• School Mathematics
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• v.17 no.1
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• pp.79-98
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• 2015

The purpose of this study was to develop the elementary mathematics textbooks as a thematic approach, to suggest meaningful directions to future textbook development and curriculum development. For this study, we suggested mathematics textbooks of the three-themes, 'Healthy Life', 'Sustainable Life', 'Living-together Life', as multi-disciplinary, inter-disciplinary, and extra-disciplinary types. With the problems that employed thematic approaches, the post-achievement scores of experimental groups who used 'Healthy Life' and 'Sustainable Life' textbooks were meaningfully higher than those of control groups. However, the post-achievement scores of experimental groups who used 'Living-together Life' textbook were not meaningfully higher than those of control groups. The attitudes towards mathematics of all three experimental groups were meaningfully higher than those of control groups. After applications of elementary mathematics textbooks as a thematic approach, we need to develop related materials, to consider various grades, levels, regions for developing better mathematics textbooks.

• Journal of Educational Research in Mathematics
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• v.24 no.2
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• pp.269-283
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• 2014

Recently, 3S Mathematics Education (Storytelling mathematics education, SMART mathematics education, and STEAM mathematics education) is emphasized. Based on recently published report on Storytelling mathematics textbook, we propose executable expression based SMART storytelling mathematics related to the elementary mathematic curriculum on 3D building blocks. We designed letters and expressions to represent three dimensional shape of 3D building blocks, and we compare its characteristics with that of LEGO blocks. We assert that text-based executable expressions not only construct what students want to make but also teachers can read students thinking process and can support educational help based on students needs. We also present linear function, quadratic function, and function variable concepts using executable expressions based on 3D building block as an example of SMART storytelling mathematics. This research was supported by the collaborated creativity mentoring project between Siheung City and college of education at Seoul National University. We hope designed executable expressions can be used for the development of SMART storytelling mathematics education.

• Journal of Educational Research in Mathematics
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• v.22 no.3
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• pp.311-329
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• 2012

This study analyzed third graders' understanding on the part-whole fraction concept in both the continuous and the discrete contexts. A set of problems were developed as an equivalent form to compare and contrast students' understanding of fraction in the two contexts. Unexpectedly, the results of this study showed that students' performance in the continuous contexts was slightly lower than their performance in the discrete contexts. Students tended to use different strategies depending on the contexts and they had difficulties in applying what they knew in the new contexts. On the basis of the detailed analyses about students' difficulties and their sources, this paper provides information on how to construct curricular materials and how to teach the basic concepts related to the part-whole fraction.

• School Mathematics
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• v.16 no.2
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• pp.285-301
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• 2014

Because a development figure is treated restrictively in elementary school, not only there are brought out the concept image, but also the definition of the development figure in textbook in not unique. Furthermore, since the comparison and analysis of 'definition element' between the materials in textbook are nor carried out, its educational value as well as the teaching for concepts and objectives does not give rise to public discussion. In this note, we will investigate the definition and teaching of the development figure in Korea and Japan. And through three viewpoints of its definition and related debate, we will consider the fundamental understanding and objectiveness of a development figure, and suggest its mathematical application. This study will promote teachers's critical and didactical insight for the didactical transposition.

• Education of Primary School Mathematics
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• v.27 no.3
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• pp.303-320
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• 2024

This study presents the development and performance evaluation of a custom GPT-based chatbot tailored to provide solutions following Polya's problem-solving stages. A beta version of the chatbot was initially deployed to assess its mathematical capabilities, followed by iterative error identification and correction, leading to the final version. The completed chatbot demonstrated an accuracy rate of approximately 89.0%, correctly solving an average of 57.8 out of 65 image-based problems from a 6th-grade elementary mathematics textbook, reflecting a 4 percentage point improvement over the beta version. For a subset of 50 problems, where images were not critical for problem resolution, the chatbot achieved an accuracy rate of approximately 91.0%, solving an average of 45.5 problems correctly. Predominant errors included problem recognition issues, particularly with complex or poorly recognizable images, along with concept confusion and comprehension errors. The custom chatbot exhibited superior mathematical performance compared to the general-purpose ChatGPT. Additionally, its solution process can be adapted to various grade levels, facilitating personalized student instruction. The ease of chatbot creation and customization underscores its potential for diverse applications in mathematics education, such as individualized teacher support and personalized student guidance.

• Journal of The Korean Association For Science Education
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• v.42 no.4
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• pp.417-428
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• 2022

This study analyzed the frequency and level of scientific practices presented in secondary science textbooks. A total of 1,378 student activities presented in 14 middle school science textbooks and 5 high school integrated science textbooks were analyzed, using the definition and level of scientific practice suggested in the NGSS. Findings show that most student activities focus on three practices. Compared to the textbooks for the previous science curriculum, the practice of 'obtaining, evaluating, and communicating information' was more emphasized, reflecting societal changes due to ICT development. However, the practice of 'asking a question', which can be an important element of student-led science learning, was still rarely found in textbooks, and 'developing and using models', 'using math and computational thinking' and 'arguing based on evidence' were not addressed much. The practices were mostly elementary school level except for the practice of 'constructing explanations'. Such repeated exposures to a few and low level of practices mean that many future citizens would be led to a naïve understanding of science. The findings imply that it is necessary to emphasize various practices tailored to the level of students. In the upcoming revision of the science curriculum, it is necessary to provide the definition of practices that are not currently specified and the expected level of each practice so that the curriculum can provide sufficient guidance for textbook writing. These efforts should be supported by benchmarking of overseas science curriculum and research that explore students' ability and teachers' understanding of scientific practices.

• Journal of Educational Research in Mathematics
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• v.17 no.4
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• pp.453-475
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• 2007

School algebra starts with introducing algebraic expressions which have been one of the cognitive obstacles to the students in the transfer from arithmetic to algebra. In the recent studies on the teaching school algebra, algebraic thinking is getting much more attention together with algebraic expressions. In this paper, we examined the processes of the transfer from arithmetic to algebra and ways for teaching early algebra through algebraic thinking factors. Issues about algebraic thinking have continued since 1980's. But the theoretic foundations for algebraic thinking have not been founded in the previous studies. In this paper, we analyzed the algebraic thinking in school algebra from historico-genetic, epistemological, and symbolic-linguistic points of view, and identified algebraic thinking factors, i.e. the principle of permanence of formal laws, the concept of variable, quantitative reasoning, algebraic interpretation - constructing algebraic expressions, trans formational reasoning - changing algebraic expressions, operational senses - operating algebraic expressions, substitution, etc. We also identified these algebraic thinking factors through analyzing mathematics textbooks of elementary and middle school, and showed the middle school students' low achievement relating to these factors through the algebraic thinking ability test. Based upon these analyses, we argued that the readiness for algebra learning should be made through the processes including algebraic thinking factors in the elementary school and that the transfer from arithmetic to algebra should be accomplished naturally through the pre-algebra course. And we searched for alternative ways to improve algebra curriculums, emphasizing algebraic thinking factors. In summary, we identified the problems of school algebra relating to the transfer from arithmetic to algebra with the problem of teaching algebraic thinking and analyzed the algebraic thinking factors of school algebra, and searched for alternative ways for improving the transfer from arithmetic to algebra and the teaching of early algebra.

• Communications of Mathematical Education
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• v.37 no.4
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• pp.635-652
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• 2023

This study conducts a comprehensive analysis of the curricular progression of the concepts and learning sequences of 'lines', specifically, 'line segments', 'straight lines', and 'rays', at the elementary school level. By examining mathematics curricula and textbooks, spanning from 2nd to 7th and 2007, 2009, 2015, and up to 2022 revised version, the study investigates the timing and methods of introducing these essential geometric concepts. It also explores the sequential delivery of instruction and the key focal points of pedagogy. Through the analysis of shifts in the timing and definitions, it becomes evident that these concepts of lines have predominantly been integrated as integral components of two-dimensional plane figures. This includes their role in defining the sides of polygons and the angles formed by lines. This perspective underscores the importance of providing ample opportunities for students to explore these basic geometric entities. Furthermore, the definitions of line segments, straight lines, and rays, their interrelations with points, and the relationships established between different types of lines significantly influence the development of these core concepts. Lastly, the study emphasizes the significance of introducing fundamental mathematical concepts, such as the notion of straight lines as the shortest distance in line segments and the concept of lines extending infinitely (infiniteness) in straight lines and rays. These ideas serve as foundational elements of mathematical thinking, emphasizing the necessity for students to grasp concretely these concepts through visualization and experiences in their daily surroundings. This progression aligns with a shift towards the comprehension of Euclidean geometry. This research suggests a comprehensive reassessment of how line concepts are introduced and taught, with a particular focus on connecting real-life exploratory experiences to the foundational principles of geometry, thereby enhancing the quality of mathematics education.

• Journal of Elementary Mathematics Education in Korea
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• v.17 no.2
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• pp.321-350
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• 2013

The purpose of this study to analysis of problem posing in 5th and 6th grade mathematics textbooks and to comprehend errors in the problem posing activity of 6th graders in elementary school. For solving the research problems, problem posing contents were extracted from mathematics textbooks and practice books for the 5th and 6th grade of elementary school in the 2007 revised national curriculum, and they were analyzed, according to each grade, domain and type. Based on the analysis results, 10 problem posing questions which were extracted and developed, were modified and supplemented through a pre-examination, and a questionnaire that problem posing questions are evenly distributed, according to each grade, domain and type, was produced. This examination was conducted with 129 6th graders, and types of error in problem posing were analyzed using collected data. The implications from the research results are as follows. First, it was found that there was a big numerical difference of problem posing questions in the 5th and 6th grade, and problem posing questions weren't properly suggested in even some domains and types, because the serious concentration in each grade, type and domain. Therefore, textbooks to be developed in the future would need to suggest more various and systematic of problem posing teaching learning activity for each domain and type. Second, the 'error resulting from the lack of information' occurred the most in the problems that 6th graders posed, followed by the 'error in the understanding of problems', 'technical errors', 'logical errors' and 'others'. This implies that a majority of students missed conditions necessary for problem solving, because they have been used to finding answers to given questions only. For such reason, there should be an environment in which students can pose problems by themselves, breaking from the way of learning to only solve given problems.

• Journal of Elementary Mathematics Education in Korea
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• v.19 no.3
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• pp.371-386
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• 2015

There has been little consensus on how to define and use the Korean mathematical terms, bi-ui-gap and bi-yul. This study compares four perspectives of bi-ui-gap and bi-yul proposed and discussed in Korean mathematics education community and examines the ways of using the terms adopted since the 6th national curriculum. Based on the analysis that previously proposed perspectives conflict each other, this study proposes as a way to synthesize different perspectives of bi-ui-gap and bi-yul by analyzing the terms in the internal and external ratio contexts. This study proposes that bi-ui-gap be used to represent 'a value of $A{\div}B$' rather than 'a value originated from a ratio A:B' or 'a fraction form ${\frac{B}{A}}$.' This study also proposes that bi-yul or bae-yul be used in the internal ratio context and a new term, such as dan-wi-yul, be created for the external ratio context.