• Journal of Elementary Mathematics Education in Korea
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• v.24 no.1
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• pp.151-168
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• 2020

The use of software is effective in developing mathematical understanding that provides mathematical problems and ensures mathematical communication. In particular, various software may provide all of the skills and conceptual activities students need to understand mathematical concepts. Based on these arguments, I analyze domestic prior studies based on the perspective of how the shape education using software affects mathematics learning. Based on the five categories of visualization, manipulation, cognitive tools, discourse promoters, and ways of thinking, domestic studies have shown that the number and categories of research related to shape education using software are limited. In addition, it was confirmed that previous studies in South Korea have been focused on the application of software rather than analysis of the changing aspects of learners' mathematics learning. These implications might be used as a basis for setting the direction of research on mathematics education related to the education of software utilization in the future.

• 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.

• Journal of Educational Research in Mathematics
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• v.24 no.2
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• pp.125-143
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• 2014

In this study, we analyzed a mathematical discussion in the Calculus II course of the Gifted Science Academy and individual interviews to determine the relationship between cognitive conflicts and commognitive conflicts. The mathematical discussion began with a question from a student who seemed to have a cognitive conflict about the osculating plane of a space curve. The results indicated that the commognitive conflicts were resolved by ritualizing and using the socially constructed knowledge, but cognitive conflicts were not resolved. Furthermore, we found that the cause of the cognitive conflict resulted from the student's imperfect analogical reasoning and the reflective discourse about it could be a learning opportunity for overcoming the conflict. These findings imply that cognitive conflicts can trigger the appearance of commognitive conflicts, but the elimination of commognitive conflicts does not imply that cognitive conflicts are resolved.

• Education of Primary School Mathematics
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• v.26 no.2
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• pp.99-113
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• 2023

In this study, I explored the possibility of using ChatGPT math education. For this purpose, students' problem-solving outputs and conversation data between pre-service teachers and a student were selected as an analysis case. A case was analyzed using ChatGPT and compared with the results of mathematics education experts. The results that ChatGPT analyzed students' problem-solving strategies and mathematical thinking skills were similar to those of math education experts. ChatGPT was able to analyze teacher questions with evaluation criteria, and the results were similar to those of math education experts. ChatGPT could also respond with mathematical theory as a source of evaluation criteria. These results demonstrate the potential of ChatGPT to analyze students' thinking and teachers' practice in mathematics education. However, there are limitations in properly applying the evaluation criteria or providing inaccurate information, so the further review of the derived information is required.

• The Mathematical Education
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• v.63 no.2
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• pp.319-334
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• 2024

The purpose of this study was to reveal the discursive constructs of AI-based mathematical objects by analyzing how concrete objects used in the optimization content of AI mathematics textbooks are transformed into discursive objects through naming and discursive operation. For this purpose, we extracted concrete objects used in the optimization contents of five high school AI mathematics textbooks and developed a framework for analyzing the discursive constructs and discursive operations of AI-based mathematical objects that can analyze discursive objects. The results of the study showed that there are a total of 15 concrete objects used in the loss function and gradient descent sections of the optimization content, and one concrete object that emerges as an abstract d-object through naming and discursive operation. The findings of this study are not only significant in that they flesh out the discursive construction of AI-based mathematical objects in terms of the written curriculum and provide practical suggestions for students to develop AI-based mathematical discourse in an exploratory way, but also provide implications for the development of effective discursive construction processes and curricula for AI-based mathematical objects.

• Journal of Educational Research in Mathematics
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• v.10 no.1
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• pp.85-102
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• 2000

The concept of variables is central to mathematics teaching and learning in junior and senior high school. Understanding the concept provides the basis for the transition from arithmetic to algebra and necessary for the meaningful use of all advanced mathematics. Despite the importance of the concept, however, much has been written in the last decade concerning students' difficulties with the concept. This Thesis is based on research to investigate the hypothesis that LOGO programming will contribute to 6th grader' learning of variables. The aim of the research were to; .investigate practice on pupils' understanding of variables before the activity with a computer; .identify functions of LOGO programming in pupils' using and understanding of variable symbols, variable domain and the relationship between two variable dependent expressions during the activity using a computer; .investigate the influence of pupils' mathematical belief on understanding and using variables. The research consisted predominantly of a case study of 6 pupils' discourse and activities concerning variable during their abnormal lessons and interviews with researcher. The data collected for this study included video recordings of the pupils'work with their spoken language.

• School Mathematics
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• v.15 no.3
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• pp.633-650
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• 2013

The aim of this paper is to explore and understand, using in-depth interviews, the participant's interests and discourse analytic expressions in studying the notion of infinity and limit. In addition we tried to understand how the participant's ways of dealing with math and thinking patterns on the polygons whose boundary is infinite but area is finite as they brought up such examples. Further follow-up questions are posed on the infinite sum of a smallest number close to 0 and the sum of infinite sets of different smallest numbers close to 0. Larger aspects of two pre-service teachers' subjective thinking patterns and colloquial discourses were sketched by contrasting the three posed tasks. Cross case discussions are provided with several suggestions for the future research directions.

• Education of Primary School Mathematics
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• v.21 no.3
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• pp.309-327
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• 2018

This study is a case study of an elementary school teacher's reflection and practice in the process of planning, executing and criticizing his lesson on division with decimals. The purpose of this study was to clarify what kinds of problems an elementary school teacher was thinking about and how his focus was changing in the process of planning and executing a lesson and criticizing his lesson with his peers. The teacher was set in three periods: a teacher planning a lesson, a teacher executing a lesson, and a teacher criticizing his or her own lesson. Each period was analyzed in eight aspects: Establishing the goals for mathematics, implementing tasks, connecting mathematical representations, facilitating mathematical discourse, posing questions, building procedural fluency from conceptual understanding, supporting productive struggles, and using evidences of students' thinking.

• The Mathematical Education
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• v.62 no.1
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• pp.95-115
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• 2023

Even the teachers who agree with the necessity of effective mathematical discussions find it difficult to orchestrate such discussions in the actual lessons. This study focused on analyzing the difficulties 15 elementary school teachers faced in applying "the five practices for orchestrating productive mathematics discussions" to their lessons. Specifically, this study analyzed the process of planning, implementing, and reflecting on the lessons to which three or four teachers as a teacher community applied the five practices. The results of this study showed that the teachers experienced difficulties in selecting and presenting tasks tailored to the student levels and class environment, monitoring all students' solutions, and identifying the core mathematical ideas in student solutions. In addition, this study revealed practical and specific difficulties that had not been described in the previous studies, such as writing a lesson plan for effective use, simultaneously performing multiple teacher roles, and visually sharing student presentations. This study is expected to provide practical tips for elementary school teachers who are eager to promote effective mathematical discussions and to provoke professional discourse for teacher educators through specific examples.

• Communications of Mathematical Education
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• v.32 no.3
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• pp.407-433
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• 2018

In order to analyze textbooks from a discursive approach, the purpose of this study is to structuralize an analytic framework based on previous literature review and apply it to analyzing the meanings and their syntheses developed by words and visual mediators appeared in the definition of graph in first-year middle school textbooks. The discursive approach consists of the communicational approach developed by Sfard(2008) and the systemic functional linguistics developed by Halliday(1985/2004). In this study, ideational meta-functions for ideational meanings and interpersonal meta-functions for interpersonal meanings were employed to analyze the meanings produced by words and visual mediators in textbooks, whereas textual meta-functions for textual meanings were used for analyzing the synthesized relationships between words and visual mediators. Results show that first, density in mathematical discourse was very high and subjects in mathematical activities were ambiguous in the ideational meanings of words, and behavior aspect was more emphasized than thinking aspect in the interpersonal meanings of words which request student participations. In the case of ideational meanings of visual mediators, there was a lack of narrative diagrams, whereas there were qualitative differences in the case of offer. Second, there was a need for promoting a wide range of diverse synthetic relationships between words and visual mediators for developing enriched mathematical meanings through the varying uses like specification, explanation, similarity, and complement. These results are so important that they provide a new analytic framework from a discursive approach to textbook analysis because not only words, but also visual mediators are analyzed as tools for producing meanings in mathematics textbooks and their synthetic relationships are also examined.