• Journal of Elementary Mathematics Education in Korea
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• v.20 no.2
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• pp.283-309
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• 2016

The purpose of this study is to investigate gifted students in elementary mathematics how they understand of situations involving multiplication and concepts of multiplication. For this purpose, first, this study analyzed the teacher's guidebooks about introducing the concept of multiplication in elementary school. Second, we analyzed multiplication problems that gifted students posed. Third, we interviewed gifted students to research how they understand the concepts of multiplication. The result of this study can be summarized as follows: First, the concept of multiplication was introduced by repeated addition and times idea in elementary school. Since the 2007 revised curriculum, it was introduced based on times idea. Second, gifted students mainly posed situations of repeated addition. Also many gifted students understand the multiplication as only repeated addition and have poor understanding about times idea and pairs set.

• Communications of Mathematical Education
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• v.18 no.1 s.18
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• pp.73-87
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• 2004

현장에서 수업을 하다 보면 의외로 학생들이 곱셈구구는 잘 외우고 있지만 곱셈의 개념에 대해서는 잘 모르고 있다는 것을 많이 발견할 수 있다. 이것은 곱셈에 대한 개념을 도입할 때 학생들이 왜 곱셈을 배우는가에 대해서 스스로 절실하게 생각해 보고 발견해 보는 경험이 부족했기 때문이라고 생각한다. 곱셈이 왜 필요하고 곱셈식으로 나타내는 것이 얼마나 좋은 방법인지 학생들이 깨달아 덧셈구조에서 곱셈구조로의 개념의 변화가 일어날 수 있도록 지도한다면 이러한 문제점을 어느 정도 해결할 수 있지 않을까 생각해본다. 따라서, 본 연구에서는 자연수의 곱셈에 대한 이론적 배경과 교육과정을 알고 이를 바탕으로 수학교육 이론에 근거한 자연수의 곱셈의 교수-학습 지도 방안에 대하여 거시적 입장에서 고찰해 보고자 한다.

• School Mathematics
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• v.15 no.4
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• pp.889-920
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• 2013

The aim of this study is to look into the didactical background for introducing the concept of multiplication and teaching multiplication facts in elementary school mathematics and offer suggestions to improve teaching multiplication in the future. In order to attain these purposes, this study deduced and examined concepts of multiplication, situations involving multiplication, didactical models for multiplication and multiplication strategies based on key ideas with respect to the didactical background on teaching multiplication through a theoretical consideration regarding various studies on multiplication. Based on such examination, this study compared and analyzed textbooks used in the United States, Finland, the Netherlands, Germany and South Korea. In the light of such theoretical consideration and analytical results, this study provided implication for improving teaching multiplication in elementary schools in Korea as follows: diversifying equal groups situations, emphasizing multiplicative comparison situations, reconsidering Cartesian product situations for providing situations involving multiplication, balancing among the group model, array model and line model and transposing from material models to structured and formal ones in using didactical models for multiplication, emphasizing multiplication strategies and properties of multiplication and connecting learned facts and new facts with one another for teaching multiplication facts.

• Journal of Elementary Mathematics Education in Korea
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• v.11 no.1
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• pp.1-21
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• 2007

The purpose of this study was to propose instructional methods using base-ten blocks in teaching the multiplication of decimal for 5th grade students by analyzing the process of their conceptual comprehension of multiplication of decimal. The students in this study were found to understand various meanings of operations (e.g., repeated addition, bundling, and area) by modeling them with base-ten blocks. They were able to identify the algorithm through the use of base-ten blocks and to understand the principle of calculations by connecting the manipulative activities to each stage of algorithm. The students were also able to determine whether the results of multiplication of decimal might be reasonable using base-ten blocks. This study suggests that appropriate use of base-ten blocks promotes the conceptual understanding of the multiplication of decimal.

• Journal of Educational Research in Mathematics
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• v.16 no.2
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• pp.157-177
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• 2006

The concepts of ratio and proportion do not develop in isolation. Rather, they are part of the individual's multiplicative conceptual field, which includes other concepts such as multiplication, division, and rational numbers. The current study attempted to clarify the beginning of this development process. One fourth student, Kyungsu, was encourage to schematize his trial-and-error-based method, which was effective in solving so-called missing-value tasks. This study describes several advancements Kyungsu made during the teaching experiment and analyzes the challenges Kyungsu faced in attempting to schematize his method. Finally, the mathematical knowledge Kyungsu needed to further develop his ratio and proportion concepts is identified. The findings provide additional support for the view that the development of ratio and proportion concepts is embedded within the development of the multiplicative conceptual field.

• School Mathematics
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• v.11 no.1
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• pp.17-37
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• 2009

Concept and model of multiplication is not single. Concepts of multiplication can be classified into three cases: repeated addition, times idea, pairs set. Models of multiplication can be classified into four cases: measurement, rectangular pattern, combinatorial problem, number line. Among diverse cases of multiplication's concept and model, which case does elementary mathematics education lay stress on? This question is a controvertible didactical point. In this thesis, (1) mathematical and didactical analysis of multiplication's concept and model is performed, (2) a concrete program of teaching multiplication which is based on times idea is contrived, (3) With this new program, the teaching experiment is performed and its result is analyzed. Through this study, I obtained the following results and suggestions. First, the degree of testee's understanding of times idea is not high. Secondly, a sort of test problem which asks the testee to find times value is more easy than the one to find multiplicative resulting value. Thirdly, combinatorial problem can be handled as an application of multiplication. Fourthly, the degree of testee's understanding of repeated addition is high. In conclusion, I observe the fact that this new program which is based on times idea could be a alternative program of teaching multiplication which could complement the traditional method.

• Journal of Elementary Mathematics Education in Korea
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• v.22 no.4
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• pp.369-384
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• 2018

Multiplication is able to be described by using repeated addition, a Cartesian product, a scalar operation, rectangular array and area in many various context. Multiplication in various problem situations is learned by various of the teaching method and the order of teaching more than any other mathematical concepts and operations in elementary school. Nevertheless, the context of multiplication leaves further room for improvement. The purpose of this study is to examine the similarities and differences between the conceptual aspects of multiplication through the literature and to analyze the appropriateness of the teaching method and the order of teaching through textbook analysis. As a result of the study, it was found that multiplication of a scalar operation was introduced too early and did not properly reflect of meaning of multiplication as a scalar operation. There is also a need to use the concept of the rectangular array or area as a meaning of multiplication two quantities.

• Journal of Gifted/Talented Education
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• v.24 no.1
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• pp.17-43
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• 2014

On the subjects of elementary 3rd grade three child prodigies who had learned the four fundamental arithmetic operations and primary concepts of fraction, this study conducted a qualitative case research to examine how they composed schema of addition and multiplication of fractions and transformed schema through recognition of precise concepts and linking of concepts with addition and multiplication of fractions as the contents. That is to say, this study investigates what schema and transformed schema child prodigies form through composition of primary mathematic concepts to succeed in relational understanding of addition and multiplication of fractions, how they use their own formed schema and transformed schema for themselves to approach solutions to problems with addition and multiplication of fractions, and how the subjects' concept formation and schema in their problem solving competence proceed to carry out transformations. As a result, we can tell that precise recognition of primary concepts, schema, and transformed schema work as crucial factors when addition of fractions is associated with multiplication of fractions, and then that the schema and transformed schema that result from the connection among primary mathematic concepts and the precise recognition of the primary concepts play more important roles than any other factors in creative problem solving with respect to addition and multiplication of fractions.

• The Mathematical Education
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• v.62 no.1
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• pp.1-21
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• 2023

The purpose of this study is to explore how the student, who interiorized three levels of units, constructed fractions as multipliers by analyzing her ways of conceiving improper fractions with three levels of units and coordinating two three-levels-of-units structures. Among the data collected from our teaching experiment with two 4th grade students meeting 13 times for three months, we focus on how Seyeon, one of the participating students, wrote numerical expressions in the form of "× fraction" for the given situations using her splitting operation for composite units. Given the importance of splitting operation for composite units for the construction of fractions as multipliers, implications for further research are discussed.

• Proceedings of the Korea Institutes of Information Security and Cryptology Conference
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• 1997.11a
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• pp.221-231
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• 1997

본 논문에서는 고속 멱승을 위한 모듈라 곱셈기를 시스토릭 어레이로 설계한다. Montgomery 알고리듬 및 시스토릭 어레이 구조를 분석하고 공통 피승수 곱셈 개념을 사용한 변형된 Montgomery 알고리듬에 대해 시스토릭 어레이 곱셈기를 설계한다. 제안 곱셈기는 각 처리기 내부 연산을 병렬화 할 수 있고 연산 자체도 간단화 할 수 있어 시스토릭 어레이 하드웨어 구현에 유리하며 기존의 곱셈기를 사용하는 것보다 멱승 전체의 계산을 약 0.4배내지 0.6배로 감소시킬 수 있다.