• The Mathematical Education
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• v.41 no.2
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• pp.157-172
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• 2002

The purpose of this study is to improve middle students'mathematical communication ability. We designed the mathematics instruction model based on Vygotsky's ZPD to develop the mathematical communication ability, and applied to 2nd grade students in Middle School. And we investigated the significant differences between the group which was instructed with mathematical communication and the group which was instructed with teacher's traditional explanation in aspects of learning achievement, mathematical disposition, and mathematical communication abilities. The results of the study are as follows : 1. There is no significant difference in learning achievement within significance level .05 between the group which was instructed with mathematical communication and the group which was instructed with teacher's traditional explanation by t-test. 2. There is a significant difference in reflection within significance level .01 and in self-confidence within significance level .10 by MANCOVA. 3. There is a significant difference in mathematical communication ability within significance level .01 between two groups by covariance analysis. In particular, there is a significant difference in reading within significance level .01 and in speaking within significance level .05 by t-test.

• East Asian mathematical journal
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• v.36 no.2
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• pp.173-201
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• 2020

Mathematical modeling has been emphasized because it offers important opportunities for students to both apply their learning of mathematics to a situation and to explore the mathematics involved in the context of the situation. However, unlike its importance, mathematical modeling has not been grounded in typical mathematics classes because teachers do not have enough understanding of mathematical modeling and they are skeptical to implement it in their lessons. The current study analyzed the data, such as video recordings, slides, and surveys for teachers, collected in four lessons of teacher education in terms of mathematical modeling. The study reported different kinds of tasks that are authentic with regards to mathematical modeling. Furthermore, in teacher education, teachers' identities have separated a mode as learners and a mode as teachers and conflicts and intentional transition were observed. Analysis of the surveys shows what teachers think about mathematical modeling with their understanding of it. In teacher education, teachers achieved different kinds of modeling tasks and experience them which are helpful to enact mathematical modeling in their lessons. However, teacher education also needs to specifically offer what to do and how to do it for their lessons.

• The Mathematical Education
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• v.45 no.3 s.114
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• pp.345-365
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• 2006

This study, to effectively teach the concepts, principles and problem solving ability of the 2nd graders' learning of numbers and operations, offers realistic problem situation and focuses on the learning based on 'mathematization', one of the most important principles of RME (Realistic Mathematics Education) which is the mathematics education trend of Netherlands influenced by Freudenthal's theory. The instruction is applied to forty-one students of the 2nd grader for six weeks in twelve series in an elementary school, located in Seoul. To investigate the effects of the mathematising experience instruction for improving mathematical abilities, the group takes tests before and after the instruction. Also the qualitative analysis on the students' mathematising aspects through students' output at the instruction process is taken into account to evaluate the instruction's effects. The result shows that the mathematising experience instruction for improving mathematical abilities is proved to improve students' understanding of mathematical concepts and principles and their problem solving ability in learning numbers and operations after carrying out this instruction. Also the result indicates that students' mathematising aspects are mostly horizontal and vertical mathematization.

• Journal of Educational Research in Mathematics
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• v.14 no.3
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• pp.239-266
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• 2004

This article presents new perspectives for analysing and diagnosing students' mathematical errors on the basis of Pascaul-Leone's neo-Piagetian theory. Although Pascaul-Leone's theory is a cognitive developmental theory, its psychological mechanism gives us new insights on mathematical errors. We analyze mathematical errors in the domain of proof problem solving comparing Pascaul-Leone's psychological mechanism with mathematical errors and diagnose misleading factors using Schoenfeld's levels of analysis and structure and fuzzy cognitive map(FCM). FCM can present with cause and effect among preconceptions or misconceptions that students have about prerequisite proof knowledge and problem solving. Conclusions could be summarized as follows: 1) Students' mathematical errors on proof problem solving and LC learning structures have the same nature. 2) Structures in items of students' mathematical errors and misleading factor structures in cognitive tasks affect mental processes with the same activation mechanism. 3) LC learning structures were activated preferentially in knowledge structures by F operator. With the same activation mechanism, the process students' mathematical errors were activated firstly among conceptions could be explained.

• Research in Mathematical Education
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• v.26 no.2
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• pp.63-82
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• 2023

In the context of Korean educational research, the number of qualitative research studies has gradually increased since 2000. It has become one of the most important research methods today. The field of math education is no exception to this trend, and qualitative approaches are now becoming one of the main research methods. This increase in qualitative research has contributed to the provision of detailed information about educational practice, but at the same time, the overall level of credibility in the results of qualitative research seems to be lower than that of quantitative research. This study started with the problem consciousness that the number of qualitative studies is increasing in the field of mathematical education, but there is a lack of discussion on the methodology of applying qualitative research methods. In this study, among the papers published in the journal related to mathematical education, papers using a qualitative approach are analyzed focusing on cross-case analysis. Based on the analysis results, the tendency to use qualitative approaches is diagnosed, ways of improving the validity and trustworthiness of qualitative research results in the field of mathematical education are examined, and implications and suggestions are presented.

• Korean Journal of Child Studies
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• v.25 no.4
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• pp.129-145
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• 2004

This study examined the effects of Literature-based Mathematical Activities using scaffolding (LMS) on the mathematical achievement, interest, and vocabulary of day care children. The experimental group of 15 boys and 15 girls was exposed to both literature and teacher's scaffolding while the comparison group of 14boys and 16 girls had traditional mathematics curriculum. The experiment was carried out for 8 weeks. ANCOVA and T-test were employed for a statistical analysis. The results revealed statistically significant differences in mathematical achievement, interest, and vocabulary between an experimental and control groups. We can conclude, therefore, that LMS is more effective in developing children's mathematical thinking abilities than a traditional mathematical curriculum.

• Journal of the Korean School Mathematics Society
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• v.16 no.2
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• pp.319-335
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• 2013

Chinese mathematical curriculum is divided 4 areas(number and algebra, space and figure, statistics and probability, practice and synthetic application). The purpose of this paper is to analyze the contents of the practice and synthetic application in yanbian elementary textbook. For this, 12-textbook which was published in yeonbeon a publishing company is analyze by topic, mathematical process, area of content and mathematical activity. mathematical process The following results have been drawn from this study. First, contextual backgrounds of practice are restricted in classroom. The contents of synthetic application are limited in connection of mathematical areas. Mathematical problem solving is a main in mathematical process, whereas reasoning activity is a few. Mathematical experience activity is a main in mathematical process, whereas synthetic activity is a few. We can use the suggestions of this paper for development of textbook and the contents of mathematical process.

• Education of Primary School Mathematics
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• v.18 no.2
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• pp.123-139
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• 2015

The purpose of this study was to investigate the effects of the experiences of productive failures on students' mathematical problem solving abilities and mathematical dispositions. The experiment was conducted with two groups. The treatment group was applied with the productive mathematics failure program, and the comparative group was taught with traditional mathematics lessons. In this study, for quantitative analysis, the students were tested their understanding of mathematical concepts, mathematical reasoning abilities, students' various strategies and mathematical dispositions before and after using the program. For qualitative analysis, the researchers analyzed the discussion processes of the students, students's activity worksheets, and conducted interviews with selected students. The results showed the followings. First, use of productive failures showed students' enhancement in problem solving abilities. Second, the students who experienced productive failures positively affected the changes in students' mathematical dispositions. Along with the more detailed research on productive mathematical failures, the research results should be included in the development of mathematics textbooks and teaching and learning mathematics.

• Bulletin of the Korean Mathematical Society
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• v.38 no.3
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• pp.517-526
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• 2001

In this paper, we study the continuous wavelet transform on the Heisenberg group H$^n$, and describe the related continuous multiscale analysis. By using the wavelet packet transform we obtain a reconstruction formula on L$^2$(H$^n$).

• East Asian mathematical journal
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• v.29 no.5
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• pp.521-527
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• 2013

The aim of this paper is to define hyperholomorphic function with sedenion variables in $\mathbb{C}^8$ and research the properties of hyperholomorphic functions of sedenion variables. We generalize the properties of hyperholomorphic functions in sedenionic analysis.