• Journal of Educational Research in Mathematics
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• v.12 no.3
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• pp.331-351
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• 2002

It is widely recommended that teachers should actively mediate students' engagement with tools such as manipulative materials. This paper is to help to parse classroom life so that both social and psychological aspects are accounted for and coordinated. Building on the theory of affordances from ecological psychology and the activity theory from sociocultural perspectives, the main strategy of this paper is to view manipulative materials as simultaneously participating in social and psychological activity systems. Within these activity systems it is charted how both mathematical affordances related to the structure of mathematical concepts and ecological affordances related to socially situated classroom practices need to be considered by teachers in effective mediation of mathematical manipulatives. This paper has three major sections. The first section develops a theoretical extension of Gibson's theory of affordances from natural to social environments. The second section introduces mathematical and ecological affordances using empirical data from a grade two elementary school classroom. The third section illustrates the need of coordinating the two affordances as embedded in different activity systems.

• Journal of the Korean Mathematical Society
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• v.57 no.6
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• pp.1485-1508
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• 2020

In this paper, we investigate the complete f-moment convergence for extended negatively dependent (END, for short) random variables under sub-linear expectations. We extend some results on complete f-moment convergence from the classical probability space to the sub-linear expectation space. As applications, we present some corollaries on complete moment convergence for END random variables under sub-linear expectations.

• Journal of the Korean School Mathematics Society
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• v.5 no.1
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• pp.1-11
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• 2002

The purpose of this study is to find out if there are meaningful differences between small rural middle schools and nearby urban ones In the mathematical diagnostic evaluation. It also says how to improve students' scholastic abilities, making up a question of attitudes towards math to know the mathematical abilities lowering cause in small rural middle schools. Findings are, 1. Students must recognize that studying math is essential and be interested in it. 2. The mathematical confidence is needed. 3. A strong will of studying math hard is important. 4. Students must have a motivational triggering, while solving math problems and then checking answers for themselves. 5. Backward countries' humanistic and social environmental factors should be overcome. In conclusion, we expect the mathematical abilities improvement, making students remove the mathematical abilities lowering cause after having a learning experience suitable for the rural community instead of the negative attitudes towards math.

• East Asian mathematical journal
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• v.26 no.2
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• pp.319-336
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• 2010

There are serious difficulties with management of general mathematics education courses because of enormous gap between freshman's ability of mathematics and lack of problem solving ability. In this paper, we try to find methods so we can reduce the difficulties. By utilizing students survey, management of Mathematics Cafe and setting example classes for Calculus and Linear Algebra we suggest effective management strategies and teaching-learning methods.

• Journal of Educational Research in Mathematics
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• v.12 no.2
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• pp.181-192
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• 2002

There are various methods of proving a proposition. Among these, 'mathematical induction' is treated in school mathematics weightly. But many students have difficulty with the proof by 'mathematical induction'. To solve this problem, analysis needs to be attempted in various aspects This study attempts to compare the teaching methods of 'mathematical induction' in South and North Korea and to acquire the implication. In fact, many differences between South and North Korea are found. These differences are caused by epistemological and psychological premise. Therefore this study investigates the epistemological and psychological aspects in North Korea and compares the textbooks in South and North Korea. Through this study, some implications are found. First, the sequence of introducing the 'mathematical Induction' needs to be considered. Second, the rich context of applying the 'mathematical induction' is needed. Finally, disagreement between curriculum and textbook in South Korea needs to be reconsidered.

• East Asian mathematical journal
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• v.36 no.2
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• pp.147-172
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• 2020

The purpose of this study is to provide to understand correctly for teachers and pre-service teachers who have the wrong conception of mathematical modeling. We present the differences modeling problems and general application problems to identify between general application and modeling problems. We propose the entire process from modeling tasks development to solve the problems of mathematical modeling. Additionally, the entire process of the possible solutions was concluded for the presented modeling problems. We proposed what students and teachers should perform at each stage of each phase of the modeling cycle. The concrete tasks were suggested for teachers and students at each phase of modeling cycles, with the specific role of the teacher in the overall process for students' modeling activities.

• East Asian mathematical journal
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• v.37 no.4
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• pp.401-426
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• 2021

In order to propose ways to implement mathematical connection between algebra and geometry, this study reinterpreted and visualized the Khayyam's geometric method solving the cubic equations using two conic sections and the Al-Kāshi's method of constructing of angle trisection using a cubic equation. Khayyam's method is an example of a geometric solution to an algebraic problem, while Al-Kāshi's method is an example of an algebraic a solution to a geometric problem. The construction and property of conics were presented deductively by the theorem of "Stoicheia" and the Apollonius' symptoms contained in "Conics". In addition, I consider connections that emerged in the alternating process of algebra and geometry and present meaningful Implications for instruction method on mathematical connection.

• Education of Primary School Mathematics
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• v.18 no.2
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• pp.123-139
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• 2015

The purpose of this study was to investigate the effects of the experiences of productive failures on students' mathematical problem solving abilities and mathematical dispositions. The experiment was conducted with two groups. The treatment group was applied with the productive mathematics failure program, and the comparative group was taught with traditional mathematics lessons. In this study, for quantitative analysis, the students were tested their understanding of mathematical concepts, mathematical reasoning abilities, students' various strategies and mathematical dispositions before and after using the program. For qualitative analysis, the researchers analyzed the discussion processes of the students, students's activity worksheets, and conducted interviews with selected students. The results showed the followings. First, use of productive failures showed students' enhancement in problem solving abilities. Second, the students who experienced productive failures positively affected the changes in students' mathematical dispositions. Along with the more detailed research on productive mathematical failures, the research results should be included in the development of mathematics textbooks and teaching and learning mathematics.

• Education of Primary School Mathematics
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• v.16 no.3
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• pp.267-283
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• 2013

Mathematical justification is the process through which one's claim is validated to be true based on proper and trustworthy data. But it serves as a catalyst to facilitate mathematical discussions and communicative interactions among students in mathematics classrooms. This study is designed to investigate the effects of mathematical justification on students' problem-solving and communicative processes occurred in a mathematics classroom. In order to fulfill the purpose of this study, mathematical problem-solving classes were conducted. Mathematical justification processes and communicative interactions recorded in problem understanding activity, individual student inquiry, small and whole group discussions are analyzed. Based on the analysis outcomes, the students who participated in mathematical justification activities are more likely to find out various problem-solving strategies, to develop efficient communicative skills, and to use effective representations. In addition, mathematical justification can be used as an evaluation method to test a student's mathematical understanding as well as a teaching method to help develop constructive social interactions and positive classroom atmosphere among students. The results of this study would contribute to strengthening a body of research studying the importance of teaching students mathematical justification in mathematics classrooms.

• Communications of Mathematical Education
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• v.23 no.3
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• pp.545-562
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• 2009

This study is trying to analyze characteristics of mathematical thinking processes of the mathematical gifted students in an objective and a systematic way, by using "Protocol Analysis Method"and "Problem Behavior Graph" which is suggested by Newell and Simon as a qualitative analysis. In this study, four middle school students with high achievement in math were selected as subjects-two students for mathematical gifted group and the other two for control group also with high scores in math. The thinking characteristics of the four subjects, shown in the course of solving problems, were elicited, analyzed and compared, through the use of the creative test questionnaires which were supposed to clearly reveal the characteristics of mathematical gifted students' thinking processes. The results showed that there were several differences between the two groups-the mathematical gifted student group and their control group in their mathematical talents. From these case studies, we could say that it is significant to find out the characteristics of mathematical thinking processes of the mathematical gifted students in a more scientific way, in the sense that this result can be very useful to provide them with the chances to get more proper education by making clear the nature of thinking processes of the mathematical gifted students.