• The Mathematical Education
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• v.62 no.1
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• pp.35-55
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• 2023

The purpose of this study is to examine not only students' cognition in the mathematical error-finding activity of the concept of irrational numbers, but also the students' learning stance regarding the use of errors and a teacher's questioning strategies that lead to changes in the level of mathematical discourse. To this end, error-finding individual activities, group activities, and additional interviews were conducted with 133 middle school students, and students' cognition and the teacher's questioning strategies for changes in students' learning stance and levels of mathematical discourse were analyzed. As a result of the study, students' cognition focuses on the symbolic representation of irrational numbers and the representation of decimal numbers, and they recognize the existence of irrational numbers on a number line, but tend to have difficulty expressing a number line using figures. In addition, the importance of the teacher's leading and exploring questioning strategy was observed to promote changes in students' learning stance and levels of mathematical discourse. This study is valuable in that it specified the method of using errors in mathematics teaching and learning and elaborated the teacher's questioning strategies in finding mathematical errors.

• The Mathematical Education
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• v.59 no.1
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• pp.17-29
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• 2020

The purpose of this study is to analyze the teacher's discourse structure of teachers according to the interaction pattern between teacher and student in the process of mathematization. To achieve this goal, we observed a semester class (44 lessons) of an experienced teacher who had practiced teaching methods for promoting student engagement for more than 20 years. Among them, one lesson case would be match the teacher's intention and the student's response and the other one lesson case would be to mismatch between the teacher's intention and the student's response was analyzed. In other words, in the process of mathematization based on students' engagement, the intention of the teacher and the reaction of the student was determined according to the cases where students did not make an error and when they made an error. A methodology used to develop a theory based on data collected through classroom observations(grounded theory). Because the purpose of the study is to identify the teacher's discourse structure to help students' mathematization, observe the teacher's discourse and collect data based on student engagement. Based on the teacher's discourse, conceptualize it as a discourse structure for students to mathematization. As a result, teacher's discourse structure had contributed to the intention of the teacher and the reaction of the student in the process of mathematization. Based on these results, we can help the development of classroom discourse for mathematization by specifying the role of the teacher to help students experience the mathematization process in the future.

• Journal of the Korean School Mathematics Society
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• v.23 no.1
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• pp.45-65
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• 2020

This research is an analysis of communication that occurs during the quadratic function teaching and learning process of middle school students, which reflects mathematical modeling. For an in-depth analysis of the communication, Sfard(2008)'s discourse theory and language analysis framework were applied. A quadratic function mathematical modeling teaching and learning were conducted for the week second (1 hour) in June 2019 for students who studied the concept of a quadratic function and who passed a specified period (3 months). The results are as follows. First, The commo-gnitive conflict occurred because of differences in prior knowledge other than quadratic function among students. Second, in the course of communication, knowledge was expanded through problem-solving from different perspectives. These results can be interpreted as allowing students to clearly reveal problems in the communication process based on their understanding of the concept of quadratic functions and to facilitate cooperation among students. of the concept of quadratic functions and to facilitate cooperation among students.

• Journal of the Korean School Mathematics Society
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• v.18 no.3
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• pp.281-309
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• 2015

The purpose of this study is provides an implication of further teaching learning process by analyze the common and difference and characteristic of mathematical self-efficiency between three peer tutoring groups discourse in the mathematical teaching leaning process that use peer tutoring. To achieve this goal, three groups formed that consist of one peer tutor who received a first grade of mathematic achievement and one peer student. Peer student of each group is divided into high grade, middle grade, low grade of mathematic achievement. Then analyze the discourse in the exponential function problem solving process. Based on the results of study, this paper provides a concrete example of merit of peer tutoring on the peer tutor. Result of study also provides a practical help to make a peer tutoring group by considering a difference of grades between peer tutor and peer student. Because there is a possibility of mutual discourse on the tutoring group that consist of similar grades.

• 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.

• East Asian mathematical journal
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• v.32 no.2
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• pp.291-300
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• 2016

The integration of mathematics education is required Fundamentally discussion about the nature and purpose of mathematics education. After the theoretical discussion of that, Practical approach of that can be correctly realized. However, It is the impression that theoretical discussions and practical action about the current discourse about integration in mathematics education are the wrong order. To understand the practical action for the integrated approach in mathematics education, theoretical discussion of the integrated approach of mathematical education is properly required.

• School Mathematics
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• v.12 no.1
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• pp.1-15
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• 2010

The study presented in this paper, which serves as a pilot study for a future comprehensive project, was to investigate how students deal with the concepts of infinity and limit. Based on the communicational approach to cognition, according to which mathematics is a kind of discourse, we tried to identify the characteristics of students' discourse on the topics. Four American and four Korean students were interviewed in English on limits and infinity and their discourse was scrutinized with an eye to common characteristics as well as culture, age, and education-related differences.

• School Mathematics
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• v.19 no.3
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• pp.571-591
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• 2017

The purpose of this study is to understand the characteristics of mathematical discourse about the length in the class that learns the length of the curve defined by definite integral. For this purpose, this study examined the discourse about length by paying attention to the usage of the word 'length' in the class participants based on the communicative approach. As a result of the research, it was confirmed that the word 'length' is used in three usages - colloquial, operational, and structural usage - in the process of communicating with the discourse participants. Particularly, each participant did not recognize the difference even though they used different usage words, and this resulted in ineffective communication. This study emphasizes the fact that the difference in usage of words used by participants reduces the effectiveness of communication. However, if discourse participants pay attention to the differences of these usages and recognize that there are different discourses, this study suggests that meta - level learning can be possible by overcoming communication discontinuities and resolving conflicts.

• East Asian mathematical journal
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• v.38 no.4
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• pp.397-414
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• 2022

This study tried to explore and understand the meaning, and the properties of noticing. The result of this study were first, the difference in mathematical noticing is distinguished in either the object which is paid attention is different or the object is same but differently interpreted or react. The cause of each difference could be described as mathematical objects such as conceptual objects and perceptual features. Second, teachers' teaching strategies, which narrow the gap in attention and play a key role in the formation of mathematical meaning, appeared in various places. This teaching strategy was implemented to distract students' attention. This study confirmed that the mathematical attention of teachers and students in math classes will differ depending on the object to which they pay attention, and that difference will be narrowed through teacher's discourse practice and teaching strategies through communication strategies.

• Journal for History of Mathematics
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• v.21 no.1
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• pp.157-166
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• 2008

Mathematical communication is an important goal of recent educational reform. The NCTM's Principle and Standards for School Mathematics, consulting an emphasis on mathematical discourse from 1991 Professional Standards for Teaching Mathematics, has a Communication Standard at each grade level. This paper examines Socrates's educational philosophy and the mathematical dialogue in Plato's. Further it examines mathematical dialogues between teachers and students from antiquity through the nineteenth century.