• Journal of Elementary Mathematics Education in Korea
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• v.22 no.2
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• pp.183-198
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• 2018

In this paper, I theoretically considered joining and separating activities and revisited the textbooks from 7 countries and Korean mathematics textbooks from 5th revised curriculum to 2015 revised curriculum to find implication for the treatment of 0 in the joining and separating activities. The 'joining' has definition and properties similar to addition, but the 'separating'is difficult to define and is not considered to have properties similar to subtraction. In the sense of computation, joining and separating can be seen as' part-part-to-whole' situations, but are just part of the addition and subtraction situations. The analysis of textbooks from 7 counties showed that Singapore and Malaysia textbooks already studied zero and then included it in joining and separating activities, but other countries did not include it as joining and separating activities. The textbooks of South Korea have consistently suggested not to include zero, but teacher's guide has shown that there is a little consistency in the treatment of zero. As a conclusion, I suggested that it was necessary to propose a proper context of the situation in order to introduce joining and separating without including 0 in terms of student level and to propose that a more consistent presentation of zero handling in the teaching in the teacher's guide.

• 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.