• Communications of Mathematical Education
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• v.15
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• pp.71-76
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• 2003

학생들의 분수 나눗셈에 대한 이해는 개념적 이해를 바탕으로 수행되어야 함에도 불구하고 분수 나눗셈은 많은 학생들이 기계적인 절차적 지식으로 획득할 가능성이 높은 내용이다. 이것은 학생들이 학교에서 분수 나눗셈을 학습할 때에 일상생활에서의 경험과 선행 학습과의 연결이 잘 이루어지지 못하고 있는 것에 큰 원인이 있다고 본다. 본 연구에서는 학생들의 분수 나눗셈의 개념적 이해를 돕기 위하여 경험적 지식과의 연결 관계를 활용한 교수 방안을 실험 교수를 통해 조사하였다. 결과로서 번분수를 활용한 수업은 분수 나눗셈의 표준 알고리즘이 수행되는 이유를 알 수 있게 하는데 도움이 되나 여러 가지 절차적 지식이 뒷받침되어야 하며 분수 막대를 직접 잘라 보는 활동을 통한 수업은 분수 나눗셈에서의 나머지를 이해하는데 효과가 있다는 것을 알았다. 결론적으로, 학생들의 경험과 학교에서 이미 학습한 분수 나눗셈들의 관련 지식들을 적절히 연결하도록 한다면 수학적 연결을 통해 분수 나눗셈의 개념적 이해를 이끌 수 있다.

• 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.

• Communications of Mathematical Education
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• v.29 no.2
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• pp.215-239
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• 2015

A goal of this study is figuring out how fraction learning centered on various representation activities influences the fraction comprehension and mathematical attitudes. The study focused on 33 4th-grade students of B elementary school in Seoul. In the study, 15 fraction learning classes comprising enactive, iconic, and symbolic representations took place over 6 weeks. After the classes, the ratio of the students who achieved relational understanding increased and the students averagely recorded 90 pt or more on the fraction comprehension test I, II and III. Two-dependent samples t-test was conducted to analyze a significant difference in mathematical attitudes between pre-test and post-test. On the test result, there was the meaningful difference with 0.01 level of significance. To conclude, the fraction learning centered on various representation activities improves students' relational understanding and fraction understanding. In addition, the fraction learning centered on various representation activities gives positive influences on mathematical attitudes since it increases learning orientation, self-control, interests, value cognition, and self-confidence of the students and decreases fears of the students.

• 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.

• Journal of Elementary Mathematics Education in Korea
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• v.16 no.2
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• pp.295-320
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• 2012

The purpose of this study is searching students' cognitive structures before and after learning division of fraction. Also the researchers investigated how their structures are connected when they solve division of fraction problems through individual interviews. The researcher suggested the instruction of division of fraction from the results.

• 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.

• Communications of Mathematical Education
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• v.15
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• pp.105-111
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• 2003

본 연구자는 아동이 분수 개념을 이해하는 정신모델 속에서 인지과정이 어떻게 나타나며, 적용되는지, 그리고 이를 바탕으로 분수 학습에 표현되는 정신모델 구성을 위한 유추의 역할을 살펴보고자 하는 것이 본 연구의 목적이다.

• Communications of Mathematical Education
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• v.23 no.1
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• pp.129-144
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• 2009

The purpose of the study was to investigate the effects of the use of RNP curriculum based on Lesh translation model on third grade students' understandings of fraction concepts and problem solving ability. Students' conceptual understandings of fractions and problem solving ability were improved by the use of the curriculum. Various manipulative experiences and translation processes between and among representations facilitated students' conceptual understandings of fractions and contributed to the development of problem solving strategies. Expecially, in problem situations including fraction ordering which was not covered during the study, mental images of fractions constructed by the experiences with manipulatives played a central role as a problem solving strategy.

• The Mathematical Education
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• v.44 no.1 s.108
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• pp.125-141
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• 2005

For many years, the educational effects of instructional manipulatives in mathematics education have been investigated in classroom practice and educational research. This paper demonstrates how pattern block, a type of instructional manipulatives could be used and integrated in elementary mathematics areas in order to develop student's mathematical thinking Further, students' thinking process with pattern blocks is analysed to show their thinking process.

• 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.