• Communications of Mathematical Education
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• v.24 no.3
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• pp.731-744
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• 2010

Nowadays in school mathematics, the skill and method for solving problems are often emphasized in preference to the theoretical principles of mathematics. Students pay attention to how to make an equation mechanically before even understanding the meaning of the given problem. Furthermore they do not get to really know about the principle or theorem that were used to solve the problem, or the meaning of the answer that they have obtained. In contemporary textbooks the conic section such as circle, ellipse, parabola and hyperbola are introduced as the cross section of a cone. But they do not mention how conic section are connected with the quadratic equation or how these curves are related mutually. Students learn the quadratic equations of the conic sections introduced geometrically and are used to manipulating it algebraically through finding a focal point, vertex, and directrix of the cross section of a cone. But they are not familiar with relating these equations with the cross section of a cone. In this paper, we try to understand the quadratic curves better through the analysis of the discussion made in the process of the discovery and eventual development of the conic section and then seek for way to improve the teaching and learning methods of quadratic curves.

• School Mathematics
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• v.11 no.1
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• pp.55-70
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• 2009

The purpose of this study is to implement Lakatos method in the teaching and learning of geometry for middle school students. In his landmark book , Lakatos suggested the following instructional approach: an initial conjecture was produced, attempts were made to prove the conjecture, the proofs were repeatedly refuted by counterexamples, and finally more improved conjectures and refined proofs were suggested. In the study, students were selected from the high achieving students who participated in the special mathematics and science program offered by the city council of Seoul. The students were given a contradictory geometric proposition, and expected to find the cause of the fallacy. The students successfully identified the fallacy following the Lakatos method. In this process they also set up a primitive conjecture and this conjecture was justified by the proof and refutation method. Some implications were drawn from the result of the study.

• School Mathematics
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• v.19 no.3
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• pp.461-480
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• 2017

The aim of this study was to analyze characteristics of teachers' knowledge about correlation with data presented in $2{\times}2$ tables. In order to achieve the aim, this study conducted didactical analysis about two-way tables through examining previous researches and developed a questionnaire with reference to the results of the analysis. The questionnaire was given to 53 middle and high school teachers and qualitative methods were used to analyze the data obtained from the written responses by the participants. This study also elaborated the framework descriptors for interpreting the teachers' responses in the light of the didactical analysis and the data was elucidated in terms of this framework. The specific features of teachers' knowledge about correlation with data presented in $2{\times}2$ tables were categorized into three types as a result. This study raised several implications for teachers' professional development for effective mathematics instruction about correlation and related concepts dealt with in probability and statistics.

• School Mathematics
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• v.14 no.1
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• pp.1-28
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• 2012

The purpose of the study are to identify factors of mathematical visualization through the thirty students of highschool 2nd year and to investigate how each visualization factor is used in mathematics problem solving process. Specially, this study performed the qualitative case study in terms of the five of thirty students to obtain the high grade in visuality assessment. As a result of the analysis, visualization factors were categorized into mental images, external representation, transformation or operation of images, and spacial visualization abilities. Also, external representation, transformation or operation of images, and spacial visualization abilities were subdivided more specifically.

• School Mathematics
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• v.18 no.1
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• pp.15-42
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• 2016

Clarifying differences of scholastic characteristics showed in male and female students is the first step for resolving the differences. It is difficult that we figure out them by one test. If we evaluate a few subjects, they can't have generality. So, we must evaluate lots of subjects through several years by all-around contents. We keep going on like that, we can get objective and valid results. Accordingly, I dealt with 2010~2014 NAEA taken by complete enumeration evaluation for elementary, middle, and high school students. From the evaluation, while I organized the achievement scores and the average of percentage of correct answers from aspects of whole test, item types, and content domains, I elicited from differences of scholastic characteristics showed in male and female students by achievement levels. On the basis of these, I explored ways which can resolve the differences in male and female students and I proposed several suggestions to look for the better ways.

• Journal of Educational Research in Mathematics
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• v.22 no.4
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• pp.517-534
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• 2012

As observing the learning of middle school mathematics students for three years, I examined the relationship between students' procedural knowledge and their conceptual knowledge as they develop those knowledges in the rational number domain. In particular, I explored the implications of an unbalanced development in a student's conceptual knowledge and procedural knowledge by considering two conditions: (a) the case of a student who has relatively strong conceptual knowledge and weak procedural knowledge, and (b) the case of a student who has relatively weak conceptual knowledge and strong procedural knowledge. Results suggest that conceptual knowledge and procedural knowledge are most productive when they develop in a balanced fashion (i.e., closely iterative or simultaneously), which calls into question the assumption that one has primacy over the other.

• School Mathematics
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• v.9 no.2
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• pp.291-312
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• 2007

As a result of observing the 10-th grade text books on mathematics now in use which show the way of introducing complex numbers for the first time, it is easy to see all the text books on mathematics use a quadratic equation $x^2+1=0$ for a new number i. However, Since using the new number i is artificial, this make students get confused in understanding the way of introducing complex numbers. And students who have problems with the quadratic equation can also have difficulty in understanding complex numbers. On the other hand, by using a coordinate plane with ordered pairs and arrows, students can understand complex numbers better because the number system can be extended systematically through intuitive methods. The problem is that how to bring and use ordered pairs and arrows to introduce complex numbers in highschool mathematics. To solve this problem, in this study, We developed a systematic and visible learning contents which make it possible to study the process of the step-by-step extension of number system that will be applied through elementary and middle school curriculum and all the way up to the introduction of complex numbers. After having applied the developed learning contents to the teaching and learning procedure, we can know that the developed learning contents are more efficient than the contents used in the text books on mathematics now in use.

• Communications of Mathematical Education
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• v.31 no.2
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• pp.187-201
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• 2017

The study in this paper, which is part of a bigger study investigating non-cognitive characteristics of Korean students at the 4-12 grade levels, aims to identify the influential characteristics that explain students' decision to give up on mathematics learning. We consider seven non-cognitive student characteristics: value, interest, attitudes, external motivation, internal motivation, learning conation and efficacy. Data were collected from 21,485 Korean students, and were analyzed with a logistic regression method using SPSS. The findings show that efficacy was the most significant indicator of students' decision to give up on mathematics learning in all three grade level bands: elementary (4th-6th), middle (7th-9th) and high (10th-12th). In particular, the causal model analysis shows that students who highly value mathematics tend to have stronger internal and external motivation, which bring about stronger interest and learning conation, which in turn lead to positive attitudes and strong efficacy regarding the learning of mathematics. It was further found that while external motivation was a significant indicator of upper grade level students' decision to give up on mathematics learning, it was only a moderate indicator for lower grade level students. The findings of this study provide useful information about which non-cognitive areas need to be focused on, in what grade levels, to help students stay on track and not fall behind in learning mathematics.

• Journal of the Korean School Mathematics Society
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• v.10 no.3
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• pp.353-367
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• 2007

The purpose of this study was to examine what errors students made in solving word problems with figures and to compare the problem-solving abilities of boys and girls for each type of word problems with figures. It's basically meant to provide information on effective teaching-learning methods about world problems with figures that were given the greatest weight among different sorts of word problems. The findings of the study were as fellows: First, there was no difference between the boys and girls in the types of error they made. Both groups made the most errors due to a poor understanding of sentences, and they made the least errors of making the wrong expression. And the students who gave no answers outnumbered those who made errors. Second, as for problem-solving ability, the boys outperformed the girls in problem solving except variable problems. There was the greatest gap between the two in solving combining problems. Third, they made the average or higher achievement in solving the types of problems that were included much in the textbooks, and made the least achievement in relation to the types of problems that were handled least often in the textbooks.

• School Mathematics
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• v.5 no.1
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• pp.77-95
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• 2003

We have web-based online discussion to implement active interaction and a variety of communicative activities. I have gathered the following research questions to study about the meaning of web-based online discussion as a mathematical communication teaching method. First, what changes are there in students mathematical communication ability in web-based online discussion\ulcorner Second, how do students evaluate the web-based online discussion experience\ulcorner In this web-based online discussion, groups of middle school first grade 34 students and each group had chatting at 8 times for 10 weeks. I analyzed what they had discussed by the prints that they had sent me by e-mail. I also surveyed what they had experienced and analyzed them. In this research, the online web based discussion has given positive influence on students' competence of speaking, writing, reading and listening which are crucial to mathematical communication. Students' mathematic thinking power improved and attitudes to mathematics have become more positive.