• Journal of Elementary Mathematics Education in Korea
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• v.19 no.3
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• pp.347-370
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• 2015

The purpose of this study is to examine the effects of mathematical modeling activities on mathematical problem solving abilities and mathematical dispositions in elementary school students. For this study, we administered mathematical modeling activities to fifth graders, which consisted of 8 topics taught over 16 classes. In the results of this study, mathematical modeling activities were statistically proven to be more effective in improving mathematical problem solving abilities and mathematical dispositions compared to traditional textbook-centered lessons. Also, it was found that mathematical modeling activities promoted student's mathematical thinking such as communication, reasoning, reflective thinking and critical thinking. It is a way to raise the formation of desirable mathematical dispositions by actively participating in modeling activities. It is proved that mathematical modeling activities quantitatively and qualitatively affect elementary school students's mathematical learning. Therefore, Educators may recognize the applicability of mathematical modeling on elementary school, and consider changing elementary teaching-learning methods and environment.

• 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.

• Journal of the Korean School Mathematics Society
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• v.13 no.3
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• pp.443-458
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• 2010

This study is about how differ math anxiety according to the features of brain preference. In order to solve questions, BPI test and math anxiety test were done to high school students in the second grade. The test sheets were analyzed by ANOVA and MANOVA using SPSS 14.0. The result was found out that math anxiety was high in the order of left-brain preferences, both-brain preferences, and right-brain preferences. High level of math anxiety among students with right-brain preferences seem to be influenced by the right brain which prefers emotional features. Therefore, students need to stimulate their left brain by writing and reading something a lot when they solve math questions. Also, teachers can lessen math anxiety of students by give them opportunities to solve step-by-step questions, using various visual teaching materials promoting students' reasoning ability which can help them solve questions in a systematic and analytic way.

• Journal of Elementary Mathematics Education in Korea
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• v.23 no.2
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• pp.193-217
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• 2019

Researchers have observed one student who had difficulty in formulating a division equation. In the context of determination of a unit rate problem based on one student's case and previous research, we tried to examine in detail how students expressed the division formula, how to select the dividend and the divisor, and how they learned about those. First, a questionnaire was developed to analyze student's reactions and applied to the research participants. Interviews were conducted to discover how the participants choose the dividends and divisors derived from their cognitive characteristics corresponding to their selection method. The research exposed that the majority of the participants had difficulty in deciding the dividends and divisors. Moreover, the research indicated information that teaching methods need to be reformed. Finally, we obtained suggestions to place emphasis on how to decide a dividend and a divisor, why they made such selection and what the equation means. We proposed a learning method for the research above.

• Journal of Educational Research in Mathematics
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• v.20 no.3
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• pp.203-219
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• 2010

Several studies have reported on how and what mathematically gifted students develop superior ability or creativity in geometry and algebra. However, there are lack of studies in probability area, though there are a few trials of probability education for mathematically gifted students. Moreover, less attention has paid to the strategies to develop gifted students' creativity. This study has drawn three teaching strategies for creativity development based on literature review embedding: cognitive conflict, multiple representations, and social interaction. We designed a series of tasks via reconstructing, so called Simpson's paradox to meet these strategies. The findings showed that the gifted students made Quite a bit of improvement in creativity while participating in reflective thinking and active discussion, doing internal and external connection, translating representations, and investigating basic assumption.

• Journal of Educational Research in Mathematics
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• v.20 no.3
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• pp.275-292
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• 2010

In this study, we discussed the way to teach algebra earlier through investigating to research trends of Early Algebra and researching about nature of subject involving algebra. There is a strong view that arithmetic and algebra have analogous forms and that algebra is on extension to arithmetic. Nevertheless, it is also possible to present a perspective that the fundamental goal and role of symbols and letters are difference between arithmetic and algebra. And, we could recognize that geometry was starting point of algebra trough historical perspectives. To consider these, we extracted some of possible directions to approaches to teach algebra earlier. To access to teaching algebra earlier, following ways are possible. (1) To consider informal strategy of young children. (2) Arithmetic reasoning considered of the algebraic relation. (3) Starting to algebraic reasoning in the context of geometrical problem situation. (4) To present young students to tool of letters and formular.

• School Mathematics
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• v.19 no.1
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• pp.95-116
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• 2017

Through the teaching experiments, we investigated a series of processes for obtaining the differential coefficient at x=0 of the exponential function $y=2^x$ based on the process of constructing the natural constant e and the understanding of it. and all of the students who participated in this study were students who had no experience of calculating the derivative of the exponential function. The purpose of this study was not to generalize the responses of students but to suggest implications for mathematical concept mapping related to calculus by analyzing various responses of students participating in experiments. It is expected that the accumulation of research data derived in this kind of research on the way of understanding and composition of learners will be an important basic data for presenting the learning model related to calculus.

• School Mathematics
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• v.19 no.1
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• pp.59-75
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• 2017

This study analyzed the $6^{th}$ graders' constructions about fraction operations and schemes and figured out the relationships quantitatively between operations and schemes through the written test of 432 students. The results of this study showed that most of students could do partitioning operation well, however, there were many students who had difficulties on iterating operation. There were more students who constructed partitioning operation prior to iterating operation than the opposite. The rate of students who constructed high schemes was lower than that of students who constructed low schemes according to the hierarchy of fraction schemes. Especially, there were many students who construct partitive unit fraction scheme but not partitive fraction scheme, because they could compose unit fraction but not do iterating it. And there were the high correlations between fraction operations and schemes. Given these result, this paper suggests implications about the teaching and learning of fraction.

• School Mathematics
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• v.19 no.1
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• pp.153-170
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• 2017

This study conducted an analysis of types of reasoning shown in students' solving a problem and processes of students' reasoning according to type of problem by posing an open-ended problem where students' reasoning activity is expected to be vigorous and a multiple-choice problem with which students are familiar. And it examined teacher's role of promoting the reasoning in solving an open-ended problem. Students showed more various types of reasoning in solving an open-ended problem compared with multiple-choice problem, and showed a process of extending the reasoning as chains of reasoning are performed. Abduction, a type of students' probable reasoning, was active in the open-ended problem, accordingly teacher played a role of encouragement, prompt and guidance. Teachers posed a problem after varying it from previous problem type to open-ended problem in teaching and evaluation, and played a role of helping students' reasoning become more vigorous by proper questioning when students had difficulty reasoning.

• Journal of Educational Research in Mathematics
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• v.27 no.3
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• pp.599-614
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• 2017

The purpose of this study is to compare and analyze middle school students' understanding of constant rate of change, in terms of observing, representing and interpreting dynamic functions in various ways using the SimCalc MathWorlds. For this purpose, parts of a class conducted for six students in the first grade of middle school were analyzed. The results suggested two implications for a class that used this program (SimCalc MathWorlds): First, we confirmed that the relationships between the two quantities that students notice in the same situation can be different. Second, the program helped students to develop a more comprehensive understanding of the meaning of the constant rate of change. The study also revealed the need to use technology in teaching and learning about functions, particularly to represent and interpret a given situation that involves the constant rate of change in various ways. Further, the results can contribute to developing contents and methods to teach functions using technology in consideration of students' different levels of understanding.