• Journal of Educational Research in Mathematics
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• v.17 no.4
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• pp.359-380
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• 2007

This study was conducted with two 6-graders to identify how were their proportional reasoning abilities, whether they evolved proportional thinking in a various context, and what had influence on their proportional thinking. The findings, as previous researches noted, suggested that the proportional expression obtaining by instrumental understanding could not provide rich opportunities for students to improve understanding about ratio and proportion and proportional reasoning abilities, while being useful for determining the answers. The students were able to solve proportional problems with incorporating their knowledge of divisor, multiples, and fraction into proportional situations, but not the lack of number sense. The students easily solved proportional problems experienced in math and other subjects but they did not notice proposition in problems with unfamiliar contexts.

• Journal of the Korean School Mathematics Society
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• v.19 no.1
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• pp.63-82
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• 2016

Mathematical notation is the main means to realize the power of mathematics. Under this perspective, this study analyzed the difficulties of learning an irrational number concept in terms of notation. I tried to find ways to overcome the difficulties arising from the notation. There are two primary ideas in the notation of irrational number using root. The first is that an irrational number should be represented by letter because it can not be expressed by decimal or fraction. The second is that $\sqrt{2}$ is a notation added the number in order to highlight the features that it can be 2 when it is squared. However it is difficult for learner to notice the reasons for using the root because the textbook does not provide the opportunity to discover. Furthermore, the reduction of the transparency for the letter in the development of history is more difficult to access from the conceptual aspects. Thus 'epistemological obstacles resulting from the double context' and 'epistemological obstacles originated by strengthening the transparency of the number' is expected. To overcome such epistemological obstacles, it is necessary to premise 'providing opportunities for development of notation' and 'an experience using the notation enhanced the transparency of the letter that the existing'. Based on these principles, this study proposed a plan consisting of six steps.

• School Mathematics
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• v.18 no.2
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• pp.257-275
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• 2016

The purpose of this study was to investigate the impact of multiple representations on students' understanding of fractions, decimals, and percent. The instructional approach integrating multiple representations was compared to traditional algorithmic instruction, a form of direct instruction. To examine and compare the impact of multiple representations instruction with traditional algorithmic instruction, pre and post tests consisting of five similar items were administered with 87 middle school students. Students' scores in these two tests and their problem solving processes were analyzed quantitatively and qualitatively. The quantitative results indicated that students taught by traditional algorithmic instruction showed higher scores on the post-test than students in the multiple representations group. Furthermore, findings suggest that instruction using multiple representations does not guarantee a positive impact on students' understanding of mathematical concepts. Qualitative results suggest that the limited use of multiple representations during a class may have hindered students from applying their use in novel problem situations. Therefore, when using multiple representations, teachers should employ more diverse examples and practice with multiple representations to help students to use them without error.

• Journal of Elementary Mathematics Education in Korea
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• v.12 no.1
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• pp.79-100
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• 2008

Freudenthal has advocated the reinvention method. In that method, the pupils start with a meaningful context, not ready-made concepts, and invent informative method through which he could arrive at the formative concepts progressively. In many face the reinvention method is contrary to the traditional method. In traditional method, which was named as 'concretization method' by Freudenthal, the pupils start with ready-made concepts, and applicate this concepts to various instances through which he could arrive at the understanding progressively. Through analysis, it turns out that Korea's seventh elementary mathematics textbook is based on concretization method. In this thesis, first of all, I will reconstruct probability unit of seventh elementary textbook according to Freudenthal's reinvention method. Next, I will perform teaching experiment which is ruled by new lesson design. Lastly, I analysed the effects of teaching experiment. Through this study, I obtained the following results and suggestions. First, the reinvention method is effective on the teaching of probability concept and algorithm. Second, in comparison with current textbook strand, my strand which made probability concept go ahead and combinatorics concept let behind is not deficiency. Third, tree diagram is effective matrix which contribute to formalization of combinatorics calculation. Lastly, except for fraction, diverse representation of probability, for example percentage or informal ratio expression must be introduced in teaching process.

• Journal of Elementary Mathematics Education in Korea
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• v.14 no.3
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• pp.633-658
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• 2010

This study aimed to analyze the debate on the Elementary School Mathematics Contents in the new National Elementary Mathematics Curriculum developed in 2006. With this, the feature of the new National Mathematics Curriculum compared with the past 7th National Elementary Mathematics Curriculum was investigated. And the drafts on developing the new National Elementary Mathematics Curriculum were investigated as well. Three main controversies were identified. The first controversy was related to the item which had been dealt in middle school curriculum and moved to elementary school in the new National Mathematics Curriculum (e.g. equations, direct proportion and inverse proportion). The second one was related to the order of teaching fraction. The third one was related to the fact that problem solving became one of the five domains in Elementary School Mathematics Curriculum. Those controversies came from a basic belief on the ranges and depths of elementary school mathematics, didactical point of view, or thoughts on what should the content in the National Mathematics Curriculum be. The issues and suggestions that were discussed in this paper might serve to improve the National Mathematics Curriculum.

• Journal of Elementary Mathematics Education in Korea
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• v.20 no.1
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• pp.105-129
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• 2016

The elements of mathematical processes include mathematical reasoning, mathematical problem-solving, and mathematical communications. Proportion reasoning is a kind of mathematical reasoning which is closely related to the ratio and percent concepts. Proportion reasoning is the essence of primary mathematics, and a basic mathematical concept required for the following more-complicated concepts. Therefore, the study aims to analyze the proportion reasoning ability of sixth graders of primary school who have already learned the ratio and percent concepts. To allow teachers to quickly recognize and help students who have difficulty solving a proportion reasoning problem, this study analyzed the characteristics and patterns of proportion reasoning of sixth graders of primary school. The purpose of this study is to provide implications for learning and teaching of future proportion reasoning of higher levels. In order to solve these study tasks, proportion reasoning problems were developed, and a total of 22 sixth graders of primary school were asked to solve these questions for a total of twice, once before and after they learned the ratio and percent concepts included in the 2009 revised mathematical curricula. Students' strategies and levels of proportional reasoning were analyzed by setting up the four different sections and classifying and analyzing the patterns of correct and wrong answers to the questions of each section. The results are followings; First, the 6th graders of primary school were able to utilize various proportion reasoning strategies depending on the conditions and patterns of mathematical assignments given to them. Second, most of the sixth graders of primary school remained at three levels of multiplicative reasoning. The most frequently adopted strategies by these sixth graders were the fraction strategy, the between-comparison strategy, and the within-comparison strategy. Third, the sixth graders of primary school often showed difficulty doing relative comparison. Fourth, the sixth graders of primary school placed the greatest concentration on the numbers given in the mathematical questions.