• Journal of Korean Elementary Science Education
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• v.42 no.3
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• pp.421-433
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• 2023

This study examined the reasoning of gifted elementary science students in a socioscientific issues (SSI) classroom discussion on COVID-19-related trash disposal challenges. This study aimed to understand the characteristics of evidence use and decision-making difficulties in each type of SSI-related reasoning. To this end, the transcripts of 17 gifted students of elementary science discussing SSIs in a classroom were analyzed within the framework of informal reasoning. The analysis framework was categorized into three types according to the primary influence involved in reasoning: rational, emotional, and intuitive. The analysis showed that students exhibited four categories of evidence use in SSI reasoning. First, in the rational reasoning category, students deemed and recorded scientific knowledge, numbers, and statistics as objective evidence. However, students who experienced difficulty in investigating such scientific data were less likely to have factored them in subsequent decisions. Second, in the emotional reasoning category, students' solutions varied considerably depending on the perspective they empathized with and reasoned from. Differences in their views led to conflicting perspectives on SSIs and consequent disagreement. Third, in the intuitive reasoning category, students disagreed with the opinions of their peers but did not explain their positions precisely. Intuitive reasoning also created challenges as students avoided problem-solving in the discussion and did not critically examine their opinions. Fourth, a mixed category of reasoning emerged: intuition combined with rationality or emotion. When combined with emotion, intuitive reasoning was characterized by deep empathy arising from personal experience, and when combined with rationality, the result was only an impulsive reaction. These findings indicate that research on student understanding and faculty knowledge of SSIs discussed in classrooms should consider the difficulties in informal reasoning and decision-making.

• Journal of Elementary Mathematics Education in Korea
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• v.19 no.4
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• pp.457-484
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• 2015

This study aims to investigate an approach to teach proportional reasoning in elementary mathematics class by analyzing the proportional strategies the students use to solve the proportional reasoning tasks and their percentages of correct answers. For this research 174 sixth graders are examined. The instrument test consists of various questions types in reference to the previous study; the proportional reasoning tasks are divided into algebraic-geometric, quantitative-qualitative and missing value-comparisons tasks. Comparing the percentages of correct answers according to the task types, the algebraic tasks are higher than the geometric tasks, quantitative tasks are higher than the qualitative tasks, and missing value tasks are higher than the comparisons tasks. As to the strategies that students employed, the percentage of using the informal strategy such as factor strategy and unit rate strategy is relatively higher than that of using the formal strategy, even after learning the cross product strategy. As an insightful approach for teaching proportional reasoning, based on the study results, it is suggested to teach the informal strategy explicitly instead of the informal strategy, reinforce the qualitative reasoning while combining the qualitative with the quantitative reasoning, and balance the various task types in the mathematics classroom.

• Journal of Educational Research in Mathematics
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• v.25 no.1
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• pp.21-58
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• 2015

The aim of this study is to look into the didactical background for teaching proportional reasoning in elementary school mathematics and offer suggestions to improve teaching proportional reasoning in the future. In order to attain these purposes, this study extracted and examined key ideas with respect to the didactical background on teaching proportional reasoning through a theoretical consideration regarding various studies on proportional reasoning. Based on such examination, this study compared and analyzed textbooks used in the United States, the United Kingdom, and South Korea. In the light of such theoretical consideration and analytical results, this study provided suggestions for improving teaching proportional reasoning in elementary schools in Korea as follows: giving much weight on proportional reasoning, emphasizing multiplicative comparison and discerning between additive comparison and multiplicative comparison, underlining the ratio concept as an equivalent relation, balancing between comparisons tasks and missing value tasks inclusive of quantitative and qualitative, algebraic and geometrical aspects, emphasizing informal strategies of students before teaching cross-product method, and utilizing informal and pre-formal models actively.

• Journal of the Korean School Mathematics Society
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• v.11 no.4
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• pp.609-627
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• 2008

The purpose of this research was to investigate the relationship between the students' strategy types and the recognition for proportional situations. The students' strategy types which were based on the results of ratio and proportion tests were divided into an additive type, a multiplicative type, and a formal type. This research analyzed the students' activities of categorization when were given the proportional problems and nonproportional problems to the students. And it also explored how to develop students' recognizing for the discrimination between the proportional situations and nonproportional situations. The results was the following. First, the students didn't discriminate the proportional situations and the nonproportional situations in the initial state but they came to discriminate little by little. Secondly, the students didn't discriminate the direct proportions and the inverse proportions until the last stage. Third, the multiplicative type was outperformed more than the formal type in solving the ratio and proportion problems but the formal type was outperformed more than the multiplicative type in discriminating between proportional situations and nonproportional situations. These results are interpreted as showing that solving ratio and proportion tasks and recognizing proportional situations are different aspects of proportional reasoning and it is necessary to understand multiplicative strategy with formal strategy in recognizing proportional situations.

• 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.

• School Mathematics
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• v.18 no.4
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• pp.819-838
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• 2016

This research analyzed proportional reasoning abilities of the 5th grade students who learned only the basis of ratio and rate and 6th grade students who also learned proportion and cross product strategy. Data were collected through the proportional reasoning tests and the interviews, and then the achievement of the students and their proportional reasoning strategies were analyzed. In the light of such analytical results, the conclusions are as follows. Firstly, there is not much difference between 5th and 6th grade students in the achievement scores. Secondly, both 5th and 6th graders are less familiar with the geometric, qualitative and comparisons tasks than the other tasks. Thirdly, not only 5th graders but also 6th graders used informal strategies much more than the formal strategy. Fourthly, some students can't come up with other strategies than the cross product strategy. Finally, many students have difficulties in discerning proportional situation and non-proportional situations. This study provided suggestions for improving teaching proportional reasoning in elementary schools in Korea as follows: focusing on letting students use their informal strategies fluently in geometric, qualitative, and comparisons tasks as well as algebraic, quantitative, and missing value tasks focusing on the concept of ratio and proportion instead of enforcing the formal strategy.

• Education of Primary School Mathematics
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• v.12 no.2
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• pp.117-132
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• 2009

The purpose of this study was analysis on types of strategies and errors when the sixth grade students were solving proportion problems of mathematics textbooks. For this study, proportion problems in mathematics textbooks were investigated and 17 representative problems were chosen. The 277 students of two elementary schools solved the problems. The types of strategies and errors in solving proportion problems were analyzed. The result of this study were as follows; The percentage of correct answers is high if the problems could be solved by proportional expression and the expression is in constant rate. But the percentage of correct answers is low, if the problems were expressed with non-constant rate.

• Journal of The Korean Association For Science Education
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• v.31 no.4
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• pp.587-599
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• 2011

The purpose of this study was to analyze variable-controlling strategy (below vcs) and the ability to infer the effect of variables in Middle school students who experienced 'Thinking Science' activities in a CASE program. For this study, 71 9th grade students experienced in CASE program for 2 years were selected as the experimental group and 72 students were selected as the control group. All students were tested with Science Reasoning TaskVII. The five types of variable-controlling strategy were extracted from students' response. According to the result of this study, the students experienced in CASE program was more successful in the variable-controlling strategy of length, quality, and shape than the control group. The types of reasoning ability of the variable effect intuitively were categorized as possibility of reasoning, impossibility of reasoning, and impossibility of reversible thinking. It has shown that the reasoning ability of the experimental group was higher than that of the control group in the length and thickness variable effect. The results of this study implied that the variable controlling activities in CASE program could be effective for learning variable controlling, and eventually, for the development of reasoning ability of the variable controlling effect. In the ability to infer the effects of variables to get difficult Intuitively, both groups were similar to the rate of cognitive level reached to the formal operation in generalization, and the student of experimental group was 1.5 times faster than the control group.

• Communications of Mathematical Education
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• v.23 no.1
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• pp.145-174
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• 2009

Based on the thinking that people can understand more clearly when the problem is related with their prior knowledge, the Purpose of this study was to analysis students' informal knowledge, which is constructed through their mathematical experience in the context of real-world situations. According to this purpose, the following research questions were. 1) What is the characteristics of students' informal knowledge about fraction before formal fraction instruction in school? 2) What is the difference of informal knowledge of fraction according to reasoning ability and grade. To investigate these questions, 18 children of first, second and third grade(6 children per each grade) in C elementary school were selected. Among the various concept of fraction, part-whole fraction, quotient fraction, ratio fraction and measure fraction were selected for the interview. I recorded the interview on digital camera, drew up a protocol about interview contents, and analyzed and discussed them after numbering and comment. The conclusions are as follows: First, students already constructed informal knowledge before they learned formal knowledge about fraction. Among students' informal knowledge they knew correct concepts based on formal knowledge, but they also have ideas that would lead to misconceptions. Second, the informal knowledge constructed by children were different according to grade. This is because the informal knowledge is influenced by various experience on learning and everyday life. And the students having higher reasoning ability represented higher levels of knowledge. Third, because children are using informal knowledge from everyday life to learn formal knowledge, we should use these informal knowledge to instruct more efficiently.

• Journal of The Korean Association For Science Education
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• v.30 no.6
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• pp.799-814
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• 2010

This study aimed at developing a set of question cards for fostering deep understanding and encouraging reasoning about fossils and analyze the characteristics of visitors' communication depending on whether to use the question cards in a fossil gallery. Through several steps, a card set consisted of nine generic questions about fossil exhibitions and guidance for using question cards were developed. Data related to visitors' communications were collected from 18 peer groups (from 5th to 9th grade) visiting the fossil gallery of Gwacheon National Science Museum. Visiting groups' interactions were videotape recorded and transcribed. 'Holding time,' the types of 'actions,' and the types of 'conversation' were analysed. Visitors' actions were divided into three categories: ‘look’, 'speech', and 'motion.' Furthermore, visitors' conversations categorized as 'speech' were subdivided into four patterns: 'enumerative,' 'consensual,' 'responsive,' and 'argumentative.' Using the question cards contributes to increase holding time and most of the visiting actions. Most of the conversation patterns also increased except the responsive pattern. In conclusion, using question cards in a fossil gallery could facilitate concentrated and meaningful visits by enhancing active verbal and non-verbal communications between exhibit and visitor or among visitors, encouraging visitors' reasoning about exhibits, and guiding visitors what and how to focus on exhibits.