• Journal of Educational Research in Mathematics
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• v.18 no.1
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• pp.25-50
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• 2008

Several previous studies suggested that simulation could be a main didactic instrument in overcoming misconception and probability modeling. However, they have not described enough how to reorganize probability knowledge as knowledge to be taught in a curriculum using simulation. The purpose of this study is to identify the theoretical knowledge needed in developing a didactic transposition method of probability knowledge using simulation. The theoretical knowledge needed to develop this method was specified as follows : pseudo-contextualization/pseudo-personalization, and pseudo-decontextualization/pseudo-deper-sonalization according to the introductory purposes of simulation. As a result, this study developed a local instruction theory and an hypothetical learning trajectory for overcoming misconceptions and modeling situations respectively. This study summed up educational intention, which was designed to transform probability knowledge into didactic according to the introductory purposes of simulation, into curriculum, lesson plans, and experimental teaching materials to present didactic ideas for new probability education programs in the high school probability curriculum.

• Journal of Elementary Mathematics Education in Korea
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• v.21 no.2
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• pp.365-389
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• 2017

This study aims to analyze elementary gifted students' inquiries on combinatoric tasks. In particular, we designed circular permutation tasks and analyzed students' inquiries on these tasks. We especially analyzed students' expressions, counting processes, and their construction of set of outcomes. The findings showed that the students utilized analogy to resolve given tasks, and they had difficulties in categorizing and re-categorizing possible outcomes of given tasks. Their improper use of analogy also caused difficulties in resolving circular permutation tasks.

• Journal of Educational Research in Mathematics
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• v.17 no.3
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• pp.253-270
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• 2007

by A.C. Clairaut was written based on the historico-genetic principle such as his . In this paper, by analyzing his we can induce six principles that Clairaut adopted to teach algebra: necessity and curiosity as a motive of studying algebra, harmony of discovery and proof, complementarity of generalization and specialization, connection of knowledge to be learned with already known facts, semantic approaches to procedural knowledge of mathematics, reversible approach. These can be considered as strategies for teaching algebra accorded with beginner's mind. Some of them correspond with characteristics of , but the others are unique in the domain of algebra. And by comparing Clairaut's approaches with school algebra, we discuss about some mathematical subjects: setting equations in relation to problem situations, operations and signs of letters, rule of signs in multiplication, solving quadratic equations, and general relationship between roots and coefficients of equations.

• School Mathematics
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• v.19 no.4
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• pp.795-817
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• 2017

Whereas noticing with relation to teacher expertise has been steadily studied in international contexts, there have been very few studies in Korea in this area. Given this, this paper reviewed the meanings of noticing based on Sherin and van Es as well as Jacobs et al. who provided foundational work and then analyzed recent studies on teacher noticing. A review of literature showed that recent international studies on noticing tend to elaborate the theoretical framework of noticing, diversify the methods of research on noticing, and extend to the range of noticing. This paper also included an analysis of domestic studies dealing with noticing either explicitly or implicitly. This paper is expected to serve as a basis to foster conceptual understanding of teacher noticing and to derive follow-up studies in Korea.

• The Mathematical Education
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• v.62 no.3
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• pp.341-362
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• 2023

This study analyzed student noticing in a lesson that emphasized relational understanding of equal signs for first graders from four aspects: centers of focus, focusing interactions, mathematical tasks, and nature of the mathematical activity. Specifically, the instructional factors that emphasize the relational understanding of equal signs derived from previous research were applied to a first-grade addition and subtraction unit, and then lessons emphasizing the relational understanding of equal signs were conducted. Students' noticing in this lesson was comprehensively analyzed using the focusing framework proposed in the previous study. The results showed that in real classroom contexts centers of focus is affected by the structure of the equation and the form of the task, teacher-student interactions, and normed practices. In particular, we found specific teacher-student interactions, such as emphasizing the meaning of the equals sign or using examples, that helped students recognize the equals sign relationally. We also found that students' noticing of the equation affects reasoning about equation, such as being able to reason about the equation relationally if they focuse on two quantities of the same size or the relationship between both sides. These findings have implications for teaching methods of equal sign.

• Communications of Mathematical Education
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• v.36 no.1
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• pp.39-57
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• 2022

This study aims to design an integral instruction method that follows the Abstraction in Context (AiC) framework proposed by Hershkowitz, Schwarz, and Dreyfus to help students in acquiring in-depth understanding of the relationship between indefinite integrals and definite integrals and to analyze how the students' understanding improved as a result. To this end, we implemented lessons according to the integral instruction method designed for eight 11th grade students in a science high school. We recorded and analyzed data from graded student worksheets and transcripts of classroom recordings. Results show that students comprehend three knowledge elements regarding relationship between indefinite integral and definite integral: the instantaneous rate of change of accumulation function, the calculation of a definite integral through an indefinite integral, and The determination of indefinite integral by the accumulation function. The findings suggest that the AiC framework is useful for designing didactical activities for conceptual learning, and the accumulation function can serve as a basis for teaching the three knowledge elements regarding relationship between indefinite integral and definite integral.

• Communications of Mathematical Education
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• v.31 no.4
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• pp.433-456
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• 2017

The purpose of this study is to suggest the directions for the development and improvement of mathematics textbooks in Korea by examining these characteristics of German textbooks. As a result, German mathematics textbooks were free for unit order and names of units. German mathematics textbooks defined a function for various real life and natural phenomena, relation after intuitively knowing the correspondence between two variables through a graph. In addition, it exercises interpreting the characteristics and information of the graph, guides the activity of graphing various functional situations, and contents to convert various expression methods such as graphs, tables, relational expressions, mathematical terms and sentences. In the German mathematics textbooks, mathematical expressions of the functional relations of the materials in various contexts of daily life, and the activities of predicting and predicting the future, were made to feel the usefulness of mathematics. It has raised functional thinking and provided problems related to other subjects, thus enhancing connectivity with other disciplines. It also included open issues and issues that required mathematical communication.

• The Mathematical Education
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• v.62 no.1
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• pp.57-78
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• 2023

Students' engagement in lessons not only determines the direction and result of the lessons, but also affects academic achievement and continuity of follow-up learning. In order to provide implications related to teaching strategies for encouraging students' engagement in elementary mathematics lessons, this study implemented lessons for middle-low achieving fifth graders using open-ended tasks and analyzed characteristics of students' engagement in the light of the framework descripors developed based on previous research. As a result of the analysis, the students showed behavioral engagement in voluntarily answering teacher's questions or enduring difficulties and performing tasks until the end, emotional engagement in actively expressing their pleasure by clapping, standing up and the feelings with regard to the topics of lessons and the tasks, cognitive engagement in using real-life examples or their prior knowledge to solve the tasks, and social engagement in helping friends, telling their ideas to others and asking for friends' opinions to create collaborative ideas. This result suggested that lessons using open-ended tasks could encourage elementary students' engagement. In addition, this research presented the potential significance of teacher's support and positive feedback to students' responses, teaching methods of group activities and discussions, strategies of presenting tasks such as the board game while implementing the lessons using open-ended tasks.

• The Mathematical Education
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• v.62 no.3
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• pp.435-455
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• 2023

This study primarily focused on the development of an Explainable Artificial Intelligence (XAI) model to discern and analyze papers with significant impact in the field of mathematics education. To achieve this, meta-information from 29 domestic and international mathematics education journals was utilized to construct a comprehensive academic research network in mathematics education. This academic network was built by integrating five sub-networks: 'paper and its citation network', 'paper and author network', 'paper and journal network', 'co-authorship network', and 'author and affiliation network'. The Random Forest machine learning model was employed to evaluate the impact of individual papers within the mathematics education research network. The SHAP, an XAI model, was used to analyze the reasons behind the AI's assessment of impactful papers. Key features identified for determining impactful papers in the field of mathematics education through the XAI included 'paper network PageRank', 'changes in citations per paper', 'total citations', 'changes in the author's h-index', and 'citations per paper of the journal'. It became evident that papers, authors, and journals play significant roles when evaluating individual papers. When analyzing and comparing domestic and international mathematics education research, variations in these discernment patterns were observed. Notably, the significance of 'co-authorship network PageRank' was emphasized in domestic mathematics education research. The XAI model proposed in this study serves as a tool for determining the impact of papers using AI, providing researchers with strategic direction when writing papers. For instance, expanding the paper network, presenting at academic conferences, and activating the author network through co-authorship were identified as major elements enhancing the impact of a paper. Based on these findings, researchers can have a clear understanding of how their work is perceived and evaluated in academia and identify the key factors influencing these evaluations. This study offers a novel approach to evaluating the impact of mathematics education papers using an explainable AI model, traditionally a process that consumed significant time and resources. This approach not only presents a new paradigm that can be applied to evaluations in various academic fields beyond mathematics education but also is expected to substantially enhance the efficiency and effectiveness of research activities.

• Journal of The Korean Association For Science Education
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• v.32 no.1
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• pp.30-45
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• 2012

Educational communities around the world have concentrated on integrative efforts among science, technology, engineering and mathematics (Science, Technology, Engineering, and Mathematics: STEM) subjects. Korea has focused on integrative education among STEAM (Science, Technology, Engineering, Arts, and Mathematics) school subjects to raise talented human resources in the fields of science and technology. The purpose of this study was to analyze secondary school science, technology, and mathematics teacher's perceptions and needs toward integrated education and integrative STEM education. A total of 251 secondary school teachers from all areas of the country who have taught science, mathematics, and technology were surveyed by using a self-reported instrument. The findings were as follows: First, teachers have used little integrated education in their classes due to insufficient time in the actual preparation of the integrated education and the lack of expertise, teaching experience, and teaching-learning materials for the integrated education, while they have positive thoughts about the need of integrated education. Second, they presented several needs to facilitate the integrated education: development of a variety of integrated programs, school administrative and financial support, and in-service teachers' training. Third, overall perception toward integrated STEM education was not sufficient, but most teachers perceived the need toward integrated STEM education due to students' development in their creativity, thinking skills, and adaptability. Fourth, they perceived that it was imperative to develop the various integrated STEM education programs, distribute the materials, and help STEM teachers' understanding toward integrated STEM education. Fifth, they perceived that the most relevant method to integrate STEM subjects was the problem solving approach. In addition, they appreciate that the integrated STEM education is highly efficient in not only developing integrated problem solving skills and STEM related literacy, but also in positively impacting the rise of talented human resources in the fields of science and technology. In order to increase the awareness of STEM-related secondary school teachers and vitalize the integrated STEM education, it is necessary to develop and spread a variety of programs, effective teaching and learning materials, and teachers' training programs.