• Research in Mathematical Education
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• v.6 no.1
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• pp.39-51
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• 2002

This study described an elementary teacher's practical knowledge of selecting and using mathematical tasks for promoting students' understanding and discourse. The informant of this ethnographic inquiry was a third grade teacher and has 10 years of teaching experience. According to the analysis of multiple data sources, this study showed that based on his beliefs about the development of understanding of mathematics and discourse, he continually employed two different types of tasks: open-ended tasks and tasks from students' mistakes and comments during discourse. Teachers' practical knowledge of teaching mathematics and the classroom norms for students' understanding and discourse are suggested to be given attention for further research on this area.

• Research in Mathematical Education
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• v.18 no.3
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• pp.187-208
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• 2014

This study engages in the features of interaction in elementary school mathematics lessons as reflected in the class discourse. 28 pre-service teachers documented the discourse during observation of their tutor-teachers' lessons. Mapping the interaction patterns was performed by a unique graphic model developed for that purpose and enabled providing a spatial picture of the discourse conducted in the lesson. The research findings present the known discourse pattern "initiation-response-evaluation / feedback" (IRE/F) which is recurrent in all the lessons and the teacher's exclusive control over the class discourse patterns. Hence, the remaining time of the lesson for the pupils' discourse is short and meaningless.

• Journal of Elementary Mathematics Education in Korea
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• v.14 no.3
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• pp.523-545
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• 2010

Mathematical communication has been emphasized not only as the process of learning mathematics but also as the objective of mathematics education. However, little studies have been conducted with regard to what to consider and how to implement in the actual classroom for promoting mathematical communication. Given this background, this paper implemented a mathematics instruction in each of 2nd, 4th, and 6th grade classrooms in which specific learning objectives were considered to promote discourse-based mathematical communication. It then analyzed the degree by which such learning objectives were achieved and the linguistic interactions between the teacher and students in each classroom. This paper finally provided issues and suggestions for effective discourse-based instruction in mathematics classroom by analyzing similarities and differences among the three classrooms.

• Communications of Mathematical Education
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• v.36 no.3
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• pp.397-415
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• 2022

The purpose of this study is to analyze the discourse structure of teachers that can help students participate in class by using mathematical metaphors that can arouse students' interest and motivation. In order to achieve this goal, we observed a semester class of a career teacher who practiced pedagogy that connects students' experiences with mathematical concepts to motivate students to learn and promote participation. Among the metaphors that the study target teachers used in a variety of mathematical concepts and problem-solving processes during the semester, we extracted the two class examples that can help develop teaching methods using metaphors. Representatively selected two classes are one class example using metaphors and, the other class example using metaphors and expanding and applying problems. As a result of analysis, the structure of teacher discourse that uses metaphors and expands and applies problems by linking students' experiences with mathematical content was found to help solve a given problem and elaborate mathematical concepts. As a result of the analysis, the discourse structure of teachers using mathematical metaphors based on communication with students could provide implications for the development of teaching methods for the recovery of mathematics education.

• School Mathematics
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• v.18 no.1
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• pp.193-214
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• 2016

Teachers' questioning plays an important role in mathematics teaching and learning by asking students to react or to participate in mathematical discourse. Previous studies on teachers' questioning have not focused on how to questioning to formulate an effective mathematical discourse which is contributed by students because studies mostly analyzed and categorized teachers' questions according to cognitive levels of questions without consideration of context. Therefore, this study explored characteristics of teachers' questioning to formulate an effective characteristics of teachers' questioning to formulate an effective mathematical discourse in mathematics classrooms. By reviewing and analyzing mathematics discourse and studies on teachers' questioning theoretically, we presented openness, sharedness, and productivity as characteristics of teachers' questioning. Through a middle school mathematics teacher's case, we examined three characteristics were necessary to formulate an effective mathematical discourse. Based on results from theoretical analysis and case analysis, we discussed that openness, sharedness, and productivity would be useful as a framework to analyze teachers' questioning.

• Journal of Elementary Mathematics Education in Korea
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• v.15 no.3
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• pp.559-577
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• 2011

The purpose of this study was to investigate the effects of discourse-based math instructions on the students' mathematical attitudes and learning achievements by providing fifth graders with an opportunity to take active part in learning during math classes and applying discourse-based math instructions, which are to expand the speaking experiences as the most fundamental way to express ideas in communication. Those research efforts led to the following results: First, the discourse-based math instructions turned out to have positive influences on flexibility, will power, curiosity, reflection, and value of mathematical attitudes. When the results were reviewed before and after the instructions without considering the subvariables of attitude, there were statistically significant differences(p<0.01), which indicates that the discourse-based math instructions exerted very positive effects on the students mathematical attitudes. Second, there were no statistically significant effects in learning achievements between the experimental and comparative group, but the experimental group, which recorded low mean scores in the pre-test, increased their mean scores by 3.81 points in the post-test, which suggests that the discourse-based math instructions had positive influences on them. Third, the subjects' responses on the questionnaire on discourse-based instructions reveal that the discourse-based math instructional provided them with an opportunity to explore solutions in various ways. In short, discourse-based math instructions have positive influences on mathematical attitudes and are effective in increasing communication ability.

• Research in Mathematical Education
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• v.17 no.1
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• pp.1-14
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• 2013

Stochastic phenomena induce us to construct a probability model and structure our thinking; corresponding models help us to understand and interpret the reality. They in turn equip us with tools to recognize, reconstruct and solve problems. Therefore, various implications in terms of methodology as well as epistemology naturally flow from different adoptions of models for probability. Right from the basic scenarios of different perspectives to explore reality, students are occasionally exposed to misunderstanding and misinterpretations. With realistic examples a multi-faceted image of probability and different interpretation will be considered in mathematical modelling activities. As an exploratory investigation, mathematical modelling activity for probability learning was elaborated through semiotic analysis. Especially, the coherence structure in mathematical modelling discourse was reviewed form a semiotic perspective. The discourses sampled from group activities were analyzed on the basis of semiotic perspectives taxonomical coherence relations.

• The Mathematical Education
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• v.59 no.2
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• pp.101-112
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• 2020

The purpose of this study is to analyze the structures of teacher's discourse according to the pattern of interaction between teachers and students in the understanding mathematical word problem. The structures of teacher's discourse could be conceptualized as a process in which the teacher starts, develops and organizes the discourse based on prior research. For this purpose, the fourth class(example, a problem of the same type as the example, formative assessment, and final assessment) was extracted from one semester of experienced teachers who have been practicing teaching methods to facilitate student participation for many years. A methodology used to develop a theory based on data collected through classroom observations. Because the purpose of the study is to identify the structures of teacher's discourse to help the problem understanding, observe the teacher's discourse and collect data based on student engagement. Results show that the structure of teacher's discourse, which consults on important aspects of interaction between teachers-students and creates mathematical meanings, helped students understand the mathematics word problem by promoting their engagement in class. Based on the structures of teacher's discourse to understand problems based on the interaction patterns between teachers and students, it can be said that teachers provided specific methodologies on how to communicate with students in order to understand problems in the future.

• The Mathematical Education
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• v.61 no.2
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• pp.273-286
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• 2022

The purpose of this study is to analyze the teacher's discourse structure in the process of solving mathematics problems based on the communication between teachers and students. To achieve this goal, we observed a semester class by a teacher with experience who practiced a teaching method that creates mathematical meanings based on students' participation in class. In order to solve problems based on the participation of students in each class, the similarities between the processes of creating the structure of the discourse were analyzed. As a result of the analysis, the teacher was able to focus on the goal in the process of starting a discourse, and in the process of developing the discourse, the problem was solved by focusing on understanding the problem. In the process of arranging the discourse, the problem-solving process and the core of the result is summarized. Based on the possibility of generalization of the teacher discourse structure, it will be able to provide practical help in the process of implementing a teaching method that solves mathematics problems by communicating with students in the future.

• 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.