• Journal of Elementary Mathematics Education in Korea
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• v.21 no.1
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• pp.1-22
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• 2017

The properties of arithmetic are considered as essential to understand the principles of calculation and develop effective strategies for calculation in the elementary school level, thanks to agreement on early algebra. Therefore elementary students' misunderstanding of the properties of arithmetic might cause learning difficulties as well as misconcepts in their following learning processes. This study aims to provide elementary teachers a part of pedagogical content knowledge about the properties of arithmetic and to induce some didactical implications for teaching the properties of arithmetic in the elementary school level. To do this, elementary school mathematics textbooks since the period of the first curriculum were analyzed. These results from analysis show which properties of arithmetic have been taught, when they were taught, and how they were taught. Based on them, some didactical implications were suggested for desirable teaching of the properties of arithmetic.

• Journal of Elementary Mathematics Education in Korea
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• v.23 no.1
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• pp.143-168
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• 2019

Along with the significance of algebraic thinking in elementary school, it has been recently emphasized that the properties of number and operations need to be explored in a meaningful way rather than in an implicit way. Given this, the purpose of this study was to analyze how third graders could understand the properties of operations in multiplication after they were taught such properties through a reconstructed unit of multiplication. For this purpose, the students from three classes participated in this study and they completed pre-test and post-test of the properties of operations in multiplication. The results of this study showed that in the post-test most students were able to employ the associative property, commutative property, and distributive property of multiplication in (two digits) × (one digit) and were successful in applying such properties in (two digits) × (two digits). Some students also refined their explanation by generalizing computational properties. This paper closes with some implications on how to teach computational properties in elementary mathematics.

• Journal of Educational Research in Mathematics
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• v.21 no.3
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• pp.239-259
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• 2011

This study investigated the elementary school students' ability on the algebraic reasoning as generalized arithmetic. It analyzed the written responses from 648 second graders, 688 fourth graders, and 751 sixth graders using tests probing their understanding of the properties of whole number operations. The result of this study showed that many students did not recognize the properties of operations in the problem situations, and had difficulties in applying such properties to solve the problems. Even lower graders were quite successful in using the commutative law both in addition and subtraction. However they had difficulties in using the associative and the distributive law. These difficulties remained even for upper graders. As for the associative and the distributive law, students had more difficulties in solving the problems dealing with specific numbers than those of arbitrary numbers. Given these results, this paper includes issues and implications on how to foster early algebraic reasoning ability in the elementary school.

• Education of Primary School Mathematics
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• v.22 no.3
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• pp.181-203
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• 2019

Even though the properties of operations in multiplication serve a fundamental basis of conceptual understanding the multiplication with whole numbers for elementary students, there has been lack of research in this field. Given this, the purpose of this study was to analyze instructional methods related to the properties of operations in multiplication (i.e., commutative property of multiplication, associative property of multiplication, distributive property of multiplication over addition) in a series of mathematics textbooks of Korea, Japan, and the US. The overall analysis was conducted in the following two aspects: (a) when and how to deal with the properties of multiplication in three instructional context (i.e., introduction, application, generalization), and (b) what models use to represent the properties of multiplication. The results of this showed that overall similarities in introducing the properties of multiplication .in (one digit) ${\times}$ (one digit) as well as emphasizing the divers representation. However, subtle but meaningful differences were analyzed in applying and generalizing the properties of multiplication. Based on these results, this paper closes with some implications on how to teach the properties of operations in multiplication properties in elementary mathematics.

• Journal of Elementary Mathematics Education in Korea
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• v.21 no.4
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• pp.643-662
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• 2017

The first appearance of the equations in elementary school mathematics is in the expression of the equal sign in the addition sentences without its definition. Most elementary school students have operational understanding of the equal sign in equations. Moreover, students' opportunities to have a clear concept of the properties of operations are limited because they are used implicitly in the textbooks. Based on this fact, it has been argued that it is necessary to introduce the properties of operations explicitly in terms of specific numbers and to deal with various types of equations for understanding a relational meaning of the equal sign. In this study, we use equations to represent the implicit properties of operations and the relational meaning of the equal sign in elementary school mathematics with respect to students' level of understanding. In addition, we give some explicit examples which show how to apply them to make efficient computations.

• Communications of Mathematical Education
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• v.35 no.4
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• pp.505-525
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• 2021

In this study, we investigated how multiplication by 2-digit numbers had been taught in elementary mathematics textbooks of Korea, Japan, Singapore, and USA. As a result of analysis, we found as follows. Korean textbooks do not teach the multiplication by 10 and the multiplication by power of 10, but Japanese, Singapore, and US textbooks explicitly teach related content. In the '×tens' teaching, Japanese and American textbooks teach formally the law of association of multiplication applied in the process of calculating the partial product of multiplication. The standard multiplication algorithm generally followed a standard method of recording partial product result according to the law of distribution, but the differences were confirmed in the multiplication model, the teaching method of the law of distribution, and the notation of the last digit '0'. Based upon these results, we suggested some proposals for improving the multiplication teaching.

• School Mathematics
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• v.13 no.4
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• pp.581-598
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• 2011

Given the growing agreement that algebra should be taught in the early stage of the curriculum, considerable studies have been conducted with regard to early algebra in the elementary school. However, there has been lack of research on how to organize mathematic lessons to develop of algebraic reasoning ability of the elementary school students. This research attempted to gain specific and practical information on effective algebraic teaching and learning in the elementary school. An exploratory qualitative case study was conducted to the fourth graders. This paper focused on the associative law of the multiplication. This paper showed what kinds of activities a teacher may organize following three steps: (a) focus on the properties of numbers and operations in specific situations, (b) discovery of the properties of numbers and operations with many examples, and (c) generalization of the properties of numbers and operations in arbitrary situations. Given the steps, this paper included an analysis on how the students developed their algebraic reasoning. This study provides implications on the important factors that lead to the development of algebraic reasoning ability for elementary students.

• The Journal of the Korea Contents Association
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• v.12 no.3
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• pp.67-76
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• 2012

This paper proposes a concept and algorithm of cloth covering. It is a physically-based model which simulates computationally a shape of cloth covering some objects. The goal of cloth covering is to conceal the details of object and to reveal only the shape outline. It has one scale parameter which controls the degree of suppressing fine-scale structures. To show viability of the proposed cloth covering, this paper performed an experiment of script recognition. The results of comparing accuracies of feature extraction using Gaussian and cloth covering showed that the cloth covering is superior to Gaussian. We discuss the reason for the superiority.

• Journal of the Korean Society for information Management
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• v.13 no.1
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• pp.173-185
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• 1996

In this paper, we propose four optimizing methods for effectively processing queries in the Booleam information retrieval system ; (i) the short-circuit evaluation scheme used for optimizing logical expressions in programming lan-guages is applied to Boolean queries.(II) use the difference of the number of index word frequencies appearing in the related documents. (IIi) reduce the number of operators in the queries by applying the distribution law in the set theory. (iv) evaluate only once for the repeated expressions in the query. These methods have been implemented and tested in KRISTAL-II system on the UNIX workstation environment.

• Review of KIISC
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• v.33 no.2
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• pp.5-11
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• 2023

양자는 물리학에서 더 이상 나눌 수 없는 물리량의 최소 단위이다. 양자에는 일반적인 물리법칙이 적용되지 않는 대신, 양자역학이라는 법칙이 적용된다. 이를 활용한 알고리즘으로 양자암호통신과 양자난수발생기가 존재한다. 양자암호통신은 기존 암호통신과는 다른 차원의 보안성을 제공하는 통신기술이다. 이는 양자를 관측하면 양자상태가 붕괴된다는 특징을 활용하여 도청자를 손쉽게 발견할 수 있게 한다. 양자난수발생기는 의사난수를 대체할 수 있는 알고리즘으로, 가장 완벽한 난수 장치로 여겨진다. 의사난수는 결정론적 알고리즘이기 때문에 값을 예측할 수 있는 반면, 양자난수는 자연 현상에서 뽑아내는 난수이기 때문에 예측할 수 없다. 다만 수학적 연산을 통해 계산하는 의사난수와는 다르게 양자난수는 난수를 추출할 장치가 필요하다. 본 고에서는 양자암호통신과 양자난수발생기의 최신 동향에 대해 확인해 보도록 한다.