• Journal of Educational Research in Mathematics
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• v.15 no.2
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• pp.107-130
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• 2005

The aims of this study are to identify Dewey's theory on mathematics education and to clarify its influence on the modern theories of mathematics education. For this purpose, we have examined Dewey's theory of knowledge named as pragmatism or instrumentalism, and studied the Dewey's theory of education in which he maintained education is the reconstruction of experiences. And then, we have examined Dewey's theory on mathematics education, such as theory of mathematics, purpose of mathematics education, contents of mathematics education, and methods of mathematics education respectively. After that, we have analyzed how his theory on mathematics education is connected with the diverse theories of modern mathematics education, such as Piaget's operational constructivism, Freudenthal's theory of realistic mathematics education, Polya's theory on mathematical problem-solving, and social constructivism. Through this study, we might say that Dewey's theory on mathematics education is a prototype of modern theories of mathematics education and a comprehensive paradigm which is very suggestive to the phenomena of mathematics education.

• School Mathematics
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• v.5 no.1
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• pp.59-76
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• 2003

Algebraic signs are important on learning and problem solving of algebra. This study investigated the contents of letters and expressions in textbooks by syntactics, semantics and pragmatics, and considered the introduction and extension processes of algebraic signs didactically. We also categorized the signs, and looked into textbook problems in view of semiotic. The result is that textbook is constructed in syntactics and semantics. Finally, the assessment of 7th grade students' competence in syntactics, semantics, syntactics+- semantics, pragmatics, and problem solving shows that students' ability in syntactics and pragmatics Is a predictive variable for algebraic problem solving.

• Journal of Elementary Mathematics Education in Korea
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• v.18 no.1
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• pp.63-81
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• 2014

Korean students have shown high achievements on the cognitive domain of mathematics in a range of international assessment tests. On the affective domain, however, significantly low achievements have been reported. Among the factors in the affective domain, this article discusses on the value of mathematics in the perspective of Michael Polanyi's philosophy, which centers personal knowledge and tacit knowing. Polanyi emphasizes abstractness and generalization in mathematics accompanied by intellectual beauty and passion. In his perspective, therefore, utilitarian aspects and usefulness of mathematics imparted through linguistic representations have limits in motivating students to learn mathematics. Students must be motivated from recognition of the value of mathematics formed through participating authentic mathematical problem solving activity with immersion, tension, confusion, passion, joy and the like.

• Communications of Mathematical Education
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• v.19 no.1 s.21
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• pp.15-24
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• 2005

오늘날 제 7차 교육과정은 학습자의 사고과정과 능력을 다양한 평가방식으로 실시하도록 권유하고 있다. 이러한 목적을 구현하기 위하여 수학과 평가는 교수-학습에 유용한 평가, 과정 중심의 평가, 다양한 방법을 활용하는 평가가 되어야 할 것이다. 이는 학습자로 하여금 스스로 학습하도록 가정하는 인식론적 변화에 바탕을 둔 최근의 평가 동향과 맥을 같이 하고 있다. 평가에서 학생의 수학활동 역시 특히 인지적 영역의 다양성을 지닌 개인에 의하여 이루어지기 때문에 수학 평가는 단편적인 정형화된 지식이 아닌 문제 해결의 전략이나 발견술과 같은 요소에서 강조되고 있는 비정형의 문제들을 통한 메타인지적인 발달과정을 고려해야 한다. 본 연구에서는 학생이 준개방형 평가문제를 해결하는 과정을 통해 자신이 얼마나 알고 있는가를 인식하며 자신의 문제 해결 전략을 점검하고 평가하는 인지적 능력에서 일어나는 변화를 알아보는 데 그 목적이 있다. 지금 현재 연구가 진행 중이며 본 연구의 결과는 다음 논문집에 발표할 예정이다.

• 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.

• Journal of Elementary Mathematics Education in Korea
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• v.20 no.4
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• pp.563-581
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• 2016

Studies on meta-affect in problem solving tried to build similar structures among affective elements as the structure of cognition and meta-cognition. But it's still need to be more systematic as meta-cognition. This study defines meta-affect as the connection of cognitive elements and affective elements which always include at least one affective element. We logically categorized types of meta-affect in problem solving, and then observed and analyzed the real cases for each type of meta-affect based on the logical categories. We found the operating mechanism of meta-affect in mathematical problem solving. In particular, we found the characteristics of meta function which operates in the process of problem solving. Finally, this study contributes in efficient analysis of meta-affect in problem solving and educational implications of meta-affect in teaching and learning in problem solving.

• Education of Primary School Mathematics
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• v.22 no.4
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• pp.223-237
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• 2019

There is a close interaction between the linguistic-syntactic representation system and the affective representation system that appear in the mathematical process. On the other hand, since the mathematical conceptual system is fundamentally metaphoric, the analysis of the mathematical concept structure through linguistic representation can help to identify the source of cognitive and affective obstacles that interfere with mathematics learning. In this study, we analyzed the problem-solving protocols of mathematical gifted children from the perspective of cognitive language and meta-affect to identify the relationship between the functional characteristics of the text and metaphor they use and the functional characteristics of meta-affect. As a result, the behavior of the cognitive and affective characteristics of mathematically gifted children differed according to the success of problem solving. In the case of unsuccessful problem-solving, the use of metaphor as an internal representation system was relatively more frequent than in the successful case. In addition, while the cognitive linguistic aspects of metaphors play an important role in problem-solving, meta-affective attributes are closely related to the external representation of metaphors.

• The Mathematical Education
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• v.42 no.4
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• pp.465-480
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• 2003

The main purpose of this work is to propose programs of mathematics education and mathematics history courses for the department of mathematics education of teacher training universities. Foundation of Mathematics Education, Mathematics Teaching and Learning Theories, Mathematics Problem Solving, Analysis and Evaluation of Mathematics Teaching Materials and Mathematics History are discussed in this article.

• School Mathematics
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• v.12 no.4
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• pp.493-506
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• 2010

In this study, we conducted classroom activities that are exploring and explaining visualized materials for problem solving of school mathematics with pre-service teachers in 2007~2009. After finishing these classroom activities, pre-service teachers recorded an afternote that includes changes of their thinking about mathematics and mathematics education through these activities in this study. We collected various opinions of pre-service mathematics teachers. From the analysis these data, we searched educational effects of our classroom activities. Through conducting the practice like these classroom activities of our study, pre-service mathematics teachers will have an opportunity of a practical training that supports the teaching of mathematical problem-solving. Moreover their PCK will be enhanced. Also, They will learn a good way to realize the aim of school mathematics curriculum.

• Journal of the Korean School Mathematics Society
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• v.20 no.2
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• pp.163-186
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• 2017

The purpose of this paper is to propose the policy change of teachers education in Korea with an analysis of America statistical literacy education. we found the difference of statistical literacy education between Korea and America with each nation's social and educational environment. We can get the need of new change for statistic teacher's education in Korea. We think of Mathematics teachers should know about the difference between statistics and mathematics at school mathematics. And they should know the new change thinking about teaching method and process assesment methods. Second, Teachers should focused on teaching of problem solving and statistical thinking ability based on data analysis than the teaching of probability and mathematical theory.