• Journal of Elementary Mathematics Education in Korea
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• v.14 no.3
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• pp.681-700
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• 2010

These days, the importance of the mathematics interaction is strongly emphasized, which leads to the need of research on how the interaction is being practiced in the math class and what can be the desirable interaction in terms of mathematical thinking. To figure out the correlation between the mathematical interaction patterns and mathematical thinking, it also classifies mathematical thinking levels into the phases of recognizing, building-with and constructing. we can say that there are all of three patterns of the mathematics interactions in the class, and although it seems that the funnel pattern is contributing to active interaction between the students and teachers, it has few positive effects regarding mathematical thinking. In other words, what we need is not the frequency of the interaction but the mathematics interaction that improves students' mathematical thinking. Therefore, we can conclude that it is the focus pattern that is desirable mathematics interaction in the class in the view of mathematical thinking.

• School Mathematics
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• v.12 no.4
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• pp.507-530
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• 2010

The purpose of this study was to help teachers for their teaching practice by analyzing the excellent lesson videos. To analyze the lesson videos between teacher and students, the researchers classified excellent lesson classes into four types as 'Discourse type', 'Representation type', 'Operation type' and 'Complex type' by mathematical communication pattern and kept close watch each lesson videos. Mathematical communication of the best discourse type classroom was analyzed in terms of questioning, explaining, and the sources of mathematical ideas. As a result, the number of Discourse type classes was 6. Operation type classes were 16 owing to characteristic of elementary class. Representation type class was 1 and Complex type class was 1. The Classes excluding Operation type was more planned by teachers. Teachers need to know about mathematical communication accurately because they designed just 5 lesson plan considering mathematical communication of students and only one of the lessons has the intellectual purpose of communication. Furthermore teachers should reflect questioning for student-to-student in their lesson plan.

• Journal of Elementary Mathematics Education in Korea
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• v.21 no.4
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• pp.621-641
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• 2017

The purposes of this study were to identify the characteristics of students with different cognitive styles in the communication process according to the types of mathematical tasks and investigate the effects of their cognitive styles and types of mathematical tasks on their mathematical communication. For this, the investigator selected subjects according to the field dependent-field independent cognitive style by Witkin et al.(1977, p. 7). Mathematical tasks were developed in the areas of numbers and operations, regularity, and measurement according to the four types of Stein & Smith(1998, p. 269), which include the Memorization, Procedures without Connections, Procedures with Connections, and Doing Mathematics tasks. The selected students were divided into homogeneous groups according to their cognitive styles, and their communication processes according to the four types of mathematical tasks were observed through participation and videotaped. The videotapes were then transcribed and analyzed in protocols. The conclusions is that mathematical tasks of high cognitive level had positive effects on the activation of significant mathematical communication among the students and that differences in approaches to tasks according to their cognitive styles influenced their communicative activities in speaking and listening.

• Journal for History of Mathematics
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• v.23 no.3
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• pp.141-168
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• 2010

Mathematical communication is necessary to exchange mathematical idea among participants in teaching-learning process. The promotion of mathematical communication competence is clearly stated in many parts of the 2007 revised curriculum. As a result, mathematical communication tasks are contained in 'high school Mathematics' textbook. At this point of time when increasing importance of mathematical communication is realized, we will check over mathematical communication and analyze communicative tasks corner in 'high school Mathematics' textbook in this paper And thereby we hope this study help prepare for practical communicative tasks corner suggesting a way for invigoration of mathematical communication.

• Journal of the Korean School Mathematics Society
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• v.11 no.2
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• pp.201-219
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• 2008

The purpose of this study was to provide useful information for teachers by analyzing various levels of teacher-student communication in elementary mathematics classes and students' mathematical thinking. This study explored mathematical communication of 3 classrooms with regard to questioning, explaining, and the source of mathematical ideas. This study then probed the characteristics of students' mathematical thinking in different standards of communication. The results showed that the higher levels of teacher-student mathematical communication were found with increased frequency of students' mathematical thinking and type. The classroom that had a higher level of Leacher-student mathematical communication was exhibited a higher level of students' mathematical thinking. This highlights the importance of mathematical communication in mathematics c1asses and the necessity of further developing skills of mathematical communication.

• Journal of Elementary Mathematics Education in Korea
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• v.19 no.3
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• pp.435-455
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• 2015

This study is aimed at analyzing the level change and features of mathematical communication in elementary students' expository writing. 20 students of 5th graders of elementary school in Seoul were given expository writing activity for 14 lessons and their worksheets was analyzed through four categories; the accuracy of the mathematical language, logicality of process and results, specificity of content, achieving the reader-oriented. This study reached the following results. First, The level of expository writing about concepts and principles was gradually improved. But the level of expository writing about problem solving process is not same. Middle class level was lower than early class, and showed a high variation in end class again. Second, features of mathematical communication in expository writing were solidity of knowledge through a mathematical language, elaboration of logic based on the writing, value of the thinking process to reach a result, the clarification of the content to deliver himself and the reader. Therefore, this study has obtained the conclusion that expository writing is worth keeping the students' thinking process and can improve the mathematical communication skills.

• Communications of Mathematical Education
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• v.30 no.3
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• pp.353-374
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• 2016

Communication is one of 6 core competencies suggested newly in mathematics curriculum revised in 2015 in Korea. Also, it's importance has been emphasized through NCTM and CCSSI. By the subject of Mathematics in Context(MiC) textbook, this study planned to explore the communication elements according to the types of communication such as discourse, representation, operation. Namely, this study dealt with 316 questions in a total of 34 tasks relevant to function content in the MiC textbook, and this study explored the communication elements on the questions of each task. To accomplish this, this study first of all was to reconstruct and establish an analytic framework, on the basis of 'D.R.O.C type' of communication developed by Kim & Pang in 2010. In addition, based on the achievement standards of function domain in mathematics curriculum revised in 2015 in Korea, this study basically compared with the function content included in MiC textbook and Korean mathematics curriculum document. Also, it tried to explore the distribution of communication elements according to the types of communication.

• Journal of Elementary Mathematics Education in Korea
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• v.13 no.2
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• pp.141-161
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• 2009

Mathematical Communication ability can be more developed through sharing thoughts with others. Therefore when we instruct students in math, it is very important for teachers to provide them with opportunity to communicate mathematically. So this study provided open-ended problems in small-group collaborative learning. And we analyzed students' mathematical communication focused on the student's level of understanding. Furthermore, to improve students' mathematical communication ability, this study tries to attract the factors that we should consider the exact date for inserting the open-ended problems into a course of math and the student's level of understanding for selecting suitable open-ended problems.

• Journal of the Korean School Mathematics Society
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• v.12 no.3
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• pp.247-265
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• 2009

In the 21C information-based society, there is an increasing demand for emphasizing communication in mathematics education. Therefore the purpose of this study was to research how properties of communication among small group members varied by mathematical problem types. 8 fourth-graders with different academic achievements in a classroom were divided into two heterogenous small groups, four children in each group, in order to carry out a descriptive and interpretive case study. 4 types of problems were developed in the concepts and the operations of fractions and decimals. Each group solved four types of problems five times, the process of which was recorded and copied by a camcorder for analysis, among with personal and group activity journals and the researcher's observations. The following results have been drawn from this study. First, students showed simple mathematical communication in conceptual or procedural problems which require the low level of cognitive demand. However, they made high participation in mathematical communication for atypical problems. Second, even participation by group members was found for all of types of problems. However, there was active communication in the form of error revision and complementation in atypical problems. Third, natural or receptive agreement types with the mathematical agreement process were mainly found for conceptual or procedural problems. But there were various types of agreement, including receptive, disputable, and refined agreement in atypical problems.

• Communications of Mathematical Education
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• v.24 no.2
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• pp.385-413
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• 2010

The purpose of this study is to set appropriate targets for school-year levels and types of mathematical communication. First, I classify mathematical communication into four types as Discourse, Representation, Operation and Complex and refer to them collectively as the 'D.R.O.C pattern'. I have listed achievement factors based on the D.R.O.C pattern hearing opinions from specialists to set a target, then set a final target after a 2nd survey with specialists and teachers. I have set targets for mathematical communication in elementary schools suitable to its status and students' levels in our country. In NCTM(2000), standards of communication were presented only from kindergarten to 12th grade students, and, for four separate grade bands(prekindergarten through grade 2, grades 3-5, grades 6-8, grades 9-12), they presented characteristics of the same age group through analysis of classes where communication was active and the stated roles of teachers were suitable to the characteristics of each school year. In this study, in order to make the findings accessible to teachers in the field, I have classified types into Discourse, Representation, Operation and Complex (D.R.O.C Pattern) according to method of delivery, and presented achievement factors in detail for low, middle and high grades within each type. Though it may be premature to set firm targets and achievement factors for each school year group, we hope to raise the possibility of applying them in the field by presenting targets and achievement factors in detail for mathematical communication.