-esteem was compared after Havruta classes that utilize math storybooks. It may not be possible to see immediate changes in children's self-esteem because positive parent and teacher feedback had the strongest influence on 5-year-old children's self-esteem, as opposed to self-learning. The results of this study provide meaningful basic data for Havruta classes that focus on questions and discussions through math story books to increase children's mathematical problem solving abilities in the child education field.

A Study on the Mathematical Problem Solving Teaching based on the Problem solving approach according to the Intuitive and the Formal Inquiry (직관적·형식적 탐구 기반의 문제해결식 접근법에 따른 수학 문제해결 지도 방안 탐색)

  • Lee, Daehyun
    • Journal for History of Mathematics
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    • v.32 no.6
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    • pp.281-299
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    • 2019
  • Mathematical problem solving has become a major concern in school mathematics, and methods to enhance children's mathematical problem solving abilities have been the main topics in many mathematics education researches. In addition to previous researches about problem solving, the development of a mathematical problem solving method that enables children to establish mathematical concepts through problem solving, to discover formalized principles associated with concepts, and to apply them to real world situations needs. For this purpose, I examined the necessity of problem solving education and reviewed mathematical problem solving researches and problem solving models for giving the theoretical backgrounds. This study suggested the problem solving approach based on the intuitive and the formal inquiry which are the basis of mathematical discovery and inquiry process. And it is developed to keep the balance and complement of the conceptual understanding and the procedural understanding respectively. In addition, it consisted of problem posing to apply the mathematical principles in the application stage.

Knowledge Construction on Mathematics Problem Solving (수학 탐구학습에서 지식 형성에 대한 연구)

  • 이중권
    • Journal for History of Mathematics
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    • v.17 no.3
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    • pp.109-120
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    • 2004
  • This study investigated three pre-service teachers' mathematical problem solving among hand-in-write-ups and final projects for each subject. All participants' activities and computer explorations were observed and video taped. If it was possible, an open-ended individual interview was performed before, during, and after each exploration. The method of data collection was observation, interviewing, field notes, students' written assignments, computer works, and audio and videotapes of pre- service teachers' mathematical problem solving activities. At the beginning of the mathematical problem solving activities, all participants did not have strong procedural and conceptual knowledge of the graph, making a model by using data, and general concept of a sine function, but they built strong procedural and conceptual knowledge and connected them appropriately through mathematical problem solving activities by using the computer technology.

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Analysis of Mathematical Problem Based on Mathematical Problem Solving Competency (수학적 문제해결역량을 위한 평가 문항의 조건과 그 실제)

  • Lee, Seon Yeong;Lee, Ji Soo;Han, Sunyoung
    • The Mathematical Education
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    • v.57 no.2
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    • pp.111-136
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    • 2018
  • This study suggests a framework for analyzing items based on the characteristics, and shows the relationship among the characteristics, difficulty, percentage of correct answers, academic achievement and the actual mathematical problem solving competency. Three mathematics educators' classification of 30 items of Mathematics 'Ga' type, on 2017 College Scholastic Ability Test, and the responses given by 148 high school students on the survey examining mathematical problem solving competency were statistically analyzed. The results show that there are only few items satisfying the characteristics for mathematical problem solving competency, and students feel ill-defined and non-routine items difficult, but in actual percentage of correct answers, routineness alone has an effect. For the items satisfying the characteristics, low-achieving group has difficulty in understanding problem, and low and intermediate-achieving group have difficulty in mathematical modelling. The findings can suggest criteria for mathematics teachers to use when developing mathematics questions evaluating problem solving competency.

Relationships between Mathematical Learning Styles and the Selection of Mathematical Problem Solving Strategies : Focused on the 1st Grade High School Students (수학 학습유형과 문제 해결 전략)

  • Yang, Eun-Kyung;Whang, Woo-Hyung
    • The Mathematical Education
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    • v.44 no.4
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    • pp.565-586
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    • 2005
  • The purpose of this paper is to analyze the selection difference of mathematical problem solving strategy by mathematical learning style, that is, the intellectual, emotional, and physiological factors of students, to allow teachers to instruct the mathematical problem solving strategy most pertinent to the student personality, and ultimately to contribute to enhance mathematical problem solving ability of the students. The conclusion of the study is the followings: (1) Students who studies with autonomous, steady, or understanding-centered effort was able to solve problems with more strategies respectively than the students who did not; (2) Student who studies autonomously or reconfirms one's learning was able to select more proper strategy and to explain the strategy respectively than the students who did not; and (3) The differences of the preference to the strategy are variable, and more than half of the students were likely to select frequently the strategy 'to use a formula or a principle' regardless of the learning style.

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A Case Study on Activating of High School Student's Metacognitive Abilities in Mathematical Problem Solving Process using Visual Basic (비주얼 베이식을 이용한 수학 문제해결 과정에서 고등학생의 메타인지적 능력 활성화)

  • 이봉주;김원경
    • The Mathematical Education
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    • v.42 no.5
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    • pp.623-636
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    • 2003
  • Metacognition is defined to be 'thinking about thinking' and 'knowing what we know and what we don't know'. It was verified that the metacognitive abilities of high school students can be improved via instruction. The purpose of this article is to investigate a new method for activating the metacognitive abilities that play a key role in the Mathematical Problem Solving Process(MPSP). Hyunsung participated in the MPSP using Visual Basic Programming. He actively participated in the MPSP. There are sufficient evidences about activating the metacognitive abilities via the activity processes and interviews. In solving mathematical problems, he had basic metacognitive abilities in the stage of understanding mathematical problems; through the experiments, he further developed his metacognitive abilities and successfully transferred them to general mathematical problem solving.

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A Psychological Model Applied to Mathematical Problem Solving

  • Alamolhodaei, Hassan;Farsad, Najmeh
    • Research in Mathematical Education
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    • v.13 no.3
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    • pp.181-195
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    • 2009
  • Students' approaches to mathematical problem solving vary greatly with each other. The main objective of the current study was to compare students' performance with different thinking styles (divergent vs. convergent) and working memory capacity upon mathematical problem solving. A sample of 150 high school girls, ages 15 to 16, was studied based on Hudson's test and Digit Span Backwards test as well as a math exam. The results indicated that the effect of thinking styles and working memory on students' performance in problem solving was significant. Moreover, students with divergent thinking style and high working memory capacity showed higher performance than ones with convergent thinking style. The implications of these results on math teaching and problem solving emphasizes that cognitive predictor variable (Convergent/Divergent) and working memory, in particular could be challenging and a rather distinctive factor for students.

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