• Title/Summary/Keyword: mathematical problem solving

### The Effects of Mathematical Modeling Activities on Mathematical Problem Solving and Mathematical Dispositions (수학적 모델링 활동이 수학적 문제해결력 및 수학적 성향에 미치는 영향)

• Ko, Changsoo;Oh, Youngyoul
• Journal of Elementary Mathematics Education in Korea
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• v.19 no.3
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• pp.347-370
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• 2015
• The purpose of this study is to examine the effects of mathematical modeling activities on mathematical problem solving abilities and mathematical dispositions in elementary school students. For this study, we administered mathematical modeling activities to fifth graders, which consisted of 8 topics taught over 16 classes. In the results of this study, mathematical modeling activities were statistically proven to be more effective in improving mathematical problem solving abilities and mathematical dispositions compared to traditional textbook-centered lessons. Also, it was found that mathematical modeling activities promoted student's mathematical thinking such as communication, reasoning, reflective thinking and critical thinking. It is a way to raise the formation of desirable mathematical dispositions by actively participating in modeling activities. It is proved that mathematical modeling activities quantitatively and qualitatively affect elementary school students's mathematical learning. Therefore, Educators may recognize the applicability of mathematical modeling on elementary school, and consider changing elementary teaching-learning methods and environment.

### Polanyi's Epistemology and the Tacit Dimension in Problem Solving (폴라니의 인식론과 문제해결의 암묵적 차원)

• Nam, Jin-Young;Hong, Jin-Kon
• Journal for History of Mathematics
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• v.22 no.3
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• pp.113-130
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• 2009
• It can be said that the teaching and learning of mathematical problem solving has been greatly influenced by G. Polya. His heuristics shows down the explicit process of mathematical problem solving in detail. In contrast, Polanyi highlights the implicit dimension of the process. Polanyi's theory can play complementary role with Polya's theory. This study outlined the epistemology of Polanyi and his theory of problem solving. Regarding the knowledge and knowing as a work of the whole mind, Polanyi emphasizes devotion and absorption to the problem at work together with the intelligence and feeling. And the role of teachers are essential in a sense that students can learn implicit knowledge from them. However, our high school students do not seem to take enough time and effort to the problem solving. Nor do they request school teachers' help. According to Polanyi, this attitude can cause a serious problem in teaching and learning of mathematical problem solving.

### 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.

### Error analysis related to a learner's geometrical concept image in mathematical problem solving (학생이 지닌 기하적 심상과 문제해결과정에서의 오류)

• Do, Jong-Hoon
• Journal of the Korean School Mathematics Society
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• v.9 no.2
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• pp.195-208
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• 2006
• Among different geometrical representations of a mathematical concept, learners are likely to form their geometrical concept image of the given concept based on a specific one. A learner's image is not always in accord with the definition of a concept. This can induce his or her errors in mathematical problem solving. We need to analyse types of such errors and the cause of the errors. In this study, we analyse learners' geometrical concept images for geometrical concepts and errors related to such images. Furthermore we propose a theoretical framework for error analysis related to a learner's concept image for a general mathematical concept in mathematical problem solving.

### A Study on the Results of Use of Open-ended Problems for Evaluation in Elementary Mathematics (초등 수학 평가를 위한 개방형 문제의 활용 결과 분석)

• Lee, Dae-Hyun
• The Mathematical Education
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• v.47 no.4
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• pp.421-436
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• 2008
• Mathematics assessment doesn't mean examining in the traditional sense of written examination. Mathematics assessment has to give the various information of grade and development of students as well as teaching of teachers. To achieve this purpose of assessment, we have to search the methods of assessment. This paper is aimed to develop the open-ended problems that are the alternative to traditional test, apply them to classroom and analyze the result of assessment. 4-types open-ended problems are developed by criteria of development. It is open process problem, open result problem, problem posing problem, open decision problem. 6 grade elementary students who are picked in 2 schools participated in assessment using open-ended problems. Scoring depends on the fluency, flexibility, originality The result are as follows; The rate of fluency is 2.14, The rate of flexibility is 1.30, and The rate of originality is 0.11 Furthermore, the rate of originality is very low. Problem posing problem is the highest in the flexibility and open result problem is the highest in the flexibility. Between general mathematical problem solving ability and fluency, flexibility have the positive correlation. And Pearson correlational coefficient of between general mathematical problem solving ability and fluency is 0.437 and that of between general mathematical problem solving ability and flexibility is 0.573. So I conclude that open ended problems are useful and effective in mathematics assessment.

### Mathematical Problem Solving for Everyone: A Design Experiment

• Quek, Khiok Seng;Dindyal, Jaguthsing;Toh, Tin Lam;Leong, Yew Hoong;Tay, Eng Guan
• Research in Mathematical Education
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• v.15 no.1
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• pp.31-44
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• 2011
• An impetus for reviving research in mathematical problem solving is the recent advance in methodological thinking, namely, the design experiment ([Gorard, S. (2004). Combining methods in educational research. Maidenhead, England: Open University Press.]; [Schoenfeld, A. H. (2009). Bridging the cultures of educational research and design. Educational Designer. 1(2). http://www.educationaldesigner.orgied/volume1/issue21]). This methodological approach supports a "re-design" of contextual elements to fulfil the overarching objective of making mathematical problem solving available to all students of mathematics. In problem solving, components critical to successful design in one setting that may be adapted to suit another setting include curriculum design, assessment strategy, teacher capacity, and instructional resources. In this paper, we describe the implementation, over three years, of a problem solving module into the main mathematics curriculum of an Integrated Programme school in Singapore which had sufficient autonomy to tailor-fit curriculum to their students.

### Future Research Topics in the Field of Mathematical Problem Solving: Using Delphi Method (수학적 문제 해결 연구에 있어서 미래 연구 주제: 델파이 기법)

• Kim, Jin-Ho;Kim, In-Kyung
• Education of Primary School Mathematics
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• v.14 no.2
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• pp.187-206
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• 2011
• Mathematical problem solving have placed as one of the important research topics which many researcher have been interested in from 1980's until now. A variety of topics have been researched: Characteries of problem; Processes of how learners to solve them and their metaoognition; Teaching and learning practices. Recently, the topics have been shifted to mathematical learning through problem solving and the connection of problem solving and modeling. In the field of mathematical problem solving where researcher have continuously been interested in, future research topics in this domain are investigated using delphi method.

### An Analysis on the Elementary Students' Mathematical Thinking in the Mathematical Problem Solving Processes (수학 문제해결 과정에서 나타나는 초등학생들의 수학적 사고 분석)

• Cho, Doo-Kyoung;Park, Man-Goo
• The Mathematical Education
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• v.47 no.2
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• pp.169-180
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• 2008
• The purpose of this study was to analyze the elementary students' mathematical thinking, which is found during mathematical problem solving processes based on mathematical knowledge, heuristics, control, and mathematical disposition. The participants were 8 fifth grade elementary students in Seoul. A qualitative case study was used for investigating the students' mathematical thinking. The data were coded according to the four components of the students' mathematical thinking. The results of the analyses concerning mathematical thinking of the elementary students were as follows: First, in terms of mathematical knowledge, the elementary students frequently used conceptual knowledge, procedural knowledge and informal knowledge during problem solving processes. Second, students tended not to find new heuristics or apply new one, but they only used the heuristics acquired from the experiences of the class and prior experiences. Third, control was found while students were solving problems. Last, mathematical disposition influenced on the mathematical problem solving processes. Teachers need to in-depth observations on the problem solving processes of students, which leads to teachers'effective assistance on facilitating students' problem solving skills.

### The Effect of Geometry Learning through Spatial Reasoning Activities on Mathematical Problem Solving Ability and Mathematical Attitude (공간추론활동을 통한 기하학습이 수학적 문제해결력과 수학적 태도에 미치는 효과)

• Shin, Keun-Mi;Shin, Hang-Kyun
• Journal of Elementary Mathematics Education in Korea
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• v.14 no.2
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• pp.401-420
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• 2010
• The purpose of this research is to find out effectiveness of geometry learning through spatial reasoning activities on mathematical problem solving ability and mathematical attitude. In order to proof this research problem, the controlled experiment was done on two groups of 6th graders in N elementary school; one group went through the geometry learning style through spatial reasoning activities, and the other group went through the general geometry learning style. As a result, the experimental group and the comparing group on mathematical problem solving ability have statistically meaningful difference. However, the experimental group and the comparing group have not statistically meaningful difference on mathematical attitude. But the mathematical attitude in the experimental group has improved clearly after all the process of experiment. With these results we came up with this conclusion. First, the geometry learning through spatial reasoning activities enhances the ability of analyzing, spatial sensibility and logical ability, which is effective in increasing the mathematical problem solving ability. Second, the geometry learning through spatial reasoning activities enhances confidence in problem solving and an interest in mathematics, which has a positive influence on the mathematical attitude.

### The Roles of Structural Similarity, Analytic Activity and Comparative Activity in Stage of Similar Mathematical Problem Solving Process (유사 문제 해결에서 구조적 유사성, 분석적 활동 그리고 비교 활동의 역할)

• Roh, Eun-Hwan;Jun, Young-Bae;Kang, Jeong-Gi
• Communications of Mathematical Education
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• v.25 no.1
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• pp.21-45
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• 2011
• It is the aim of this paper to find the requisites for the target problem solving process in reference to the base problem and to search the roles of those. Focusing on the structural similarity, analytic activity and comparative activity in stage of similar mathematical problem solving process, we tried to find the roles of them. We observed closely how four students solve the target problem in reference to the base problem. And so we got the following conclusions. The insight of structural similarity prepare the ground appling the solving method of base problem in the process solving the target problem. And we knew that the analytic activity can become the instrument which find out the truth about the guess. Finally the comparative activity can set up the direction of solution of the target problem. Thus we knew that the insight of structural similarity, the analytic activity and the comparative activity are necessary for similar mathematical problem to solve. We think that it requires the efforts to develop the various programs about teaching-learning method focusing on the structural similarity, analytic activity and comparative activity in stage of similar mathematical problem solving process. And we also think that it needs the study to research the roles of other elements for similar mathematical problem solving but to find the roles of the structural similarity, analytic activity and comparative activity.