• Journal of the Korean School Mathematics Society
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• v.15 no.1
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• pp.53-80
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• 2012

This study was designed to find the characteristics of mathematical errors and discourse in simultaneous equations and inequalities for migrant students from North Korea. 5 sample students participated, who attended in an alternative school for the migrant students from North Korea at the study in Seoul, Korea. A total of 8 lesson units were performed as an extra curriculum activity once a week during the 1st semester, 2011. The results indicated that students showed technical errors, encoding errors, misunderstood symbols, misinterpreted language, and misunderstood Chines characters of Koreans and the discourse levels improved from the zero level to the third level, but the scenes of the third level did not constantly happen. Nevertheless, the components of discourse, explanation & justification, were activated and as a result, evaluation & elaboration increased in ERE pattern on communication.

• Research in Mathematical Education
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• v.23 no.2
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• pp.63-92
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• 2020

Student engagement in high-level, cognitively demanding instruction is pivotal for student learning. However, many teachers are unable to maintain such instruction, especially in instances of non-responsive students. This case study of three middle school teachers explores prompts that aim to move classroom discussions past student silence. Prompt sequences were categorized into Progressing, Focusing, and Redirecting Actions, and then analyzed for maintenance of high levels of cognitive demand. Results indicate that specific prompt types are prone to either raise or diminish the cognitive demand of a discussion. While Focusing Actions afforded students opportunities to process information on a more meaningful level, Progressing Actions typically lowered cognitive demand in an effort to get through mathematics content or a specific method or procedure. Prompts that raise cognitive demand typically start out as procedural or concrete and progress to include students' thoughts or ideas about mathematical concepts. This study aims to discuss five specific implications on how teachers can use prompting techniques to effectively maintain cognitively challenging discourse through moments of student silence.

• The Mathematical Education
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• v.46 no.4
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• pp.423-443
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• 2007

Based on the framework of Huffered-Ackles, Fuson and Sherin(2004), data were analyzed in terms of 3 components: explaining(E), questioning(Q) and justifying(J) of students' mathematical concepts and problem solving in a math classroom. The students used varied presentations to explain and justify their mathematical concepts and ideas. They corrected their mathematical errors or misconceptions through discourses. In addition, they constructed and clarified their concepts and thinking while they were interacted. We were able to recognize there was a special feature in discourses that encouraged the students to construct and develop their mathematical concepts. As they participated in math class and received feedback on their learning, the whole class worked cooperatively in a positive way. Their discourse was improved from the level of the actual development to the level of the potential development and the pattern of interaction moved from ERE(Elicitaion-Response-Elaboration to PD(Proposition Discussion).

• Journal of Educational Research in Mathematics
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• v.25 no.4
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• pp.525-547
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• 2015

This study analyzed the written texts of textbook and the teacher's discourse explaining 'the relationship between quadratic functions and quadratic equations' in the 9th grade high school mathematics class. Data consisted of the lecture recordings and the textbooks were analyzed based on the Halliday's systemic functional linguistics. According to the results, the written texts of the textbook used lexico-grammatical strategies such as generalization using hyponomy of meanings, mathematical objectification through nominalization and materialization of meaning through change in themes to compose mathematical concepts. The textbook generalized from an example in the description of formulating mathematical concepts, and in this process the organizational interactions of discourse-semantic level and lexico-grammartical level appeared. On the other hand, the teacher's doscourse appeared the change in transitivity and the addition of the reasons and the process. Also the teacher used explanation process of formulating the relationship between quadratic functions and quadratic equations. The linguistic characteristics of the teacher were linguistic implication and omission of lexemes due to contextual ommission. And there was no use of structural lexico-grammatical resources that influence the discourse-semantic level. This results provide a new framework for analyzing mathematical discourse, and suggest the lexico-grammatical strategies that can be used to explain mathematical concepts by teachers in math classrooms.

• 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.

• 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.

• 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.

• Journal of Educational Research in Mathematics
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• v.12 no.2
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• pp.163-180
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• 2002

The purpose of this paper is to reconsider the meaning of mathematical literacy based on the investigation of the nature of mathematical knowledge communicated in university level mathematics classes. The analysis of classroom discourse has revealed three different kinds of mathematical knowledge circulated in mathematics class, which include 'factual mathematics', 'mathematical fantasy', and 'mathematical savior faire.' The fact that a mathematics teacher delivers diverse categories of mathematics knowledge suggests that the mathematical literacy is not confined to the development of technical competence. More specifically, the kinds of mathematical knowledge identified above tell that mathematical literacy developed through learning mathematics reflects the cultural norms and values of doing mathematics. This means that mathematical literacy is not merely involve with technical competence but rather with cultural competence. In this regard, this paper highlights the meaning of mathematical literacy as a cultural identity, which has been underestimated in the theory and practice of mathematics education dominated by technocracy of the twentieth century In particular, the notion of mathematical savior faire implies that teaching and teaming mathematics ultimately deals with a system of cultural meaning. Hence, through learning mathematics, a learner gets transformed as a whole person according to the cultural norms and values. In this regard, it is concluded that mathematical literacy can be considered as a necessary condition to become a competent member of mathematics community sharing cultural norms of doing mathematics as well as a repertoire of mathematical skills.

• The Mathematical Education
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• v.50 no.3
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• pp.263-284
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• 2011

We took note of the fact that there were not many studies on improvement of mathematics learning in the field of statistics for the minority students from the families who belonged to the Low-SES. This study was to help them understand the concepts and principles of mathematics, motivate them for mathematics learning, and have them feel familiar with it. The subjects were 12 students from the low-SES families among the sophomores of 00 High School in Gyeonggi-do. Although it could not be achieved effectively in the short-term of learning for the slow learners, their understanding of basic concepts and confidence, interests and concerns in statistical learning were remarkably changed, compared to their work in the beginning period. Our discourse classes using various topics and examples were well perceived by the students whose performance was improved up to the 3rd thinking level of Mooney's framework. Also, a meaningful instructional model for slow learners(IMSL) was found through the discourse.

• Journal of Elementary Mathematics Education in Korea
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• v.15 no.2
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• pp.385-415
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• 2011

To investigate the more effective mathematical communication process, a recommended teacher and a selected class as an exemplary model was analyzed with Flanders system. The mathematical communicative level was examined to measure content level using the framework analysing the mathematical communicative level(Park & Pang) based on describing levels of math-talk learning community(Hufferd-Ackles). The purposes of this paper are to describe the verbal flow pattern between teacher and students in the elementary school class for mathematically gifted students, and to propose the effective communication model of math-talk with analysis of verbal teaching behavior in the active class. In addition the whole and the parts of the exemplary class sample is respectively analysed to be used practically by elementary school teachers. The results show the active communication process with higher level presents a pattern 'Ask Question${\rightarrow}$Activity (Silence, Confusion or work)${\rightarrow}$Student-Initiated Talk${\rightarrow}$Activity (Silence, Confusion or work), and the teacher's verbal behavior promoting math communication actively is exhibited by indirect influence especially accepting or using ideas.