• Journal of Elementary Mathematics Education in Korea
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• v.13 no.2
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• pp.211-229
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• 2009

The purpose of this study is analysis of to investigate relation proportion problem of mathematics textbooks of 7th curriculum to proportional reasoning(relative thinking, unitizing, partitioning, ratio sense, quantitative and change, rational number) of Lamon's proposal at sixth grade students. For this study, I develop two test papers; one is for proportion problem of mathematics textbooks test paper and the other is for proportional reasoning test paper which is devided in 6 by Lamon. I test it with 2 group of sixth graders who lived in different region. After that I analysis their correlation. The result of this study is following. At proportion problem of mathematics textbooks test, the mean score is 68.7 point and the score of this test is lower than that of another regular tests. The percentage of correct answers is high if the problem can be solved by proportional expression and the expression is in constant proportion. But the percentage of correct answers is low, if it is hard to student to know that the problem can be expressed with proportional expression and the expression is not in constant proportion. At proportion reasoning test, the highest percentage of correct answers is 73.7% at ratio sense province and the lowest percentage of that is 16.2% at quantitative and change province between 6 province. The Pearson correlation analysis shows that proportion problem of mathematics textbooks test and proportion reasoning test has correlation in 5% significance level between them. It means that if a student can solve more proportion problem of mathematics textbooks then he can solve more proportional reasoning problem, and he have same ability in reverse order. In detail, the problem solving ability level difference between students are small if they met similar problem in mathematics text book, and if they didn't met similar problem before then the differences are getting bigger.

• Communications of Mathematical Education
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• v.25 no.3
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• pp.537-556
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• 2011

This paper focuses on proportional reasoning being emphasized in today's elementary math, and analyzes the way students use their proportional reasoning abilities and strategies according to their academic achievement levels in solving proportional problems. For this purpose, various types of proportional problems were presented to 173 sixth-grade elementary school students and they were asked to use a maximum of three types of proportional reasoning strategies to solve those problems. The experiment results showed that upper-ranking students had better ability to use, express and perceive more types of proportional reasoning than their lower-ranking counterparts. In addition, the proportional reasoning strategies preferred by students were shown to be independent of academic achievement. But there was a difference in the proportional reasoning strategy according to the types of the problems and the ratio of the numbers given in the problem. As a result of this study, we emphasize that there is necessity of the suitable proportional reasoning instruction which reflected on the difference of ability according to student's academic achievement.

• 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 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.

• 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.

• 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.

• Journal of The Korean Association For Science Education
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• v.19 no.1
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• pp.117-127
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• 1999

The present study investigated Korean and the US college students' scientific reasoning skills involving hypothesis-testing skills and tested the hypothesis that hypothesis-testing skills are more advanced ones than other scientific reasoning skills investigated in this study. Seven hundred and seventy-four(774) Korean and five hundred and sixty-eight(568) the US students were sampled in university level. The Test of Scientific Reasoning was used as a scientific reasoning test. The test is consisted of two conservational reasoning, two proportional reasoning, one pendulum, two probability reasoning, two controlling variable, one correlational reasoning, and two hypothesis-testing reasoning tasks. Korean students showed a significant higher score in proportional and probability reasoning tasks than the US students. However, the Korean showed a significant lower score in conservation and correlation reasoning tasks than their American counterparts. Further, Korean and the US college students showed a notably poor performance in hypothesis-testing skills comparing with other scientific reasoning skills, which supported the hypothesis that hypothesis-testing skills are more advanced ones than other scientific reasoning skills. In addition, the Korean showed a severe deficiency in candle-burning task which required the skill that students have to design a scientific test-procedure to test theoretical hypotheses. This study also discussed on the educational implications of the results of the present study.

• Journal of Educational Research in Mathematics
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• v.23 no.1
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• pp.1-16
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• 2013

The primary purpose of this study is to survey multiplicative thinking levels and its characteristics of third graders in elementary school and to analyze how to use it when they solve the proportional problems. As results, the transition thinking ranked the highest among the four kinds of thinking levels when the $3^{rd}$ graders solved the multiplication problems. It means that the largest numbers of students still can not distinguish the additive and multiplicative situations completely and remain in the transition thinking, which thinks both additively and multiplicatively. In addition, the performance of solving proportional problems was distinguished from the levels of thinking. Through this study, we can give some implications of the importance of multiplicative thinking and instructional methods related to multiplication.

• Journal of Educational Research in Mathematics
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• v.18 no.1
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• pp.103-121
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• 2008

The primary purpose of this study was to gather knowledge about $5^{th},\;6^{th},\;and\;7^{th}$ graders' proportional reasoning ability by investigating their reactions and use of strategies when encounting proportional or nonproportional problems, and then to raise issues concerning instructional methods related to proportion. A descriptive study through pencil-and-paper tests was conducted. The tests consisted of 12 questions, which included 8 proportional questions and 4 nonproportional questions. The following conclusions were drawn from the results obtained in this study. First, for a deeper understanding of the ratio, textbooks should treat numerical comparison problems and qualitative prediction and comparison problems together with missing-value problems. Second, when solving missing-value problems, students correctly answered direct-proportion questions but failed to correctly answer inverse-proportion questions. This result highlights the need for a more intensive curriculum to handle inverse-proportion. In particular, students need to experience inverse-relationships more often. Third, qualitative reasoning tends to be a more general norm than quantitative reasoning. Moreover, the former could be the cornerstone of proportional reasoning, and for this reason, qualitative reasoning should be emphasized before proportional reasoning. Forth, when dealing with nonproportional problems about 34% of students made proportional errors because they focused on numerical structure instead of comprehending the overall relationship. In order to overcome such errors, qualitative reasoning should be emphasized. Before solving proportional problems, students must be enriched by experiences that include dealing with direct and inverse proportion problems as well as nonproportional situational problems. This will result in the ability to accurately recognize a proportional situation.

• School Mathematics
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• v.19 no.2
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• pp.345-367
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• 2017

The purpose of this study is to investigate the proportional reasoning of middle school students during the process of expressing and interpreting the graphs. We collected data from a teaching experiment with four 7th grade students who participated in 23 teaching episodes. For this study, the differences between student A and student B-who joined theteaching experiment from the $1^{st}$ teaching episode through the $8^{th}$ -in understanding graphs are compared and the reason for their differences are discussed. The results showed different proportional solving strategies between the two students, which revealed in the course of adjusting values of two given variables to seek new values; student B, due to a limited ability for proportional reasoning, had difficulty in constructing graphs for given situations and interpreting given graphs.