• Journal of Elementary Mathematics Education in Korea
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• v.14 no.2
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• pp.241-262
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• 2010

This study was carried out to identify the cognitive obstacles while using addition and subtraction with fractions, and to analyze the sources of cognitive obstacles. For this purpose, the following research questions were established : 1. What errors do elementary students make while performing the operations with fractions, and what cognitive obstacles do they have? 2. What sources cause the cognitive obstacles to occur? The results obtained in this study were as follows : First, the student's cognitive obstacles were classified as those operating with same denominators, different denominators, and both. Some common cognitive obstacles that occurred when operating with same denominators and with different denominators were: the students would use division instead of addition and subtraction to solve their problems, when adding fractions, the students would make a natural number as their answer, the students incorporated different solving methods when working with improper fractions, as well as, making errors when reducing fractions. Cognitive obstacles in operating with same denominators were: adding the natural number to the numerator, subtracting the small number from the big number without carrying over, and making errors when doing so. Cognitive obstacles while operating with different denominators were their understanding of how to work with the denominators and numerators, and they made errors when reducing fractions to common denominators. Second, the factors that affected these cognitive obstacles were classified as epistemological factors, psychological factors, and didactical factors. The epistemological factors that affected the cognitive obstacles when using addition and subtraction with fractions were focused on hasty generalizations, intuition, linguistic representation, portions. The psychological factors that affected the cognitive obstacles were focused on instrumental understanding, notion image, obsession with operation of natural numbers, and constraint satisfaction.

• Communications of Mathematical Education
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• v.37 no.2
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• pp.213-231
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• 2023

The purpose of this study was to analyze and derive pedagogical implications from elementary mathematics textbooks that align with the revised 2015 curriculum. Specifically, the focus was on the chapters related to simplifying fractions, finding a common denominator, and performing addition and subtraction of Fractions with Different Denominators. The analysis revealed that the overall structure of these chapters was similar across the textbooks, but variations existed in terms of the main activities and the textbook organization. Furthermore, different textbooks employed various types and quantities of visual representations. When designing lesson directions and content, it is crucial to consider the strengths and weaknesses of each visual representation.

• School Mathematics
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• v.18 no.4
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• pp.793-818
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• 2016

The purpose of this study is to explore in detail $5^{th}$ grade students' understanding on the big ideas related to addition of fraction with different denominators: fixed whole unit, necessity of common measure, and recursive partitioning connected to algorithms. We conducted teaching experiments on 15 fifth grade students who had learned about addition of fractions with different denominators using the current textbook. Most students approached to the big ideas related to addition of fractions in a procedural way. However, some students were able to conceptually understand the interpretations and algorithms of fraction addition by quantitatively thinking about the context and focusing on the structures of units. Building on these results, this study is expected to suggest specific implications on instruction methods for addition of fractions with different denominators.

• Education of Primary School Mathematics
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• v.26 no.3
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• pp.181-197
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• 2023

The importance of reasoning processes based on fractional concepts and number senses, rather than a formalized procedural method using common denominators, has been noted in a number of studies in relation to compare the magnitudes of unlike fractions. In this study, a unlike fraction magnitudes comparison test was conducted on fourth-grade elementary school students who did not learn equivalent fractions and common denominators to analyze the reasoning perspectives of the correct and wrong answers for each of the eight problem types. As a result of the analysis, even students before learning equivalent fractions and reduction to common denominators were able to compare the unlike fractions through reasoning based on fractional sense. The perspective chosen by the most students for the comparison of the magnitudes of unlike fractions is the 'part-whole perspective', which shows that reasoning when comparing the magnitudes of fractions depends heavily on the concept of fractions itself. In addition, it was found that students who lack a conceptual understanding of fractions led to difficulties in having quantitative sense of fraction, making it difficult to compare and infer the magnitudes of unlike fractions. Based on the results of the study, some didactical implications were derived for reasoning guidance based on the concept of fractions and the sense of numbers without reduction to common denominators when comparing the magnitudes of unlike fraction.

• School Mathematics
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• v.18 no.3
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• pp.625-645
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• 2016

This study clarified the big ideas related to teaching addition and subtraction of fractions with different denominators based on quantitative reasoning with unit and recursive partitioning. An analysis of this study urged us to re-consider the content related to the addition and subtraction of fraction. As such, this study analyzed textbooks and teachers' manuals developed from the fourth national mathematics curriculum to the most recent 2009 curriculum. In addition and subtraction of fractions with different denominators, it must be emphasized the followings: three-levels unit structure, fixed whole unit, necessity of common measure and recursive partitioning. An analysis of this study showed that textbooks and teachers' manuals dealt with the fact of maintaining a fixed whole unit only as being implicit. The textbooks described the reason why we need to create a common denominator in connection with the addition of similar fractions. The textbooks displayed a common denominator numerically rather than using a recursive partitioning method. Given this, it is difficult for students to connect the models and algorithms. Building on these results, this study is expected to suggest specific implications which may be taken into account in developing new instructional materials in process.

• Journal of Educational Research in Mathematics
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• v.27 no.3
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• pp.537-555
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• 2017

This paper compared and contrasted Korean and Singaporean textbooks in order to explore the direction and possibility of teaching the big ideas related to the addition and subtraction of fractions with different denominators proposed by Lee & Pang (2016a). Firstly, we examined the teaching sequences related to the addition of fractions with different denominators in a series of elementary mathematics textbooks of Korea and Singapore. We then analyzed what types of representations are used and how the representations are presented for the big ideas related to the addition of fractions with different denominators. The results of the analysis showed that the contents related to fraction addition are addressed more gradually and systematically in Singaporean textbooks compared to Korean counterparts. The graphical representations appeared in the Singaporean textbooks provide specific implications for teaching the big ideas of the addition of fractions with different denominators. Based on such implications, we expect that the big ideas related to the addition of fractions with different denominators will be addressed explicitly and systematically in Korean textbooks.

• Journal of the Korean School Mathematics Society
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• v.25 no.4
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• pp.307-332
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• 2022

This action research was carried out to help students learn fractions computation by making and using semi-concrete fraction manipulatives that can be used continuously in math classes. For this purpose, the researcher and students made semi-concrete fraction manipulatives and learned how to use these through reviewing the previously learned fraction contents over 4 class sessions. Afterward, through the 14 classes (7 classes for learning to reduce fractions and to a common denominator, 7 classes for adding and subtracting fractions with different denominators) in which the principle inquiry learning model was applied, students actively engaged in learning activities with fraction manipulatives and explored the principles underneath the manipulations of fraction manipulatives. Students could represent various fractions using fraction manipulatives and solve fraction computation problems using them. The achievement evaluation after class found that the students could connect the semi-concrete fraction manipulatives with fraction representation and symbolic formulas. Moreover, the students showed interest and confidence in mathematics through the classes using fraction manipulatives.

• Cross-Cultural Studies
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• v.30
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• pp.53-71
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• 2013

The aim of this study is to compare and analyze the similarities and differences in traditional perspective about women between Algery and Korea. Through this study, we found out following common denominators: sexual discrimination and denigration of women. Under the patriarchal system in Korea and Algery in the past, women were considered to be inferior to men and treated as men's possessions. The noteworthy feature is the perspective of mother. In both countries, the image of woman as a mother is regarded as the source of life and a central axis leading our society. It is very remarkable that we could find a lot of common ground despite that there are a lot of social, cultural and geometrical differences. Therefore, through this study, it is proved that the proverbs tell us the universality among people in the world regardless of culture and region.

• International Commerce and Information Review
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• v.11 no.4
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• pp.347-372
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• 2009

International investment has been gaining the importance in the economic growth, employment and technological spillover for many countries at the time of unrestrained flow of the production resources, inter alia, the capital. International investment is prerequisite for Korea to overcome its resource-scarcity. This paper studied some contentious issues of international investment and attempted to suggest negotiating position for Korea on future FTAs. We have made theoretical research of the issues and derived common denominators from four previous FTAs which Korea has concluded. Based on both theories and evidences, we suggest that Korea be ready to have more open attitude for incoming international investment, that is, foreign direct investment(FDI) in future FTA negotiations although Korea should have rather flexible strategy on international investment issues, on the basis of the reciprocity.

• Communications of Mathematical Education
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• v.23 no.3
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• pp.707-734
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• 2009

The purpose of the study was to investigate how children understand addition and subtraction of fractions and how their understanding influences the solutions of fractional word problems. Twenty students from 4th to 6th grades were involved in the study. Children's understanding of operations with fractions was categorized into "joining", "combine" and "computational procedures (of fraction addition)" for additions, "taking away", "comparison" and "computational procedures (of fraction subtraction)" for subtractions. Most children understood additions as combining two distinct sets and subtractions as removing a subset from a given set. In addition, whether fractions had common denominators or not did not affect how they interpret operations with fractions. Some children understood the meanings for addition and subtraction of fractions as computational procedures of each operation without associating these operations with the particular situations (e.g. joining, taking away). More children understood addition and subtraction of fractions as a computational procedure when two fractions had different denominators. In case of addition, children's semantic structure of fractional addition did not influence how they solve the word problems. Furthermore, we could not find any common features among children with the same understanding of fractional addition while solving the fractional word problems. In case of subtraction, on the other hand, most children revealed a tendency to solve the word problems based on their semantic structure of the fractional subtraction. Children with the same understanding of fractional subtraction showed some commonalities while solving word problems in comparison to solving word problems involving addition of fractions. Particularly, some children who understood the meaning for addition and subtraction of fractions as computational procedures of each operation could not successfully solve the word problems with fractions compared to other children.