• Research in Mathematical Education
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• v.3 no.2
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• pp.89-98
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• 1999

The purpose of this review of literature is to investigate what kinds of research have been done on social construction of mathematics understanding among elementary students in small groups. Only empirical studies were reviewed, and then grouping was done in terms of the purpose of the study. This grouping identified three categories: 1) Social and mathematical norms in mathematics classroom, 2) Teaching productive communication behaviors for active learning in small group, and 3) Participation roles and communication behaviors in different group structure. To enhance social construction of mathematics understanding in small group settings two suggestions are made: the importance of the selection of collaborative tasks or problems and teachers' beliefs about mathematics and the teaching an learning of mathematics.

• East Asian mathematical journal
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• v.30 no.4
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• pp.439-449
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• 2014

In the history of mathematics education, different opinions as to how to view the phenomenon of mathematics education have been suggested in various ways. As those conflicting opinions have caused fundamental tensions in the phenomenon of mathematics education, they remain fundamental standpoints that have been continuously advocated until now - not limited in a certain period. It can be argued that this situation was caused by partial or fragmentary understanding of the phenomenon of mathematics education. If we are pursuing not a partial knowledge but a complete understanding of mathematics education, how should it be formed to comprehensively study the entire phenomenon of mathematics education? To answer this question, Complex structure in phenomenon of Mathematics Education can be proposed. It is an explanation for the opposing opinions existing in the phenomenon of mathematics education. The purpose of this paper is to understand the phenomenon of mathematics education as a whole.

• The Mathematical Education
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• v.41 no.2
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• pp.173-187
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• 2002

The purpose of this study through ethnographic inquiry is to describe how an elementary teacher teaches mathematics with understanding. The ways that teachers'beliefs affect instructional activities, what means understanding from the view of cognitive psychology, and ethnographic research tradition were reviewed to anchor theoretical background of this study. A third-grade teacher and his 45 students were selected in order to capture vivid and thick descriptions of the teaching and learning activities of mathematics. Three major sources of data, that is, participant-observation with video taping, formal and informal interviews with the teacher and his students, and a variety of official documents were collected. These data were analyzed through two phases: data analysis in the field and after the fieldwork. According to data analysis, ‘teaching mathematics with understanding’ was identified as the teachers central belief of teaching mathematics. In order to implement his belief in teaching practices, the teacher made use of three strategies: ⑴ valuing individual student's own way of understanding, ⑵ bring students' everyday experiences into mathematics classroom, and ⑶ lesson objectivies stated by students. It is suggested for future research that concrete and specific norms of mathematics classroom for the improvement of mathematics understanding are needed to be identified and that experienced and skillful teachers' practical knowledge should be incorporated with theories of teaching mathematics and necessarily paid more attention by mathematics educators.

• Research in Mathematical Education
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• v.13 no.3
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• pp.235-250
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• 2009

Researchers at Truman State University in Missouri, located in the heartland of the United States, have been using materials adapted from the English translations of the sixth national primary mathematics curriculum from Korea for professional development and assessment with groups of Missouri teachers for the purpose of enhancing teachers' understanding of the fundamentals of mathematics since 2002 [gecKo Mathematics (2008). Korean Mathematics in American Classrooms. Edited by J. Grow-Maienza. Adapted from Korean Mathematics (2001). Kirksville, MO: Truman State University. http://kmath.truman.edu/]. A professional development initiative for 50 teachers conducted in Missouri this past year is reported here. Significant gains in teacher understanding of fundamental mathematics concepts and pedagogy necessary for student achievement in primary mathematics were found as a result of the initiative.

• 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?

• Research in Mathematical Education
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• v.4 no.1
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• pp.1-22
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• 2000

The purpose of this study was to investigate the effects of using graphing calculators on students' understanding of the linear and quadratic function concepts. The populators of this study are tenth graders at high school in Seoul, one class for the treatment group and another class for the comparison group, and experiment period is 14 weeks including two weeks for school regular exams.Function tests used in the study was proposed which described a conceptual knowledge of functions in terms of the following components: a) Conceptual understanding, b) Interpreting a function in terms of a verbal experission, c) Translating between different representations of functions, and d) Mathematical modeling a real-world situation using functions. Even though the group test means of the individual components of conceptual understanding, interpreting, translating, mathematical modeling did not differ significantly, there is evidence that the two groups differed in their performance on conceptual understanding. It was shown that students learned algebra using graphing calculators view graphs more globally. The attitude survey assessed students' attitudes and perceptions about the value of mathematics, the usefulness of graphs in mathematics, mathematical confidence, mathematics anxiety, and their feelings about calculators. The overall t-test was not statistically significant, but the students in the treatment group showed significantly different levels of anxiety toward mathematics.

• The Mathematical Education
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• v.39 no.1
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• pp.49-58
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• 2000

The purpose of this study is to investigate how to teach algorithms in mathematics class. Until recently, traditional school mathematics was primarily treated as drill and practice or memorizing of algorithmic skills. In an attempt to shift the focus and energies of mathematics teachers toward problem solving, conceptual understanding and the development of number sense, the recent reform recommendations do-emphasize algorithmic skills, in particular, paper-pencil algorithms. But the development of algorithmic thinking provides the foundation for student's mathematical power and confidence in their ability to do mathematics. Hence, for learning algorithms meaningfully, they should be taught with problem solving and conceptual understanding.

• Journal of Elementary Mathematics Education in Korea
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• v.9 no.2
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• pp.137-159
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• 2005

As what exactly understands a meaning of mathematics terms, is a starting point of mathematical thinking, it plays a very important role in the mathematics learning. What understood mathematics terms which were defined here, includes not only the terms of comprising its definition, but also all of the understanding in context, situation, intention and purpose, which came to give its definition. Due to this reason, it needs to be examined how much students are correctly understanding about mathematics terms which appear in the texts, and to seek for its cause for the terms which are felt to be difficult. Accordingly, this study investigated into mathematics terms which are used for the field of geometry in the elementary school mathematics textbooks, and tried to analyze students' understanding level about each term.

• The Mathematical Education
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• v.52 no.1
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• pp.97-109
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• 2013

Research in undergraduate mathematics education has been active very recently. The purpose of the paper is to investigate how college students make ion from some known informations about integer and rational numbers in algebra. Three college students were involved in the study. We analyze student's personal answers in order to find where their misunderstandings and difficulties come from based on the theoretical frameworks on mathematical understanding such as APOS-model and P-K-model. Finally we discuss about constructivist teaching ways for algebra and propose new paradigm for teaching undergraduate mathematics.

• The Mathematical Education
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• v.52 no.3
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• pp.379-398
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• 2013

The purpose of this research is to study a perception of multicultural education for preservice teachers who major in mathematics. The research has been done on the data collected from 126 preservice teachers in Gangwon-do who major in mathematics. The data collected include experience of multiculturalism, multicultural efficacy, multicultural understanding and multicultural sensitivity. The data have been analyzed by reliability test, t-test, one-way anova and pearson correlation. Most of preservice teachers who major in mathematics have had no experience of multiple cultures. But they have shown a high perception on multicultural education and a significant positive correlation on their experience of multiculturalism, multicultural efficacy and multicultural sensitivity. Furthermore, the female preservice teachers' multicultural efficacy, multicultural understanding and multicultural sensitivity are much more high than the male preservice teachers'. The difference between different sex has been statistically significant.