• School Mathematics
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• v.15 no.2
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• pp.481-501
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• 2013

The purpose of this study is to review the role of dragging in dynamic geometry environments. Dragging is a kind of dynamic representations that dynamically change geometric figures and enable to search invariances of figures and relationships among them. In this study dragging in dynamic geometry environments is divided by three perspectives: dynamic representations, instrumented actions, and affordance. Following this review, six conclusions are suggested for future research and for teaching and learning geometry in school geometry as well: students' epistemological change of basic geometry concepts by dragging, the possibilities to converting paper-and-pencil geometry into experimental mathematics, the role of dragging between conjecturing and proving, geometry learning process according to the instrumental genesis perspective, patterns of communication or discourse generated by dragging, and the role of measuring function as an affordance of DGS.

• Journal of Educational Research in Mathematics
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• v.16 no.2
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• pp.95-113
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• 2006

The study tries to differentiate the levels of mathematical reasoning from inductive reasoning to formal reasoning for teaching gradually. Because the formal point of view without the relation to objects has limitations in the creation of a new knowledge, our mathematics education needs consider the such characteristics. We propose an intuitive level of proof related in concrete operations and perceptual experiences as an intermediating step between inductive and formal reasoning. The key activity of the intuitive level is having insight on the generality of reasoning. The details of the process should pursuit the direction for going away from objects and near to formal reasoning. We need teach the mathematical reasoning gradually according to the appropriate level of reasoning more differentiated.

• The Mathematical Education
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• v.41 no.3
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• pp.273-289
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• 2002

It tends to be emphasized that mathematics is the important discipline to develop students' mathematical reasoning abilities such as deduction, induction, analogy, and visual reasoning. This study is aimed for investigating the present state about mathematical reasoning in secondary school. We survey teachers' opinions and analyze the results. The results are analyzed by frequency analysis including percentile, t-test, and MANOVA. Results are the following: 1. Teachers recognized mathematics as knowledge constructed by deduction, induction, analogy and visual reasoning, and evaluated their reasoning abilities high. 2. Teachers indicated the importances of reasoning in curriculum, the necessities and the representations, but there are significant difference in practices comparing to the former importances. 3. To evaluate mathematical reasoning, teachers stated that they needed items and rubric for assessment of reasoning. And at present, they are lacked. 4. The hindrances in teaching mathematical reasoning are the lack of method for appliance to mathematics instruction, the unpreparedness of proposals for evaluation method, and the lack of whole teachers' recognition for the importance of mathematical reasoning

• Journal of Elementary Mathematics Education in Korea
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• v.20 no.1
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• pp.131-148
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• 2016

Mathematical formal justification may be seen as a bridge towards the proof. By requiring the mathematically gifted students to prove the generalized patterned task rather than the implementation of deductive justification, may present challenges for the students. So the research questions are as follow: (1) What are the difficulties the mathematically gifted elementary students may encounter when formal justification were to be shifted into a generalized form from the given patterned challenges? (2) How should the teacher guide the mathematically gifted elementary students' process of transition to formal justification? The conclusions are as follow: (1) In order to implement a formal justification, the recognition of and attitude to justifying took an imperative role. (2) The students will be able to recall previously learned deductive experiment and the procedural steps of that experiment, if the mathematically gifted students possess adequate amount of attitude previously mentioned as the 'mathematical attitude to justify'. In addition, we developed the process of questioning to guide the elementary gifted students to formal justification.

• Journal of Elementary Mathematics Education in Korea
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• v.14 no.1
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• pp.65-80
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• 2010

The aims of our study are to investigate the nature of mathematical reasoning and the teaching of mathematical reasoning in school mathematics. We analysed the process of shaping deduction in ancient Greek based on Netz's study, and discussed on the comparison between his study and Freudenthal's local organization. The result of our analysis shows that mathematical reasoning in elementary school has to be based on children's natural language and their intuitions, and then the mathematical necessity has to be formed. And we discussed on the sequences and implications of teaching of the sum of interior angles of polygon composed the discovery by induction, justification by intuition and logical reasoning, and generalization toward polygons.

• Journal of the Korean School Mathematics Society
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• v.14 no.3
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• pp.295-323
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• 2011

This study is based on the recognition that teacher educators have to focus their attention on developing pre-service teachers' statistical reasoning for statistics education of school mathematics. This paper investigated knowledge on pre-service teachers' statistical reasoning. Statistical Reasoning Assessment (SRA) is performed to find out pre-service teachers' statistical reasoning ability. The research findings are as follows. There was meaningful difference in the statistical area of statistical reasoning ability with significant level of 0.05. This proved that 4 grades pre-service teachers were more improve on statistical reasoning than 2 grades pre-service teachers. Even though most of the pre-service teachers ratiocinated properly on SRA, half of pre-service teachers appreciated that small size of sample is more likely to deviate from the population than the large size of sample. A few pre-service teachers have difficulties in understanding "Correctly interprets probabilities(be able to explain probability by using ratio" and "Understands the importance of large samples(A small sample is more likely to deviate from the population)".

• Communications of Mathematical Education
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• v.23 no.2
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• pp.461-481
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• 2009

The semiotic approach to the mathematics education has been studied in last 20 years by PME, ICME conferences. New cultural developments in multi-media, digital documents and digital arts and cultures may influence mathematical education and teaching and learning activities. Hence semiotical interest in the mathematics education research and practice will be increasing. In this paper the basic ideas of semiotics, such as Peirce triad and Saussure's dyad, are introduced with some mathematical applications. There is some similarities between traditional research topics for concept, representation and social construction in mathematics education research and semiotic approach topics for the same subjects. some semiotic applications for an arithmetic problem for work, induction, deduction and abduction syllogisms with respect to Peirce's triad, its meaning in scientific discoveries and learning in geometry and symmetry.

• School Mathematics
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• v.8 no.4
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• pp.379-396
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• 2006

The purpose of this study is to analyze characteristics of problem solving in mathematics for gifted students through case study on solving the mathematical problem for gifted students, and to investigate what are relationships with the cognitive and affective characteristics. To this end, this study was to analyze the characteristics on the problem solving in mathematics by using qualitative research method after it selected two students who had specific education for brilliant students. As a result, this study has shown that it had high preference for question with clear answer, high preference for individual inquiry learning, high adhesion to answer for question, and high adhesion for assignment on characteristics of process of problem solving, but there was much difference in spirit of competition. As to the characteristics of thoughts in problem solving, this study has shown that it had high grasp capacity, intuitive insight, and capacity for visualization, but there were differences in capacity for generalization and adaptability. However, both two students had low values in deductive thought. In addition, as to the home environment and cognitive and affective characteristics, they were not related to the characteristics on problem solving directly, but it has shown that it affected each other indirectly. As to the conclusion of this study, this researcher thinks that it will be valuable documentation in order to improve curriculum, development of textbooks, and teaching method for special education for the gifted students and education for secondary mathematics.

• Journal of the Korean School Mathematics Society
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• v.16 no.1
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• pp.31-61
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• 2013

The purpose of this study is to confirm constructivists' assumption that when a little low level learners are taken in learner-centered instruction based on a constructivism they can also construct knowledge by themselves. To achieve this purpose, the researchers compare the effects of learner-centered instruction based on the constructivism and teacher-centered instruction based on the objective epistemology where second graders learn multiplication facts through the each treatment on learners' reasoning ability and achievement. Some conclusions are drawn from results as follows. First, learner-centered instruction based on a constructivism has significant effect on learners' reasoning ability. Second, learner-centered instruction has slightly positive effect on learners' deductive reasoning ability. Third, learner-centered instruction has more an positive influence on understanding concepts and principles of not-presented mathematical knowledge than teacher-centered instruction when implementing it with a little low level learners.

• Journal of Educational Research in Mathematics
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• v.23 no.4
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• pp.585-604
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• 2013

This study is based on the problem that most middle school students cannot recognize the generality of geometrical theorems even after having proved them. By considering this problem from the point of view of empirical verification, the particularity of geometrical representations, and the role of geometrical variables, we suggest that some experiences in dynamic geometry environment (DGE) can help students to recognize the generality of geometrical theorems. That is, this study aims to observe students' cognitive changes related to their recognition of the generality and to provide some educational implications by making students experience some geometrical explorations in DGE. To do so, we selected three middle school students who couldn't recognize the generality of geometrical theorems although they completed their own proofs for the theorems. We provided them exploratory activities in DGE, and observed and analyzed their cognitive changes. Based on this analysis, we discussed the effects of DGE on studensts' recognition of the generality of geometrical theorems.