• School Mathematics
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• v.10 no.2
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• pp.155-179
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• 2008

Multiplication problems for the 7th curriculum focus on functional realms featuring the memorization and application of the multiplication table, exposing learners only to additive thinking characterized by simple counting and drawing. A diversity of research has yet to be conducted for the transition to multiplicative thinking that highlights the capability to solve problems by using multiplication and division in the expanded number scope like 'prime numbers', 'fractional numbers', and 'ratio/rates' and to describe accurately how they solved. This research was designed to develop and utilize teaching-learning materials for the transition of fifth graders' additive thinking to advanced multiplicative one and to analyze the application results in order to identify validity in material development. The following conclusions were made. First, the development and application of teaching-learning materials for multiplicative thinking cultivation facilitated the transition from additive thinking featuring simple counting and drawing to multiplicative thinking characterized by multiplication and accurate description in a more complicated and expanded number scope. Second, the development of materials featuring 'basic'-'intermediate'-'in-depth' courses by activity enabled learners to benefit from learning by level and expansion in number scope. Third, the use of topics and materials closely connected to daily lives stimulated learners' curiosity, helping them concentrate more on given problems. Fourth, communication between teachers and students or among learners themselves was promoted by continuously encouraging them to explain and by reviewing their documents identifying rules or patterns.

• Journal of the Korean School Mathematics Society
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• v.13 no.1
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• pp.23-43
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• 2010

This study is to investigate how much highschool students, who have learned functional concepts included in the Middle school math curriculum, understand chapters of the function, to analyze the types of errors which they made in solving the mathematical problems and to look for the proper instructional program to prevent or minimize those ones. On the basis of the result of the above examination, it suggests a classification model for teaching-learning methods and teaching material development The result of this study is as follows. First, Students didn't fully understand the fundamental concept of function and they had tendency to approach the mathematical problems relying on their memory. Second, students got accustomed to conventional math problems too much, so they couldn't distinguish new types of mathematical problems from them sometimes and did faulty reasoning in the problem solving process. Finally, it was very common for students to make errors on calculation and to make technical errors in recognizing mathematical symbols in the problem solving process. When students fully understood the mathematical concepts including a definition of function and learned procedural knowledge of them by themselves, they did not repeat the same errors. Also, explaining the functional concept with a graph related to the function did facilitate their understanding,

• The Mathematical Education
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• v.62 no.3
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• pp.363-380
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• 2023

This study analyzed the difficulties and mathematical modeling knowledge improvement that an elementary school teacher experienced in modifying a mathematics textbook task to a mathematical modeling task. To this end, an elementary school teacher with 10 years of experience participated in teacher-researcher community's repeated discussions and modified the average task in the data and pattern domain of the 5th grade. The results are as followings. First, in the process of task modification, the teacher had difficulties in reflecting reality, setting the appropriate cognitive level of mathematical modeling tasks, and presenting detailed tasks according to the mathematical modeling process. Second, through repeated task modifications, the teacher was able to develop realistic tasks considering the mathematical content knowledge and students' cognitive level, set the cognitive level of the task by adjusting the complexity and openness of the task, and present detailed tasks through thought experiments on students' task-solving process, which shows that teachers' mathematical modeling knowledge, including the concept of mathematical modeling and the characteristics of the mathematical modeling task, has improved. The findings of this study suggest that, in terms of the mathematical modeling teacher education, it is necessary to provide teachers with opportunities to improve their mathematical modeling task development competency through textbook task modification rather than direct provision of mathematical modeling tasks, experience mathematical modeling theory and practice together, and participate in teacher-researcher communities.

• Journal of The Korean Association of Information Education
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• v.21 no.5
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• pp.497-507
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• 2017

Research on software education and linking and convergence of other subjects has been mainly focused on mathematics and science subjects. The dissatisfaction of various preferences and types of learning personality cause to learning gap. In addition, it is not desirable considering the solution of various fusion problems that can apply the computational thinking. In this way, it is possible to embrace the diverse tendencies and preferences of students through the linkage with the English subject, which is a linguistic approach that deviates from the existing mathematical and scientific approach. By combining similarities in the process of learning a new language of English education and software education. For this purpose, based on the analysis of teaching - learning model of elementary English subject and software education, we developed a class model by modifying existing English subject and software teaching - learning model to be suitable for linkage. Then, the learning elements applicable to software education were extracted from the contents of elementary school English curriculum, and a program applied to the developed classroom model was designed and the practical application method of learning was searched.

• Communications of Mathematical Education
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• v.27 no.3
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• pp.267-281
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• 2013

In this paper, we explore the possibility that ladder diagram games can be used for the introduction of the function and composite function. A ladder diagram with at most one rung is a bijection. Thus a ladder diagram with r rungs is the composition of r one-to-one correspondence. In this paper, we use ladder diagrams to give simple proofs of some fundamental facts about one-to-one correspondence. Also, we suggest Story-telling for introduction of function in middle school and high school. The ladder diagram approach to one-to-one correspondence not only grabs our students' attention, but also facilitates their understanding of the concept of functions.

• The Journal of Asian Finance, Economics and Business
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• v.7 no.11
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• pp.1049-1057
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• 2020

The shift from elite education to mass education in Vietnam has met the demand for education for everybody as well as for quality human resource talent for an emerging nation. Under the resource constraint, understanding the quality dimensions of education and its priority level is important for effective and efficient policies. This study was carried out using both qualitative and quantitative methodologies to develop quality criteria and a ranking model. Two rounds of in-depth interviews were conducted with fifteen experts in the field, who were rectors, employers, and recruitment specialists to develop the quality framework applied in Vietnamese universities under total quality management (TQM), starting from the input of the senior secondary school leavers, through a teaching process to the output. The first round of interviews were unstructured questionnaires designed to explore the main factors in quality assessment model. The second round affirmed the experts' agreement on the assessment model. Then, fuzzy logic was applied to rank eight criteria in the quality assessment model into priority order: cost, teaching and administrative staff, leadership, curriculum, student-related factors, internationalization, admissions, and campus. The results are critical for identifying the necessary actions to enhance the education quality and to further research on the optimal quality model.

• Journal of Elementary Mathematics Education in Korea
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• v.9 no.1
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• pp.65-84
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• 2005

The purpose of this study was to analyze the contents and designs of the developed 22 teaching and programs for the gifted students in elementary mathematics. The focus of the analysis were the participants and the characteristics of the contents, and were to reflect them on the areas of the 7th elementary mathematics curriculum and Renzulli's Enrichment Triad Model. The results of the study as follows: First, the programs for the low grade gifted students are very few compared to those of the high grade students. For earlier development of the young gifted students, we need to develop more programs for the young gifted students. Second, there are many programs in the area of geometry, whereas few programs are developed in the area of measurement. We need to develop programs in the various areas such as measurement, probability and statistics, and patterns and representations. Third, most programs do not follow the steps of the Renzulli's Enrichment Triad Model, and the frequency of appearance of the steps are the 1st, 2nd, and 3rd enrichments, sequentially. We need to develop hierarchical programs in which the sequency and relations are well orchestrated. Fourth, the frequency of appearance is as follows as sequentially: types of exploration of topics, creative problem solving, using materials, project types, and types of games and puzzles. In the development of structure of the program, the following factors should be considered: name of the chapter, overview of the chapter, objectives, contents by steps, evaluation, reading materials, and extra materials.

• The Mathematical Education
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• v.63 no.2
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• pp.255-272
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• 2024

This study aims to design mathematics-integrated classes that cultivate artificial intelligence (AI) thinking and to analyze students' AI thinking within these classes. To do this, four classes were designed through the integration of the AI4K12 Initiative's AI Big Ideas with the 2015 revised elementary mathematics curriculum. Implementation of three classes took place with 5th and 6th grade elementary school students. Leveraging the computational thinking taxonomy and the AI thinking components, a comprehensive framework for analyzing of AI thinking was established. Using this framework, analysis of students' AI thinking during these classes was conducted based on classroom discourse and supplementary worksheets. The results of the analysis were peer-reviewed by two researchers. The research findings affirm the potential of mathematics-integrated classes in nurturing students' AI thinking and underscore the viability of AI education for elementary school students. The classes, based on AI Big Ideas, facilitated elementary students' understanding of AI concepts and principles, enhanced their grasp of mathematical content elements, and reinforced mathematical process aspects. Furthermore, through activities that maintain structural consistency with previous problem-solving methods while applying them to new problems, the potential for the transfer of AI thinking was evidenced.

• Journal of Educational Research in Mathematics
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• v.15 no.2
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• pp.177-196
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• 2005

In the Korean curriculum, students learn the concept of sample, sampling and other concepts related to sample and sampling, when they have reached the 10th grade of high school. But before the 10th grade, they have an activity about data collection, data analysis and the formulation of conclusion. We then investigated and analyzed the informal knowledge of students before they receive formal instructions. The results enabled the identification of the maximum response rate for each question that each student agreed or disagreed with. In particular, it didn't agree with how students consider the characteristic of population in the process of sampling, and the students agreed on a sampling process without considering the characteristic of the population or the components that consist the population. It showed that 5th grade students didn't investigate the data connected with sampling, and didn't understand the validity of sample survey process. While, 6th grade students equally understood sample size, sampling process, the reliance of data acquired through sample survey that applied to the source of judgment. But in details, it revealed that student had a misconception, or stayed at a subjective judgment level. The significant point is that many high school students didn't adequately understood a sample size with sampling. Though statistics instruction has traditionally been delayed until upper secondary education, this inquiry convinced us that this delay is unnecessary.

• Journal for History of Mathematics
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• v.21 no.4
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• pp.61-78
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• 2008

In this paper, we discuss about De Morgan's view on the development of algebra according to following distinctions: arithmetic, universal arithmetic, symbolic algebra, significant algebra. De Morgan thought that the differences between arithmetic and universal arithmetic lie in the usage of letters and the immediate performance of computation. In his viewpoint, universal arithmetic is a transitional phase, in which absurd phenomena occur, from arithmetic to algebra and these absurd phenomena call for algebra. The feature of De Morgan's view on the development of algebra is that symbolic calculus which consist of symbol system without symbol's meaning is acquired, then as extended meanings are furnished to symbols, symbolic calculus become logical so significant calculus is developed. For example, Single algebra is developed, as an extended meaning is furnished to a symbol -1, and double algebra is developed, as an extended meaning is furnished to a symbol $\sqrt{-1}$. According to De Morgan, a symbol system is derived from the incompleteness of a prior symbol system.