• The Mathematical Education
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• v.59 no.4
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• pp.389-403
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• 2020

This study aims to examine how information processing competency as one of the mathematical competencies has been interpreted and applied in mathematics education by analyzing tasks in middle school mathematics textbooks under the 2015 revised national curriculum. Based on the sub-elements of information processing competency organized by Park et al.(2015), we analyzed 191 tasks in 30 different middle school mathematics textbooks using descriptive statistics and ANOVA. Also, we investigated the meaning of information processing competency embedded in the tasks by distinguishing the characteristics of several different types of tasks. The results from this study showed that the number of tasks related to information processing competency in mathematics textbooks was too small and there was a huge difference across the textbooks in terms of the sub-elements. Even though there were four sub-elements of information processing competency, 'the use of manipulative and technological tools' was extremely dominant in the tasks in general. Even many of them used technology and manipulatives superficially. Furthermore, any textbook did not provide tasks dealing with all the four sub-elements. Such an unbalanced and fragmented approach to information processing competency could produce biased knowledge and insufficient experiences for information processing competency. It calls for further investigation and discussion about how to improve information processing competency in school mathematics.

• The Mathematical Education
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• v.60 no.4
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• pp.431-449
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• 2021

Elementary mathematics textbooks present contents for enhancing problem solving competency. Still, teachers find teaching problem solving to be challenging. To understand the supports textbooks are suggesting, this study examined tasks from the challenging/thinking and inquiry mathematics. We analyzed 288 mathematical activities based on an analytic framework from the 2015 revised mathematics curriculum. Then, we employed latent class analysis to classify 83 mathematical tasks as a new approach to categorize tasks. As a result, execution of the problem solving process was emphasized across grade levels but understanding of problems was varied by grade levels. In addition, higher grade levels had more opportunities to be engaged in collaborative problem solving and problem posing. We identified three task profiles: 'execution focus', 'collaborative-solution focus', 'multifaceted-solution focus'. In Grade 3, about 80% of tasks were categorized as the execution profile. The multifaceted-solution was about 40% in the thinking/challenging mathematics and the execution profile was about 70% in Inquiry mathematics. The implications for developing mathematics textbooks and designing mathematical tasks are discussed.

• Journal of Educational Research in Mathematics
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• v.20 no.3
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• pp.203-219
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• 2010

Several studies have reported on how and what mathematically gifted students develop superior ability or creativity in geometry and algebra. However, there are lack of studies in probability area, though there are a few trials of probability education for mathematically gifted students. Moreover, less attention has paid to the strategies to develop gifted students' creativity. This study has drawn three teaching strategies for creativity development based on literature review embedding: cognitive conflict, multiple representations, and social interaction. We designed a series of tasks via reconstructing, so called Simpson's paradox to meet these strategies. The findings showed that the gifted students made Quite a bit of improvement in creativity while participating in reflective thinking and active discussion, doing internal and external connection, translating representations, and investigating basic assumption.

• Journal of Korean Home Economics Education Association
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• v.33 no.4
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• pp.85-101
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• 2021

The purpose of this study was to make suggestions for improvement by analyzing the activity tasks in the clothing life area in middle school 「Technology & Home Economics」 textbooks of the 2015 revised curriculum. For this purpose, the multiple intelligence teaching-learning strategy analysis criteria were reconstructed and used for analysis. The activity tasks of the clothing life area of 「Technology & Home Economics I」 textbooks from 12 different publishers were analyzed based on the reconstructed analysis criteria, and the content validity was verified by 11 experts. The content validity, assessed by CVI was 0.94. According to the results, the logical·mathematical intelligence accounted for the highest proportion with 31.02%, followed by linguistic intelligence(23.81%), visual/spatial intelligence(17.08%), intrapersonal intelligence(14.71%), interpersonal intelligence(5.79%), bodily/kinesthetic intelligence(5.22%), naturalistic intelligence(2.37%), and musical intelligence(0.00%). The results showed that the teaching-learning strategies most frequently implemented in clothing life area were logical/mathematical intelligence, linguistic intelligence, visual/spatial intelligence, and intrapersonal intelligence. On the other hand, teaching-learning strategies related to interpersonal intelligence, bodily/kinesthetic intelligence, and naturalistic intelligence were used at a relatively low proportion. Therefore, it is recommended to expand the teaching-learning strategies of interpersonal, bodily/kinesthetic, naturalistic and musical intelligence, for a more balanced intelligence development of students.

• Communications of Mathematical Education
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• v.23 no.1
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• pp.73-83
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• 2009

Mathematics Olympiad aims to identify and encourage students who have superior ability in mathematics, to enhance students' understanding in mathematics while stimulating interest and challenge, to increase learning motivation through self-reflection, and to speed up the development of mathematical talent. Participating mathematical competition, students are going to solve a variety of types of mathematical problems and will be able to enlarge their understanding in mathematics and foster mathematical thinking and creative problem solving ability with logic and reasoning. In addition, parents could have an opportunity valuable information on their children's mathematical talents and guidance of them. Although there should be presenting diversified mathematical problems in competitions, the real situations is that resent most mathematics Olympiads present mathematical problems which narrowly focus on types of solving problems. In order to diversifying types of problems in mathematics Olympiads and making mathematics popular, this study will discuss a Olympiad for problem solving ability, a Olympiad for exploring mathematics, a Olympiad for task solving ability, and a mathematics fair, etc.

• The Mathematical Education
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• v.60 no.1
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• pp.1-19
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• 2021

This study investigates students' conceptions of fractions from a measurement approach while providing a technological environment designed to support students' understanding of the relationships between quantities and adjustable units. 13 third-graders participated in this study and they were involved in a series of measurement tasks through task-based interviews. The tasks were devised to investigate the relationship between units and quantity through manipulations. Screencasting videos were collected including verbal explanations and manipulations. Drawing upon the theory of semiotic mediation, students' constructed concepts during interviews were coded as mathematical words and visual mediators to identify conceptual profiles using a fine-grained analysis. Two students changed their strategies to solve the tasks were selected as a representative case of the two profiles: from guessing to recursive partitioning; from using random units to making a relation to the given unit. Dragging mathematical objects plays a critical role to mediate and formulate fraction understandings such as unitizing and partitioning. In addition, static and dynamic representations influence the development of unit concepts in measurement situations. The findings will contribute to the field's understanding of how students come to understand the concept of fraction as measure and the role of technology, which result in a theory-driven, empirically-tested set of tasks that can be used to introduce fractions as an alternative way.

• Journal of Elementary Mathematics Education in Korea
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• v.15 no.1
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• pp.19-38
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• 2011

The purpose of this study was to analyze the responses and the behavioral characteristics between mathematically promising students and normal students in solving open-ended problems. For this study, 55 mathematically promising students were selected from the Science Education Institute for the Gifted at Seoul National University of Education as well as 100 normal students from three 6th grade classes of a regular elementary school. The students were given 50 minutes to complete a written test consisting of five open-ended problems. A post-test interview was also conducted and added to the results of the written test. The conclusions of this study were summarized as follows: First, analysis and grouping problems are the most suitable in an open-ended problem study to stimulate the creativity of mathematically promising students. Second, open-ended problems are helpful for mathematically promising students' generative learning. The mathematically promising students had a tendency to find a variety of creative methods when solving open-ended problems. Third, mathematically promising students need to improve their ability to make-up new conditions and change the conditions to solve the problems. Fourth, various topics and subjects can be integrated into the classes for mathematically promising students. Fifth, the quality of students' former education and its effect on their ability to solve open-ended problems must be taken into consideration. Finally, a creative thinking class can be introduce to the general class. A number of normal students had creativity score similar to those of the mathematically promising students, suggesting that the introduction of a more challenging mathematics curriculum similar to that of the mathematically promising students into the general curriculum may be needed and possible.

• School Mathematics
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• v.9 no.4
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• pp.487-506
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• 2007

The aims of this study is figure out the characteristics of justification patterns and mathematical representation which are derived from 14 mathematically gifted middle school students in the process of solving the spatial tasks on Archimedean solid. This study shows that mathematically gifted students apply different types of justification such as empirical, or deductive justification and partial or whole justification. It would be necessary to pay attention to the value of informal justification, by comparing the response of student who understood the entire transformation process and provided a reasonable explanation considering all component factors although presenting informal justification and that of student who showed formalization process based on partial analysis. Visual representation plays an valuable role in finding out the Idea of solving the problem and grasping the entire structure of the problem. We found that gifted students tried to create elaborated symbols by consolidating mathematical concepts into symbolic re-presentations and modifying them while gradually developing symbolic representations. This study on justification patterns and mathematical representation of mathematically gifted students dealing with spatial geometry tasks provided an opportunity for understanding their the characteristics of spacial geometrical thinking and expending their thinking.

• Journal of Elementary Mathematics Education in Korea
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• v.16 no.3
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• pp.321-336
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• 2012

Cognitive subject imposes structures on an object to shape it into a structured thing. Structures that the subject imposes on an object in a given problem context can be diverse horizontally and vertically. In view of the horizontal diversity of structure, problem-solving activities focusing on various structures may enrich the present problem-solving education which emphasizes applying and comparing a couple of problem-solving strategies. Finding an algebraic formula for a figural pattern should be regarded as a new starting point of searching for more various structures. In view of the vertical diversity of structure, it should be aware that students may see different structures from the structure that their teacher expect them to see. The vertical diversity of structure enables us to provide students with experience of progress.

• School Mathematics
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• v.15 no.1
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• pp.101-120
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• 2013

International comparative studies of students' performance in mathematics have shown that Korean students possess very negative attitudes toward mathematics, while they are ranked as one of the highest in the cognitive achievement of mathematics. This has prompted mathematics educators to seek for a way to improve the quality of mathematics education. In this context, this research has been conducted to investigate the learning style of Korean middle school students under the assumption that it is of essence to understand the characteristics of our students as mathematics learners. For the purpose, in-depth interview had been conducted and sixteen middle students participated in the interview. The students were chosen to represent the average group of their age-cohorts based on their performance in mathematics and their SES. The interview was designed as a semi-structured clinical interview. In the interview, the students were given mathematical tasks dealing with central themes in the domain of function. Each student was given about 30 to 50 minutes to solve the tasks. After an interviewee finished the tasks, s/he was asked to explained how s/he solved the tasks. The researchers asked additional questions to clarify the students' understanding of the mathematical themes in the tasks and to identify their strategies for learning mathematics. The analysis of the in-depth interview has primarily identified the characteristics of the students' understanding of the main themes in function and then has been extended to investigate their characteristic styles for learning mathematics. The analysis of the interview identified the learning styles of the students as 'inductive learning based on prototypical cases', 'repeated practice of exemplar mathematics problems', 'disengaged learning', and 'double standards in learning mathematics'. Based on the results of the analysis, this research presents the implications for the improvement of mathematics education.