• Title/Summary/Keyword: mathematical problem solving

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The Sociodynamical Function of Meta-affect in Mathematical Problem-Solving Procedure (수학 문제해결 과정에 작용하는 메타정의의 사회역학적 기능)

  • Do, Joowon;Paik, Suckyoon
    • Education of Primary School Mathematics
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    • v.20 no.1
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    • pp.85-99
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    • 2017
  • In order to improve mathematical problem-solving ability, there has been a need for research on practical application of meta-affect which is found to play an important role in problem-solving procedure. In this study, we analyzed the characteristics of the sociodynamical aspects of the meta-affective factor of the successful problem-solving procedure of small groups in the context of collaboration, which is known that it overcomes difficulties in research methods for meta-affect and activates positive meta-affect, and works effectively in actual problem-solving activities. For this purpose, meta-functional type of meta-affect and transact elements of collaboration were identified as the criterion for analysis. This study grasps the characteristics about sociodynamical function of meta-affect that results in successful problem solving by observing and analyzing the case of the transact structure associated with the meta-functional type of meta-affect appearing in actual episode unit of the collaborative mathematical problem-solving activity of elementary school students. The results of this study suggest that it provides practical implications for the implementation of teaching and learning methods of successful mathematical problem solving in the aspect of affective-sociodynamics.

The Effects of Mathematical Games with Motion on Young Children's Development (운동요소가 포함된 수학게임이 유아발달에 미치는 효과)

  • Chang, Bo-Kyung
    • Korean Journal of Human Ecology
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    • v.19 no.2
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    • pp.271-283
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    • 2010
  • This study was planned to investigate the effects of mathematical games with motion on young children's development. The study was performed to compose mathematical games with motion and just mathematical games for young children. The games were set up to be executed 16 times for 8 weeks. The results of this study were as follows: Mathematical games with motion had a significant effect on young children's mathematical problem-solving ability. Mathematical games with motion had a significant effect in every category on young children's ability for motion competence and mathematical games with motion had a significant effect on young children's socio-emotional development. There were significant differences between the control group and the experimental group except for the independence from teachers and peer interaction. Mathematical games with motion had a significant effect on young children's language ability.

An Analysis of the Transformation Process of Representation through Interaction in Mathematical Problem Solving (수학적 문제해결에서 상호작용을 통한 표상의 변환 과정 분석)

  • Lee, Min Ae;Kang, Wan
    • Journal of Elementary Mathematics Education in Korea
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    • v.16 no.3
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    • pp.427-450
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    • 2012
  • Using representations is essential for students to organize their thinking, to solve problems and to communicate each other. Students express information or situations suggested by problems easily and organize and infer them systematically using representations. Also, teachers are able to comprehend students' levels of understanding and thinking process better through them, and influence their representations. This study was conducted to understand mathematical representations of students uprightly and to seek implications for proper teaching of representations, by analyzing representations of students in mathematical problem solving process and the transformation process of representation via interactions.

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The Effect of Problem Posing Teaching on Mathematical Problem-Solving Ability and Creativity (문제제기 수업이 수학 문제해결력과 창의력에 미치는 효과)

  • Lee, Sang-Won
    • The Mathematical Education
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    • v.44 no.3 s.110
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    • pp.361-374
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    • 2005
  • I analyzed the effect of problem posing teaching and teacher-centered teaching on mathematical problem-solving ability and creativity in order to know the efffct of problem posing teaching on mathematics study. After we gave problem posing lessons to the 3rd grade middle school students far 28 weeks, the evaluation result of problem solving ability test and creativity test is as fellows. First, problem posing teaching proved to be more effective in developing problem-solving ability than existing teacher-centered teaching. Second, problem posing teaching proved to be more effective than teacher-centered teaching in developing mathematical creativity, especially fluency and flexibility among the subordinate factors of mathematical creativity. Thus, 1 suggest the introduction of problem posing teaching activity for the development of problem-solving ability and mathematical creativity.

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Flexibility of Mind and Divergent Thinking in Problem Solving Process (수학적 사고의 유연성과 확산적 사고)

  • Choi, Youn-Gi;Do, Jong-Hoon
    • The Mathematical Education
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    • v.44 no.1 s.108
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    • pp.103-112
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    • 2005
  • This paper is designed to characterize the concept of flexibility of mind and analyze relationship between flexibility of mind and divergent thinking in view of mathematical problem solving. This study shows that flexibility of mind is characterized by two constructs, ability to overcome fixed mind in stage of problem understanding and ability to shift a viewpoint in stage of problem solving process, Through the analysis of writing test, we come to the conclusion that students who overcome fixed mind surpass others in divergent thinking and so do students who are able to shift a viewpoint.

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The Effect of Polya's Heuristics in Mathematical Problem Solving of Mild Disability Students (경도장애 학생들의 수학적 문제해결을 위한 폴리아의 전략 효과 연구)

  • Han, Kyung-Hwa;Kim, Young-Ok
    • East Asian mathematical journal
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    • v.32 no.2
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    • pp.253-289
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    • 2016
  • This study attempted to figure out new teaching method of mathematics teaching-learning by applying Polya's 4-level strategy to mild disability students at the H Special-education high school where the research works for. In particular, epilogue and suggestion, which Polya stressed were selected and reconstructed for mild disability students. Prior test and post test were carried by putting the Polya's problem solving strategy as independent variable, and problem solving ability as dependent variable. As a result, by continual use of Polya's program in mathematics teaching course, it suggested necessary strategies to solve mathematics problems for mild disability students and was proven that Polya's heuristic training was of help to improve problem solving in mathematics.

A Psychological Model for Mathematical Problem Solving based on Revised Bloom Taxonomy for High School Girl Students

  • Hajibaba, Maryam;Radmehr, Farzad;Alamolhodaei, Hassan
    • Research in Mathematical Education
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    • v.17 no.3
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    • pp.199-220
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    • 2013
  • The main objective of this study is to explore the relationship between psychological factors (i.e. math anxiety, attention, attitude, Working Memory Capacity (WMC), and Field dependency) and students' mathematics problem solving based on Revised Bloom Taxonomy. A sample of 169 K11 school girls were tested on (1) The Witkin's cognitive style (Group Embedded Figure Test). (2) Digit Span Backwards Test. (3) Mathematics Anxiety Rating Scale (MARS). (4) Modified Fennema-Sherman Attitude Scales. (5) Mathematics Attention Test (MAT), and (6) Mathematics questions based on Revised Bloom Taxonomy (RBT). Results obtained indicate that the effect of these items on students mathematical problem solving is different in each cognitive process and level of knowledge dimension.

A Study on the Factors and Effect of Immediacy in Intuition (직관의 즉각성 요인과 효과에 대한 고찰)

  • Lee Dae-Hyun
    • The Mathematical Education
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    • v.45 no.3 s.114
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    • pp.263-273
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    • 2006
  • The purpose of this paper is to research the factors and the effects of immediacy in mathematics teaching and learning and mathematical problem solving. The factors of immediacy are visualization, functional fixedness and representatives. In special, students can apprehend immediately the clues and solution using the visual representation because of its properties of finiteness and concreteness. But the errors sometimes originate from 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. And this phenomenon is the same in functional fixedness and representatives which are the factors of immediacy The methods which overcome the errors of immediacy is that problem solvers notice the limitation of the factors of immediacy and develop the meta-cognitive ability. And it means we have to emphasize the logic and the intuition in mathematical teaching and learning. Clearly, we can't solve all mathematical problems using only either the logic or the intuition.

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A Rationale of Mathematical Problem Solving on a Small Group-Focusing on Collaborative Interaction

  • Lee, Young-suk
    • Research in Mathematical Education
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    • v.5 no.1
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    • pp.77-86
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    • 2001
  • The purpose of this study is to examine a theoretical framework for the interactions of learning in a small group setting of mathematical problem solving. Many researchers already have described the theoretical background for the small group settings in problem solving. However, most of the literatures merely have reported findings of achievement and rising of test scores. They ignored the observation of process taken during the small group work and have not determined how various psychological, social and academic effects are created. As results of the study, two types, mutual collaboration and asymmetric collaboration, of interactions are observed as the interactions of learning, which are conceived as the cores of authentic mathematical activities.

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A Study on the Metacognition Mathematical Problem - Solving (수학문제해결 수행에서의 메타인지에 대한 고찰)

  • 유승욱
    • Journal of the Korean School Mathematics Society
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    • v.1 no.1
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    • pp.111-119
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    • 1998
  • So far the studies on mathematical problem-solving education have failed to realize the anticipated result from students. The purpose of this study is to examine the reasons from the metacognitional viewpoint, and to think of making meta-items which enables learners to study through making effective use of the meaning of problem-solving and through establishing a general, well-organized theory on metacognition related to mathematic teaching guiedance. Metacognition means the understanding of knowledge of one's own and significance in the situation that can be reflection so as to express one's own knowledge and use it effectively when was questioned. Mathematics teacher can help students to learn how to control their behaviors by showing the strategy clearly, the decision and the behavior which are used in his own planning, supervising and estimating the solution process himself. If mathematics teachers want their students to be learners not simply knowing mathematical facts and processes, but being an active and positive, they should develop effective teaching methods. In fact, mathematics learning activities are accomplished under the complex condition arising from the factors of various cognition activities. therefore, mathematical education should consider various factors of feelings as well as a factor as fragmentary mathematical knowledge.

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