• Journal of Educational Research in Mathematics
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• v.25 no.4
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• pp.499-524
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• 2015

In the present study, we propose four participating $8^{th}$ grade students' genetic decomposition of congruent transformation and investigate the role of their dragging activities while understanding the concept of congruent transformation in GSP(Geometer's Sketchpad). The students began to use two major schema, 'single-point movement' and 'identification of transformation' simultaneously in their transformation activities, but they were inclined to rely on the single-point movement schema when dealing with relatively difficult tasks. Through dragging activities, they could expand the domain and range of transformation to every point on a plane, not confined to relevant geometric figures. Dragging activities also helped the students recognize the role of a vector, a center of rotation, and an axis of symmetry.

• Journal for History of Mathematics
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• v.22 no.4
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• pp.129-144
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• 2009

The purpose of this study is what exactly De Morgan contributed to abstract algebra and mathematical logic. He recognised the purely symbolic nature of algebra and was aware of the existence of algebras other than ordinary algebra. He madealgebra as a science by introducing the ordered field and made the base for abstract algebra. He was one of the reformer of classical mathematical logic. Looking into De Morgan's works, we made it clear that the developments of algebra and mathematical logic in 19C.

• School Mathematics
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• v.6 no.4
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• pp.389-409
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• 2004

This article presents a case study in which three middle school students developed models in modeling activity using a tool. We research the interaction of model development process and the activities operating a tool in the modeling. And we investigate whether students are able to create generalizable model, after a tool mediates students' thought process and students internalize the perceptive activity operating a tool. The analysis of our case study led to three results. First, as students were able to integrate perceptive activity operating a tool and cognitive activity, they reasoned about the relationships among changing quantities and developed the model. Second, students corrected and refined developed models with reflecting the perceptive activity operating a tool. Third, as students internalized perceptive activity, students were able to create generalizable model, which is a graph of height as a function of the amount of water that's in the beaker.

• School Mathematics
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• v.17 no.4
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• pp.613-632
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• 2015

In this study, we hope to reveal teacher knowledge necessary to address student errors and difficulties about ratio and rate. The instruments and interview were administered to 3 in-service primary teachers with various education background and teaching experiments. The results of this study are as follows. Specialized content knowledge(SCK) consists of profound knowledge about ratio and rate beyond multiplicative comparison of two quantities and professional knowledge about the definitions of textbook. Knowledge of content and students(KCS) is the ability to recognize students' understanding the concept and the representation about ratio and rate. Knowledge of content and teaching(KCT) is made up of knowledge about various context and visual models for understanding ratio and rate.

• School Mathematics
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• v.19 no.4
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• pp.691-712
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• 2017

It is an important to develop teachers' statistical reasoning or thinking by teacher education. In this study, the "comparing two data sets" tasks is focused as a way to develop pre-service elementary teachers' reasoning about core ideas of statistics such as distribution, variability, center, and spread. 6 teams of each 4 pre-service elementary teachers participated on the tasks and their presentations are analyzed based on Pfannkuch's (2006) teachers' inference model in comparing two data sets. As a result, they paid attention to the distribution and variability in the statistical problem solving by the "comparing two data sets" tasks, and used their contextual knowledge to make a statistical decision. In addition, they used some statistics and graphs as the reference for statistical communication, which is expected to provide implications for improving statistical education. The finding implies that the "comparing two data sets" tasks can be used to develop statistical reasoning of pre-service elementary teachers. Some recommendations are suggested for teacher education by these tasks.

• School Mathematics
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• v.11 no.4
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• pp.567-581
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• 2009

Many articles have reported that zero causes children's arithmetic errors. This article was designed to measure the effect of zero on children's arithmetic performances. For this, 222 of 3,4,5,6 graders in elementary school were tested with pencil and paper. The test were categorized into four parts: basic number fact, column subtraction, column multiplication, and column division. These data showed that the negative effect of zero on children's arithmetic was limited to several areas, concretely, multiplication facts with zero, column subtraction with numbers which have two successive zeros, column multiplication with numbers which have zero in a middle position, long division with zeros. But there was no evidence that students could self-control these negative effects of zero as grade went up. It implies that we should keep attention to children's arithmetic performance with zero in some special areas.

• The Mathematical Education
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• v.57 no.3
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• pp.215-229
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• 2018

Despite the importance of learning to do mathematical proofs, researchers have reported that not only secondary school students but also undergraduate students have difficulties in learning proofs. In this study, we introduced a new toll for learning proofs and explored the reliability and the validity of peer assessment on proofs. In the course of a university in Seoul, students were given weekly proof assignments prior to class. After solving the proofs, each student had to assess other students' proofs. The inter-rater reliabilities of weekly peer assessment was higher than .9 over 90 percent of the observed cases. To examine the validity of peer assessment, we check whether students' assessments were similar to expert assessment. Analysis showed that the equivalence has been quite high throughout the semester and the validity was low in the middle of the semester but rose by the end of the semester. Based on these results, we believe instructors can consider the application of peer assessment on proving tasks as a tool to help students learn.

• The Mathematical Education
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• v.44 no.2 s.109
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• pp.229-264
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• 2005

This thesis is about a comparative study how they use technology in math education in both Korea and U.S.A. The subjects of investigation are the representative math education journals in Korea and America-Mathlove of Korea and Mathematics Teacher of U.S.A. I have chosen and studied contents that is related to technology in the two journals which were published for 10 years from 1995 to 2004. The followings are the theme of the study. Theme 1 (The situation of environment) : I have examined the usage situation of technology in Korea and America, by studying and analysing the rates and types of sentences contained technology in the two journals. Theme 2 (The situation of substances) : By studying and analysing substances and materials of two journals, I have made a study what changes technology of math education in U.S.A and Korea made for math learning contents and materials. Theme 3 (the situation of methods) : I made a study about how technology has affected the methods of teaching and learning math in both Korea and U.S.A by analysing and studying the methods which they have applied to math education.

• Education of Primary School Mathematics
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• v.23 no.3
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• pp.135-156
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• 2020

The purpose of this study is to analyze the effect of average unit learning on the knowledge of the representative value of 5th grade elementary school students. In the information-oriented society, the ability to organize and summarize the data has become an essential resource. In the process of correctly analyzing statistical data and making reasonable decisions, the summary of the data plays an important role, and it is necessary to learn the concept of representative values in order to describe the center of the data in a series of numbers. For research, an informal knowledge type possessed by a fifth grade elementary school student with respect to a representative value before learning an average unit is examined and compared with the representative value after learning the average unit. A suggestion point for representative value guidance in school mathematics is provided while examining the change in knowledge with respect to the representative value. Seeing the informal types of elementary school students' representative values will help them learn how to formalize the concept of representative values in middle and high schools. It will give suggestions about the concept of representative values and the method of instruction that should be dealt with in elementary schools. The informal knowledge about the representative value can help with formal representative value that will be learned later. Therefore, This study's discussions on statistical learning of elementary school students are expected to present meaningful implications for statistical education.

• The Mathematical Education
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• v.44 no.1 s.108
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• pp.113-124
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• 2005

In this study, we have analysed and compared the cognitive, affective, and emotional aspects of the mathematically gifted, the scientifically gifted, and common middle school students in cognitive, affective, and emotional aspects. The mathematically gifted students are proved to have better continuous/simultaneous information processing, more positive mathematical disposition, more preference to difficult tasks, and higher EQ than the common students do. On another hand, no difference is found between the mathematically gifted and the scientifically gifted students in creative problem solving ability however, the mathematically gifted have more self-confidence, more curiosity for mathematics, stronger will, and more disposition to monitor and reflect, and more efficient self-control than the scientifically gifted do. In short, the mathematically gifted are superior to common students in mostly all aspects, and better than the scientifically gifted in the affective part.