• Journal of the Korean School Mathematics Society
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• v.17 no.3
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• pp.409-435
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• 2014

This study examines relations between the 5th graders' fraction operation skills and error types on constructed-response items. As results, first, the participants have lower fraction operation skills on 'multiplication of fraction' than 'addition and subtraction of fraction'. Second, the participants have different error types depend on their constructed-response items. Most of error types which group with high ability made was 'leap of solving process', both groups error type with medium ability as well as low ability is 'misunderstanding of questions'. Third, the operation skills on 'addition and subtraction of fraction' have an influence on their operation skills on 'multiplication of fraction', and error types of 'understanding of questions' and 'understanding of solving process' have the most effects on the influence.

• Journal of Elementary Mathematics Education in Korea
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• v.19 no.4
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• pp.563-588
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• 2015

In elementary school, didactical transposition is inevitable due to several reasons. In mathematics, addition and multiplication are taught as binary operations, subtraction and division are taught as unary operations. But in elementary school, we try to teach all the four operations as binary operations by didactical transposition. In 'Mastering' the concepts of the four operations, the way of concept introduction is dealt importantantly. So it is different from understanding the four operations. In this study, we analyzed the four operations of natural numbers and fractions from two perspectives: concept understanding (how to introduce concepts and how to choose an operation) and connection between the operations. As a result, following implications were obtained. In division of fractions, students attempted a connection with multiplication of fractions right away without choosing an operation, based on the situation. Also, to understand division of fractions itself, integrate division of fractions presented from the second semester of the fifth grade to the first semester of the sixth grade are needed. In addition, this result can be useful in the future textbook development.

• School Mathematics
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• v.11 no.1
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• pp.71-91
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• 2009

The purpose of this study was to analyze operation sense in detail with regard to division of fraction. For this purpose, two sixth grade students who were good at calculation were clinically interviewed three times. The analysis was focused on (a) how the students would understand the multiple meanings and models of division of fraction, (b) how they would recognize the meaning of algorithm related to division of fraction, and (c) how they would employ the meanings and properties of operation in order to translate them into different modes of representation as well as to develop their own strategies. This paper includes several episodes which reveal students' qualitative difference in terms of various dimensions of operation sense. The need to develop operation sense is suggested specifically for upper grades of elementary school.

• Education of Primary School Mathematics
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• v.22 no.2
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• pp.129-147
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• 2019

Because of the various concepts and meanings of fractions and the difficulty of learning, studies to improve the teaching methods of fraction have been carried out. Particularly, because there are various methods of teaching depending on the type of fractions or the models or methods used for problem solving in fraction operations, many researches have been implemented. In this study, I analyzed the fractional operations of CCSSM-CA and its U.S. textbooks. It was CCSSM-CA revised and presented in California and the textbooks of Houghton Mifflin Harcourt Publishing Co., which reflect the content and direction of CCSSM-CA. As a result of the analysis, although the grades presented in CCSSM-CA and Korean textbooks were consistent in the addition and subtraction of fractions, there are the features of expressing fractions by the sum of fractions with the same denominator or unit fraction and the evaluation of the appropriateness of the answer. In the multiplication and division of fractions, there is a difference in the presentation according to the grades. There are the features of the comparison the results of products based on the number of factor, presenting the division including the unit fractions at first, and suggesting the solving of division problems using various ways.

• Education of Primary School Mathematics
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• v.26 no.3
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• pp.125-140
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• 2023

In elementary school mathematics, the addition and subtraction of fractions are difficult for students to understand but very important concepts. This study aims to examine the teaching methods and visual aids utilized in the context of common denominator fraction addition and subtraction. The analysis focuses on evaluating the lesson flow and the utilization of visual representations in one national textbook and ten certified textbooks aligned with the current 2015 revised curriculum. The results show that each textbook is composed of chapter sequences and topics that reflect the curriculum faithfully, with each textbook considering its own order and content. Additionally, each textbook uses a different variety and number of visual representations, presumably intended to aid in learning the operations of fractions through the consistency or diversity of the visual representations. Identifying the characteristics of each textbook can lead to more effective instruction in fraction operations.

• 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.

• 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.

• Journal of Elementary Mathematics Education in Korea
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• v.21 no.1
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• pp.23-47
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• 2017

The purpose of this study is to analyze the types of errors that may occur in the four arithmetic operations of the fractions after classified according to the level of academic achievement for sixth-grade elementary school student who Learning of the four arithmetic operations of the fountain has been completed. The study was proceed to get the information how change teaching content and method in accordance with the level of academic achievement by looking at the types of errors that can occur in the four arithmetic operations of the fractions. The test paper for checking the type of errors caused by calculation of fractional was developed and gave it to students to test. And we saw the result by error rate and correct rate of fraction that is displayed in accordance with the level of academic achievement. We investigated the characteristics of the type of error in the calculation of the arithmetic operations of fractional that is displayed in accordance with the level of academic achievement. First, in the addition of the fractions, all levels of students showing the highest error rate in the calculation error. Specially, error rate in the calculation of different denominator was higher than the error rate in the calculation of same denominator Second, in the subtraction of the fractions, the high level of students have the highest rate in the calculation error and middle and low level of students have the highest rate in the conceptual error. Third, in the multiplication of the fractions, the high and middle level of students have the highest rate in the calculation error and low level of students have the highest rate in the a reciprocal error. Fourth, in the division of the fractions, all levels of students have the highest r rate in the calculation error.

• School Mathematics
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• v.14 no.2
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• pp.191-212
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• 2012

In the field of arithmetic in mathematics education, there has been lack of fine-grained investigations addressing the relationship between students' construction of division knowledge with fractional quantities and their whole number division knowledge. This study, through the analysis of part of collected data from a year-long teaching experiment, presents a possible constructive itinerary as to how a student could modify her unit-segmenting scheme to deal with various fraction measurement division situations: 1) unit-segmenting scheme with a remainder, 2) fractional unit-segmenting scheme. Thus, this study provides a clue for curing a fragmentary approach to teaching whole number division and fraction division and preventing students' fragmentary understanding of the same arithmetical operation in different number systems.

• Journal of The Korean Association of Information Education
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• v.4 no.1
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• pp.32-39
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• 2000

The traditional programs developed by the existing CAI technique have the fixed curricular, which make it difficult to deliver various study materials that fit the learners of various levels. In addition, a lack of the flexibility prevents from helping to make their methodology in studying uniform open minded. In order to solve these problems, we have designed and implemented a learner interface that can exclude the limits in the learners active study in solving the fractional operation. In addition to the user interface, this study includes a diagnosis module that can intellectually extract the status of learners understanding, ostensible bugs, and the associated misconceptions through the interface. The experimentation based on the learner interface and the diagnosis module shows that this system correctly diagnoses the level of learners' understanding and the errors in learning, which greatly helps the individualized study.