• Education of Primary School Mathematics
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• v.21 no.2
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• pp.111-130
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• 2018

In this study, I compared and analyzed the contents of Korean, Japanese, Singapore, American, and Finnish textbooks about fraction which is one of the important and difficult concepts in elementary school mathematics. This is aimed to get the implications for meaningful fractional teaching and learning by analyzing the advantages and disadvantages of the methods and time of introducing the concept because fraction has the diversity of the sub-concepts and the introducing methods or process. As a result of the analysis, the fraction was introduced as part-whole(area) in all five countries' textbooks, but the use of number line, conversion between improper fraction and mixed number, whether to deal with part-whole(set) model. Furthermore, there are differences in the methods in obtaining of the equivalent fraction and the order of arrangement in comparison of fraction. Through this analysis, we discussed the reconsideration of the introducing contexts of fractions, the use of number line when introducing fractions, and the problem of segmentation and classification of contents.

• Education of Primary School Mathematics
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• v.25 no.4
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• pp.377-394
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• 2022

Criticism has been raised that the way of teaching weights in the 3rd and 4th graders of elementary school is different between the 2015 revised math curriculum and the 2015 revised science curriculum, causing confusion among elementary school teachers and students. This study tried to confirm the social recognition that should be considered in the process of didactic transformation which means transformation from knowledge to used into knowledge to taught and to compare the variations of didactic transformations differently according to didactic intentions. The research analyzes and synthesizes the root of the meaning of weight, weight in the international standard system of units SI, weight implemented in Korean mathematics curriculum and textbooks, Singaporean mathematics curriculum and textbooks, USA mathematics curriculum and textbooks, and Korean science curriculum and textbooks. Through this analysis, a pedagogical perspective on how to define and teach weight in elementary school as knowledge to be taught was derived.

• The Mathematical Education
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• v.61 no.3
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• pp.499-519
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• 2022

Ratio and rate are key topics in the area of 'Patterns', but there are various perspectives on them. This study compared and analyzed the perspectives of Korean and Singaporean mathematics textbooks on ratio and rate, and explored how teaching and learning methods develop according to each perspective in terms of quantitative reasoning. To this end, we reorganized the analysis criteria based on some studies, and analyzed the textbooks of the two countries in relation to context, relationship, and representation. The results of the study are as follows. Regarding the context, there were differences in the situations, types of units and use of units of the problems presented in textbooks. In terms of relationship, there were differences in the types of two quantities and relationship of quantities. Lastly, there were differences in the representation of ratio and rate. Through these results, we found that elementary mathematics textbooks in Korea and Singapore take different perspectives on ratio and rate. In particular, the perspective taken by Korean textbooks on ratio and rate had unique points different from that of other previous studies. Considering this Korean perspective, we suggested some implications that could help improve textbooks related to ratio and rate and teach them meaningfully.

• Communications of Mathematical Education
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• v.36 no.2
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• pp.229-252
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• 2022

This study analyzed the introduction of addition and subtraction, including the composition and decomposition of numbers in the Korean, Singaporean, American, and Japanese elementary mathematics textbooks. The analytic foci of this study included visual models and their connections with the given problem contexts, the introduction of addition/subtraction or addition/subtraction sentences and their connections with the visual models, and additional activities for students to develop a relational understanding of the equal sign. The results of the analysis demonstrated diverse connections, mainly because the problem contexts, visual models, and the introduction of addition/subtraction or addition/subtraction sentences were implemented differently for each textbook. There were differences among the textbooks in what order of problem contexts were presented. Regarding the use of visual models, two textbooks tended to use one model consistently, whereas the other textbooks used various models depending on the problem contexts. There were subtle but significant differences in introducing addition/subtraction or addition/subtraction sentences. For a relational understanding of the equal sign, all textbooks included activities emphasizing that both sides of the equal sign are equal. Based on the results of this study, this paper closes with several implications related to the problem contexts to introduce addition/subtraction and addition/subtraction sentences as well as the use of visual models, which can serve as a basis for a new unit for the subsequent textbook.

• Journal of the Korean School Mathematics Society
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• v.22 no.4
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• pp.501-520
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• 2019

This study compared and analyzed Korean, American, Singaporean, and Japanese middle school mathematics curriculum standards and the learning contents in statistics. Through a comparative analysis of the curriculums of these four countries, I found several overall features and differences between the curriculums. First, all four countries emphasized statistical education in a real-life context. Second, all four countries emphasized the use of technological tools. Third, there is a middle school grade in which only Korea does not deal with statistical domains. Fourth, the statistical areas of the United States, Singapore, and Japan focused on identifying trends or variability in data distribution. Fifth, I have found some contents that only Korea does not deal with. Based on this, the following recommendations were developed for the development of the next curriculum and new textbooks in Korea. First, the statistics curriculum should be changed from one that focuses on understanding statistical concepts to one that focuses on statistical activity that utilizes these concepts. Second, in terms of middle school statistical curriculum contents, the addition of interquartile range (IQR) and box plots as learning contents should be considered. IQR and box plots are simple and practical techniques for the comparison of multiple sets of data that can be easily learned and drawn by middle school level students and applied to real-life-related statistical data to expand statistical literacy. Through this study, it is suggested that IQR and box plots need to be included in the statistical curriculum of middle schools in Korea.

• Education of Primary School Mathematics
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• v.21 no.4
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• pp.445-459
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• 2018

The purpose of this study is to provide a method to help elementary school students learn ratio-related concepts effectively through visual representations. This study was conducted to identify the differences in the composition of ratio-related concepts between Korean and Singaporean textbooks, reconstruct a unit of proportional expressions and distributions by using visual representations and confirm the differences in performance between an experimental and a comparison group of 6th grade students. While the experimental group mathematics lessons is from the reconstructed textbook, the comparison group lessons is from an existing textbook that does not include any reconstructive representations. A t-test of mean was applied to determine the differences between the experimental and comparison group. Analysis revealed significant differences in the mean between the experimental group and the comparison group, and the intermediate level group showed more improvement compared to the higher and lower level groups. An implication of this study is that the application of visual representations can assist students' understanding of ratio-related concepts.