• Research in Mathematical Education
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• v.17 no.1
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• pp.47-61
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• 2013

This paper aims to explore whether Learning Study improves teachers' subject content knowledge, pedagogical content knowledge, and attitude toward teaching mathematics. A Learning Study was conducted in a Hong Kong primary school for a research lesson on comparing the size of fractions to explore the new teacher roles.

• Research in Mathematical Education
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• v.17 no.4
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• pp.221-241
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• 2013

The data for the present paper was a part of a large research project conducted to assess preservice teachers' knowledge related to fractions and place value at a southwestern public university in 2007. The study utilized convenience sampling, consisting of 150 elementary preservice teachers who were enrolled in a mathematics methods course before their student teaching. The results demonstrated preservice teachers' knowledge of teaching comparison, addition, subtraction, and multiplication of fractions was insufficient even though these should be basic knowledge. Teacher preparation programs should emphasize profound knowledge for teaching fractions using representations.

• School Mathematics
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• v.11 no.4
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• pp.685-706
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• 2009

This dissertation is aimed to investigate the reason why a contextualization is needed to help the meaningful teaching-learning concerning multiplications and divisions of fractions, the way to make the contextualization possible, and the methods which enable us to use it effectively. For this reason, this study intends to examine the differences of situations multiplying or dividing of fractions comparing to that of natural numbers, to recognize the changes in units by contextualization of multiplication of fractions, the context is set which helps to understand the role of operator that is a multiplier. As for the contextualization of division of fractions, the measurement division would have the left quantity if the quotient is discrete quantity, while the quotient of the measurement division should be presented as fractions if it is continuous quantity. The context of partitive division is connected with partitive division of natural number and 3 effective learning steps of formalization from division of natural number to division of fraction are presented. This research is expected to help teachers and students to acquire meaningful algorithm in the process of teaching and learning.

• The Mathematical Education
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• v.40 no.2
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• pp.195-215
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• 2001

The purpose of this paper is to present a specific set of home teaching methods in hopes to prevent slow learner of the elementary mathematics. This paper deals with the number and operations, one of five topics in the elementary mathematics A survey of two hundred elementary school teachers was made to see the teacher's opinions of the role of home studying and to concretize the contents of the research topics. There were asked which is the most essential contents for the concrete loaming and which is the most difficult monad that might cause slow leaner. And those were found to be; counting, and arithmetic operations(addition and subtraction) of one or two-digit numbers and multiplication and their concepts representations and operations(addition and subtraction) of fractions. The home teaching methods are based on the situated learning about problem solving in real life situations and on the active teaming which induces children's participation in the process of teaching and learning. Those activities in teaching each contents are designed to deal with real objects and situations. Most teaching methods are presented in the order of school curriculum. To teach the concepts of numbers and the place value, useful activities using manipulative materials (Base ten blocks, Unifix, etc.) or real objects are also proposed. Natural number's operations such as addition, subtraction and multiplication are subdivided into small steps depending upon current curriculum, then for understanding of operational meaning and generalization, games and activities related to the calculation of changes are suggested. For fractions, this paper suggest 10 learning steps, say equivalent partition, fractional pattern, fractional size, relationship between the mixed fractions and the improper fraction, identifying fractions on the number line, 1 as a unit, discrete view point of fractions, comparison of fractional sizes, addition and subtraction, quantitative concepts. This research basically centers on the informal activities of kids under the real-life situation because such experiences are believed to be useful to prevent slow learner. All activities and learnings in this paper assume children's active participation and we believe that such active and informal learning would be more effective for learning transfer and generalization.

• Education of Primary School Mathematics
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• v.25 no.3
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• pp.213-232
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• 2022

With the importance of number line in learning fractions, this study investigated how 4th grade students understand fractions and its operations in number line. The questionnaire consisted 22 items which were related to representing fractions, comparing the size of fractions, and operating addition and subtraction of fractions. Both structured number line and sub-structured number line were presented in the items. As results of the study, the overall success rates were not high and even some items showed higher incorrect answer rates than the success rates. Also, the students showed a difficulty in solving non-structured number line tasks. It was also noticeable that students showed several types of incorrect answers, which means that students had incomplete understanding of both fractions and number line. This paper is expected to shed light on elementary students' understanding of fractions and number line and to provide implications of how to deal with number line in teaching and learning fractions in the elementary school.

• 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.

• The Mathematical Education
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• v.56 no.2
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• pp.193-212
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• 2017

This study focuses on cuisenaire rods that can be used when teaching fractions to elementary school students. First of all, this study critically examines the use of cuisenaire rods in learning of fraction proposed by various researches. Then, based on this review, this study explores in detail the use of cuisenaire rods in teachers' manuals developed from the revised curriculum by 2009 and in lessons related to fraction. The results of this study show that there are subtle differences in how to use cuisenaire rods in learning fractions and these subtle differences have a significant impact on students' understanding of the fractions. Therefore, the teachers should be able to accurately grasp the differences and utilize appropriate methods for teaching purpose. The followings are some of the implications for teachers or textbook developers when using cuisenaire rods in fraction learning: First, we should use cuisenaire rods in ways that can fully exploit the interpretations of the fraction as a part-whole and the fraction as a ratio. Second, we should focus on quantitative reasoning with unit to determine what each cuisenaire rod refers to. Third, it is necessary to take a more careful and sensitive approach to the use of cuisenaire rods. Teachers and textbook developers should constantly explore ways to make good use of mathematical manipulatives to help students understand conceptually in fractional learning. Furthermore, when teaching various mathematical topics using different manipulatives, I expect that there will be sufficient discussions and specific studies on how to use each of these manipulatives.

• Research in Mathematical Education
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• v.17 no.1
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• pp.15-27
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• 2013

Division of fractions is always a difficult topic for primary school students. Most of the presentations in teaching the topic in textbooks are procedural, asking students to invert the second fraction and multiply it with the first one, that is, $$\frac{a}{b}{\div}\frac{c}{d}=\frac{a}{b}{\times}\frac{d}{c}$$. Such procedural approach in teaching diminishes both the understanding of structure in mathematics and the interest in learning the subject. This paper discussed the formulation of teaching the division of fractions, which based on research lessons in some primary five classrooms. The formulated lessons started with an analogy to division of integers and working with division of fractions with equal denominators and then extended to division of fractions in general. It is found that the using of analogy helps students to invent their procedure in working the division problem. Some procedures found by students are discussed, with the focus on the development of their invention and mathematical thinking.

• Research in Mathematical Education
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• v.10 no.3 s.27
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• pp.189-203
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• 2006

Teaching of fractions is very challengeable for elementary and middle school teachers. Many teachers feel uncomfortable teaching the subject. How shall we introduce the concept of fractions? Shall we focus more on concept development or computational procedures and skills? What methodology can be used in teaching those important topics? These are the kind of questions many teachers and researchers try to answer. In this article, the authors are to look at this issue from a cross nation perspective, by examining how the Chinese mathematics curriculum and the Chinese teachers deal with this subject.

• Journal of Elementary Mathematics Education in Korea
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• v.14 no.3
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• pp.807-825
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• 2010

Educational interest has been paid to ADHD students. Because of being easily distracted, lacking concentration, and committing hyperactive acts, they lag much behind other students in academic grades and their teachers have many difficulties in teaching them. This study aims to provide a case of enhancing an ADHD student's fraction-related achievement. To do this, we investigated his mathematical abilities in a preliminary study, devised an individualized teaching for the fractions unit, and applied them to him. And analyzing the results from observations and interviews of the student we can induce the following results: First, the ADHD student showed such types of errors in relation to fraction as lack of the concept of dividing into equal parts, lack of the concept of numerator and denominator, and errors in adding or subtracting fractions anc mixed fractions whose denominators were the same. And secondly, the fraction-related achievements of the ADHD student have improved thanks to the systematic teaching plan based on the accurate understanding of his academic gap relative to other students, his learning attitude, and his time difference. In addition, this study suggests several implications for ADHD students' learning of fractions.