• 대한수학교육학회지:수학교육학연구
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• 제11권2호
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• pp.239-256
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• 2001

The notion of metaphor has been increasingly popular in research of mathematics education. In particular, metaphor becomes a useful unit for analysis to provide a profound insight into mathematical reasoning and problem solving. In this context, this paper takes metaphor as an analytic unit to examine the relationship between objectivity and subjectivity in mathematical reasoning. Specifically, the discourse analysis focuses on the code switching between literal language and metaphor in mathematical discourse. It is shown that the linguistic code switching is parallel with the switching between two different kinds of mathematical knowledge, that is, factual knowledge and mathematical imagination, which constitute objectivity and subjectivity in mathematical reasoning. Furthermore, the pattern of the linguistic code switching reveals the dialectical relationship between the two poles of mathematical reasoning. Based on the understanding of the dialectical relationship, this paper provides some educational implications. First, the code-switching highlights diverse aspects of mathematics learning. Learning mathematics is concerned with developing not only technicality but also mathematical creativity. Second, the dialectical relationship between objectivity and subjectivity suggests that teaching and teaming mathematics is socioculturally constructed. Indeed, it is shown that not all metaphors are mathematically appropriated. They should be consistent with the cultural model of a mathematical concept under discussion. In general, this sociocultural perspective on mathematical metaphor highlights the sociocultural organization of teaching and loaming mathematics and provides a theoretical viewpoint to understand epistemological diversities in mathematics classroom.

• 한국수학교육학회지시리즈D:수학교육연구
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• 제26권3호
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• pp.253-270
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• 2023

This study aims to investigate the extent to which Korean high school textbooks incorporate opportunities for students to engage in the mathematical modeling process through tasks related to exponential and logarithmic functions. The tasks in three textbooks were analyzed based on the actions required for each stage in the mathematical modeling process, which includes identifying essential variables, formulating models, performing operations, interpreting results, and validating the outcomes. The study identified 324 units across the three textbooks, and the reliability coefficient was 0.869, indicating a high level of agreement in the coding process. The analysis revealed that the distribution of tasks requiring engagement in each of the five stages was similar in all three textbooks, reflecting the 2015 revised curriculum and national curriculum system. Among the 324 analyzed tasks, the highest proportion of the units required performing operations found in the mathematical modeling process. The findings suggest a need to include high-quality tasks that allow students to experience the entire process of mathematical modeling and to acknowledge the limitations of textbooks in providing appropriate opportunities for mathematical modeling with a heavy emphasis on performing operations. These results provide implications for the development of mathematical modeling activities and the reconstruction of textbook tasks in school mathematics, emphasizing the need to enhance opportunities for students to engage in mathematical modeling tasks and for teachers to provide support for students in the tasks.

• East Asian mathematical journal
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• 제27권4호
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• pp.381-389
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• 2011

The flexible mathematical thinking - the ability to generate and connect various representations of concepts - is useful in understanding mathematical structure and variation in problem solving. In particular, the flexible mathematical thinking with the inventive mathematical thinking, the original mathematical problem solving ability and the mathematical invention is a core concept, which must be emphasized in all branches of mathematical education. In this paper, the author considered a case of flexible mathematical thinking with an inventive problem solving ability shown by his student via real analysis courses. The case is on the proofs of the equivalences of three different definitions on the concept of limit superior shown in three different real analysis books. Proving the equivalences of the three definitions, the student tried to keep the flexible mathematical thinking steadily.

• 한국수학교육학회지시리즈A:수학교육
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• 제49권4호
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• pp.501-522
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• 2010

In this study, 'Instruments of the achievement attribution in mathematical learning' was develop to investigate the reasons of mathematical learning achievement by reflecting Korean middle school and high school students' psychological characters and learning context in mathematical learning. To develop the appropriate items for the achievement attribution in mathematical learning, after reviewing attribution literature thoroughly, first version of the instrument was developed and Exploratory Factor Analysis and Confirmatory Factor Analysis were conducted. Then, to reduce the effect of the gender difference and achievement level difference, Differential Item Functioning was performed. Also, using Multiple group Confirmatory Factor Analysis, this instrument was investigated to see whether this can be used for both middle school and high school. The final items for success attribution are 3 items for luck, 3 items for effort, 2 items for ability. The failure attribution were composed of 3 items for luck, 3 items for effort, 2 items for ability, and 2 items for other. The instrument was developed by using large samples and psychometric analysis. Therefore, mathematic teachers can use this instrument efficiently to make a foundation for better learning environment so students' cognitive area and affective area can be harmonized.

• 한국수학교육학회지시리즈E:수학교육논문집
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• 제23권3호
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• pp.545-562
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• 2009

PBG(Problem Behavior Graph; 문제해결 행동 그래프)는 인지 심리학자인 Newell과 Simon에 의해 제안된 것으로 연구 대상자가 문제를 해결할 때 인지 활동을 그래프 형식을 이용하여 그려놓은 것이다. 본 연구에서는 중학교에 재학 중인 수학 영재의 수학적 문제 해결에서 이루어지는 인지적인 과정을 추적하기 위하여, 사고구술법(Think-aloud method)으로 추출된 수학 영재 학생들의 사고 과정을 언어 프로토콜로 나타내고 분석한 것을 토대로 PBG를 구성하는 사례를 제시한다. 이를 통하여 수학 영재 학생들이 문제 해결 과정 중 인지 활동으로 거치게 되는 절차와 사고 과정 특성 지도를 살펴보고 대상 학생들이 여러 번의 시행착오 후 전체적인 과정을 수정하며 수행해 나가게 되는 방법과 문제의 최종적인 해결안을 도출해 내는 경로 탐색 과정을 종합적으로 살펴볼 수 있었다.

• International Journal of Advanced Culture Technology
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• 제10권1호
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• pp.265-273
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• 2022

The aim of this study is to investigate the relationship between the object ability, basic movement ability, and mathematical ability of young children. Next, through this study, the influence of young children's object manipulation ability and basic movement ability on mathematical ability was investigated. The subjects of this study were 80 children aged 5 years old. As a research tool, the non-mobile movement and mobile movement, the basic movement development test scale, and the young children's picture-mathematical ability test scale were used. This survey was conducted from October 2018 to January 2019. For data analysis, correlation analysis and hierarchical multiple regression analysis were performed using the spss program. As a result of the study, it was found that there was a significant positive correlation between the non-mobile ability, movement ability, object manipulation ability and mathematical ability of young children. It was found that young children's ability to manipulate objects and non-movement abilities had positive effect on their mathematical abilities. The movement ability of young children had both negative and positive effects on mathematical ability, but it was not found to be statistically significant. This study is meaningful in that it investigated the effects of non-mobile movement, mobile movement ability, and object manipulation ability, which are sub-capabilities of basic movement ability, which had not been investigated so far, on the mathematical ability of young children.

• 한국수학교육학회지시리즈A:수학교육
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• 제42권2호
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• pp.193-202
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• 2003

In this paper, we analysis 226 papers in the journal of the Korea Society of Mathematical Education Series A for recent 10 years. We classified the papers by the contents, method and the level of schools. In particular, we analysis the contents of concerns focused on the paper about geometry education.

• 한국수학교육학회지시리즈A:수학교육
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• 제45권2호
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• pp.155-163
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• 2006

In this paper, we focus on the analysis of the results of CAS-K (Creative Attitude Scale-Korea) including 33 items of 7 factors. Using the analysis gives us the information about students' creative attitude for each factor. We introduce three methods of the analysis about the results of CAS-K; total scores analysis, mean value of each factor analysis, and CAS-K map analysis. We develop the CAS-K map based on the mean value of each factor and three categories of factors. These categories are divergent attitude (fluency, appropriateness), problem solving attitude (positiveness, independency, concentration), and convergent attitude (convergency, accuracy). This analysis of the results of CAS-K can be a source of creative attitude to foster mathematical creativity.

• 한국수학교육학회지시리즈A:수학교육
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• 제46권4호
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• pp.465-482
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• 2007

The purpose of this study was to explore how pre-service elementary school teachers participate in a course specifically designed to help them learn how to analyze instruction in terms of the levels of cognitive demand of mathematical tasks. This paper describes what prospective teachers learned while reading the cases of "implementing standards-based mathematics instruction", analyzing all tasks of one unit in one elementary mathematics textbook, observing master teachers' mathematics instruction as well as their colleagues during the practicum period, and developing their own cases on the basis of the design and implementation of instruction focused on mathematical tasks. This paper includes various reflections of the prospective teachers.

• 한국수학교육학회지시리즈E:수학교육논문집
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• 제24권2호
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• pp.365-384
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• 2010

본 연구는 교육대학 학생들의 초등수학 개념 이해 정도를 조사 분석한 연구로서 두 가지 문제에 관심을 두었다. 첫째, 교육대학 학생들은 등호 기호와 변수에 대하여 어떻게 이해하고 있는가?, 둘째, 초등수학에서 다루는 수학 개념을 얼마 정확하게 이해하고 있는가? 이 연구는 J 대학교 교육대학 학생들을 대상으로 수행되었으며, 앞으로 교육대학에서의 초등수학교육 개선에 활용되어지기를 희망한다.