• 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.

• Journal of Elementary Mathematics Education in Korea
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• v.20 no.4
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• pp.601-625
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• 2016

In this study, I hoped to reveal the understanding of pre-service elementary teachers about proportional reasoning and the traits of proportional reasoning strategy used by pre-service elementary teachers. The results of this study are as follows. Pre-service elementary teachers should deal with various proportional reasoning tasks and make a conscious effort to analyze proportional reasoning task and investigate various proportional reasoning strategies through teacher education program. It is necessary that pre-service elementary teachers supplement the lacking tasks such as qualitative reasoning and distinction between proportional situation and non-proportional situation. Finally, It is suggested to preform the future research on teachers' errors and mis-conceptions of proportional reasoning.

• Journal of Educational Research in Mathematics
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• v.25 no.2
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• pp.189-206
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• 2015

There has been a recurring call for using visual representations in textbooks to improve the teaching and learning of proportional reasoning. However, the quantity as well as quality of visual representations used in textbooks is still very limited. In this article, we analyzed visual representations presented in a Grade 6 textbook from two perspectives of proportional reasoning, multiple-batches perspective and variable-parts perspective, and discussed the potential of the double number line and the double tape diagram to help develop the idea 'things covary while something stays the same', which is critical to reason proportionally. We also classified situations that require proportional reasoning into five categories and provided ways of using the double number line and the double tape diagram for each category.

• Education of Primary School Mathematics
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• v.25 no.1
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• pp.57-79
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• 2022

Current mathematics It is necessary to ensure that ratio and proportion concept is not distorted or broken while being treated as if they were easy to teach and learn in school. Therefore, the purpose of this study is to analyze the activities presented in the textbook. Based on prior work, this study reinterpreted the proportional reasoning task from the proportional perspective of Beckmann and Izsak(2015) to the multiplicative structure of Vergnaud(1996) in four ways. This compared how they interpreted the multiplicative structure and relationships between two measurement spaces of ratio and rate units and proportional expression and proportional distribution units presented in the revised textbooks of 2007, 2009, and 2015 curriculum. First, the study found that the proportional reasoning task presented in the ratio and rate section varied by increasing both the ratio structure type and the proportional reasoning activity during the 2009 curriculum, but simplified the content by decreasing both the percentage structure type and the proportional reasoning activity. In addition, during the 2015 curriculum, the content was simplified by decreasing both the type of multiplicative structure of ratio and rate and the type of proportional reasoning, but both the type of multiplicative structure of percentage and the content varied. Second, the study found that, the proportional reasoning task presented in the proportional expression and proportional distribute sections was similar to the previous one, as both the type of multiplicative structure and the type of proportional reasoning strategy increased during the 2009 curriculum. In addition, during the 2015 curriculum, both the type of multiplicative structure and the activity of proportional reasoning increased, but the proportional distribution were similar to the previous one as there was no significant change in the type of multiplicative structure and proportional reasoning. Therefore, teachers need to make efforts to analyze the multiplicative structure and proportional reasoning strategies of the activities presented in the textbook and reconstruct them according to the concepts to teach them so that students can experience proportional reasoning in various situations.

• School Mathematics
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• v.15 no.4
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• pp.723-742
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• 2013

The purpose of this study was to analyze children's proportional reasoning process on an ill-structured "architectural drawing" problem solving and to investigate their level and characteristics of proportional reasoning. As results, they showed various perspective and several level of proportional reasoning such as illogical, additive, multiplicative, and functional approach. Furthermore, they showed their expanded proportional reasoning from the early stage of perception of various types of quantities and their proportional relation in the problem to application stage of their expanded and generalized relation. Students should be encouraged to develop proportional reasoning by experiencing various quantity in ration and proportion situations.

• 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.

• Archives of design research
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• v.13 no.4
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• pp.155-162
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• 2000

Is golden proportion, which has been classical beauty among aesthetic rules and orders, avaiable in the present \ulcorner or Does ${\surd}$rectangle proportion replace the classical proportion \ulcorner It is a main theme in this thesis to answer the above questions. This study is basically about favorite proportion in the field of fine art, architecture and design. For this study, 2oo students participate in the answering to the questionnaire. The conclusions which result from the above surveys are as follows ; The results of the first survey is the preference of ${\surd}$2 rectangle to other ${\surd}$rectangles. The second result is the preference of golden proportion as 1 : 1.618 to ${\surd}$2 rectangle as 1 : 1.414. This survey proves that ${\surd}$rectangle proportion as modern proportion does not substitute the golden proportion with the classic proportion.

• 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 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 Educational Research in Mathematics
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• v.23 no.4
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• pp.505-516
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• 2013

The purpose of this paper is to analyse the essence of proportional reasoning and to analyse the contents of the textbooks according to the mathematics curriculum revised in 2007, and to seek the direction for developing the proportional reasoning in the elementary school mathematics focused the task variables. As a result of analysis, it is found out that proportional reasoning is one form of qualitative and quantitative reasoning which is related to ratio, rate, proportion and involves a sense of covariation, multiple comparison. Mathematics textbooks according to the mathematics curriculum revised in 2007 are mainly examined by the characteristics of the proportional reasoning. It is found out that some tasks related the proportional reasoning were decreased and deleted and were numerically and algorithmically approached. It should be recognized that mechanical methods, such as the cross-product algorithm, for solving proportions do not develop proportional reasoning and should be required to provide tasks in a wide range of context including visual models.