• The Mathematical Education
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• v.42 no.2
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• pp.229-245
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• 2003

In this paper, we present a review of research perspectives and investigations in collegiate mathematics education from the four decades of development in the journal published by Korea Society of Mathematical Education. Research of mathematics education at the tertiary level, which had been a minor area in mathematics education, has made a significant development in the last decade in Europe md U.S.A. In this context, international journals for research in mathematics education were selected to comparatively examine and identify research trends and tasks in collegiate mathematics education. Based on the analysis of domestic at international journals, we present recommendations for further the development of Korean collegiate mathematics education research. First it is necessary to diversify the topics of educational research. Korean research of mathematics education at the tertiary level has been limited to the issues of curriculum developments, teacher education and computer technology. It is necessary to pursue more various topics such as conceptual development mathematical attitude and belief gender, socio-cultural aspect of teaching and teaming mathematics. Second, it is necessary to apply research methods for systematic investigations. It is important to note that international research of mathematics education introduces variety of research methods such as observation, interview, and survey in order to develop grounded theory of mathematics education. We end with pedagogical implications of the analyses presented and general conclusions concerning the perspectives for the future in collegiate mathematics education.

• Research in Mathematical Education
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• v.8 no.1
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• pp.19-30
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• 2004

This research applies the discursive approach to investigate the social transformation of students' conceptual model of differential equations. The analysis focuses on the students' use of metaphor in class in order to find kinds of metaphor used, their characteristics, and a pattern in the use of metaphor. Based on the analysis, it is concluded that the students' conceptual model of differential equations gradually becomes transformed with respect to the historical and cultural structure of the communal practice of mathematics. The findings suggest that through participating in the daily practice of mathematics as a historical and cultural product, a learner becomes socially transformed to a certain kind of a cultural being with historicity. This implies that mathematics education is concerned with the formation of historical and cultural identity at a fundamental level.

• Communications of Mathematical Education
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• v.19 no.4 s.24
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• pp.733-767
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• 2005

During the past decades, there has been a fundamental change in the objectives and nature of mathematics education, as well as a shift in research paradigms. The changes in mathematics education emphasize learning mathematics from realistic situations, students' invention or construction solution procedures, and interaction with other students of the teacher. This shifted perspective has many similarities with the theoretical . perspective of Realistic Mathematics Education (RME) developed by Freudental. The RME theory focused the guide reinvention through mathematizing and takes into account students' informal solution strategies and interpretation through experientially real context problems. The heart of this reinvention process involves mathematizing activities in problem situations that are experientially real to students. It is important to note that reinvention in a collective, as well as individual activity, in which whole-class discussions centering on conjecture, explanation, and justification play a crucial role. The overall purpose of this study is to examine the developmental research efforts to adpat the instructional design perspective of RME to the teaching and learning of differential equation is collegiate mathematics education. Informed by the instructional design theory of RME and capitalizes on the potential technology to incorporate qualitative and numerical approaches, this study offers as approach for conceptualizing the learning and teaching of differential equation that is different from the traditional approach. Data were collected through participatory observation in a differential equations course at a university through a fall semester in 2003. All class sessions were video recorded and transcribed for later detailed analysis. Interviews were conducted systematically to probe the students' conceptual understanding and problem solving of differential equations. All the interviews were video recorded. In addition, students' works such as exams, journals and worksheets were collected for supplement the analysis of data from class observation and interview. Informed by the instructional design theory of RME, theoretical perspectives on emerging analyses of student thinking, this paper outlines an approach for conceptualizing inquiry-oriented differential equations that is different from traditional approaches and current reform efforts. One way of the wars in which thus approach complements current reform-oriented approaches 10 differential equations centers on a particular principled approach to mathematization. The findings of this research will provide insights into the role of the mathematics teacher, instructional materials, and technology, which will provide mathematics educators and instructional designers with new ways of thinking about their educational practice and new ways to foster students' mathematical justifications and ultimately improvement of educational practice in mathematics classes.

• Proceedings of the Korea Society of Mathematical Education Conference
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• 2007.06a
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• pp.7-19
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• 2007

During the past 20 years, a small but potentially powerful initiative has established itself in the mathematics education landscape: Mathematics Across the Curriculum (MAC). This curricular reform movement was designed to address a serious problem: Not only are students unable to demonstrate understanding of mathematical ideas and their applications, but also they harbor misconceptions about the meaning and purpose of mathematics. This paper chronicles the brief history of the MaC movement. The sections of the paper correspond loosely tn the typical steps one might take to solve a mathematics problem. The Problem Takes Shape presents a discussion of the social and economic forces that led to the need for increased articulation between mathematics and other fields in the American educational system. Understanding the Problem presents the potential value of exploiting these connections throughout the curriculum and the obstacles such action might encounter. Devising a Plan provides an overview of the support systems provided to early MAC initiatives by government and professional organizations. Implementing the Plan contains a brief description of early collegiate programs, their approaches and their differences. Extending the Solution details the adoption of MAC principles to the K-12 sector and throughout the world. The paper concludes with Retrospective, a brief discussion of lessons learned and possible next steps.

• Communications of Mathematical Education
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• v.15
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• pp.281-286
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• 2003

The primary purpose of this study was to investigate how and to what extent 'representations' affect the students' understanding and the growth of understanding in a technology [GSP]-based collegiate mathematics classroom. There are three themes related as frames of the study along with this purpose, which are mentioned in the first chapter and extended in the second chapter: technology in mathematics education; images on computer screen - visualization and representation; understanding and growth of understanding. Three research questions guided this study: 1) How do students present each component of representations when they study 'transformations' in a technology [GSP]-based classroom? If there is any difference between the first and second presentation for each component, how are they different?; 2) How and to what extent do representations affect the students' understanding and the growth of understanding in a technology [GSP]-based classroom?; What types of benefits and obstacles are there when students study 'transformations' in a technology [GSP]-based classroom?

• Bulletin of the Korean Mathematical Society
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• v.61 no.3
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• pp.611-619
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• 2024

For a finite group G, let 𝜓(G) denote the sum of element orders of G. If ${\psi}^{{\prime}{\prime}}(G)\,=\,{\frac{\psi(G)}{{\mid}G{\mid}^2}}$, we show here that the image of 𝜓'' on the class of all Dihedral groups whose order is twice a composite number greater than 4 is dense in $[0,\,{\frac{1}{4}}]$. We also derive some properties of 𝜓'' on the class of all dihedral groups whose order is twice a prime number.

• Communications of Mathematical Education
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• v.24 no.4
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• pp.891-907
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• 2010

This study analyzed the Fundamental Theorem of Calculus from the historical, mathematical, and instructional perspectives. Based on the in-depth analysis, this study suggested an alternative way of teaching the Fundamental Theorem of Calculus.