• 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.

• Journal of Educational Research in Mathematics
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• v.26 no.4
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• pp.663-682
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• 2016

This study conducted an analysis of strategies that the 3rd to 6th grade elementary students used when they were solving problems of comparing the size of the fractions with like and unlike denominators, and unit fractions. Although there were slight differences in the students' use of strategies according to the problem types, students were found to use the 'part-whole strategy', 'transforming strategy', and 'between fractions strategy' frequently. But 'pieces strategy', 'unit fraction strategy', 'within fraction strategy', and 'equivalent fraction strategy' were not used frequently. In regard to the strategy use that is appropriate to the problem condition, it was found that students needed to use the 'unit fraction strategy', and the 'within fraction strategy', whereas there were many errors in their use of the 'between fractions strategy'. Based on the results, the study attempted to provide pedagogical implications in teaching and learning for comparing the size of the fractions.

• 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 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.11 no.4
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• pp.643-664
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• 2009

This study was aimed to understand the problems that students experience during the self--directed study of a mathematics digital textbook and to find the implications for the design of digital textbook. For this study, we analyzed the process of self-directed learning on 'division of fractions with same denominator' using digital textbook by eight 6th graders. Students asked to use think aloud method while they study the unit. Their learning process was videotaped and analyzed by researchers after the experiment. After the self-directed learning, students filled out a test items and participated interview with a researcher. The result showed that students experienced several misconceptions and errors while using a digital textbook. The types of misconceptions and errors were cataegorized as "misconceptions and errors caused by a mathematics textbook" and "misconceptions and errors caused by a digital textbook". Especially, students showed several important misconceptions and errors because of the design factors. This implies we need to consider the causes of misconceptions for the design of a digital textbook.