• Journal of Elementary Mathematics Education in Korea
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• v.19 no.4
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• pp.563-588
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• 2015

In elementary school, didactical transposition is inevitable due to several reasons. In mathematics, addition and multiplication are taught as binary operations, subtraction and division are taught as unary operations. But in elementary school, we try to teach all the four operations as binary operations by didactical transposition. In 'Mastering' the concepts of the four operations, the way of concept introduction is dealt importantantly. So it is different from understanding the four operations. In this study, we analyzed the four operations of natural numbers and fractions from two perspectives: concept understanding (how to introduce concepts and how to choose an operation) and connection between the operations. As a result, following implications were obtained. In division of fractions, students attempted a connection with multiplication of fractions right away without choosing an operation, based on the situation. Also, to understand division of fractions itself, integrate division of fractions presented from the second semester of the fifth grade to the first semester of the sixth grade are needed. In addition, this result can be useful in the future textbook development.

• Education of Primary School Mathematics
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• v.21 no.3
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• pp.289-307
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• 2018

Although mixed calculation of natural numbers is important in that it completes arithmetic calculation of natural numbers in elementary school, few studies have been conducted regarding its instruction methods. Given this, this study analyzed Korean mathematics textbooks (from the fifth textbooks to the 2009 revised textbooks) along with Japanese and Singaporean textbooks in terms of the parentheses and the order of operations regarding mixed calculation of natural numbers. The results of this study showed that there were differences in introducing the parentheses and representing them in an explicit way per textbooks. In the Korean textbooks, the order of operations was presented mostly with the real-life contexts but it was not always in a diagrammatic representation. In contrast, in the Singaporean textbooks, the order of operations was presented without the real-life contexts and the use of calculators was emphasized. In the Japanese textbooks, the order of operations was presented with the real-life contexts and a hierarchy of operations was emphasized. Based on these results, this study suggested several implications of textbook development and instructional methods regarding mixed calculations of natural numbers.

• Journal of Elementary Mathematics Education in Korea
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• v.12 no.1
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• pp.1-25
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• 2008

The purpose of this study was to identify pre-service teachers' Pedagogical Content Knowledge (PCK) about decimal calculation. A written questionnaire was developed dealing with decimal calculation. A total of 152 pre-service teachers from 3 universities were selected for this study; they had taken an elementary mathematics teaching method course and had no teaching experience. The results were as follows: First, with regard to the method of decimal calculation, most pre-service teachers were familiar with algorithms introduced in the textbook. But with regard to the meaning of decimal calculations, they had difficulties in understanding decimal multiplication or decimal division with decimal number. Second, pre-service teachers recognized reasons of errors as well as errors patterns that student might make. But this recognition was limited mainly to errors related to natural number calculation. Third, pre-service teachers frequently commented about decimals algorithms, picture models, the meanings of decimal calculations, and connections to natural number calculations. Many of them represented the meanings of decimal calculations through picture models as to help students' understanding, while they just mentioned algorithms or treated decimal calculation as natural number calculations with decimal point.

• School Mathematics
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• v.7 no.4
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• pp.403-425
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• 2005

The study aims to get real picture of primary mathematics education based on RME in the Netherlands focusing on number and operations strand by reflecting and analyzing the documents in relation to the primary school mathematics curriculum. In order to attain these purposes, the present paper describes the core goals for mathematics education, Dutch Pluspunt textbook series for the primary school, and a learning-teaching trajectory by TAL project which are determinants of the Dutch primary school mathematics curriculum. Under these reflections on the documents, it is analyzed what is the characteristics of number and operations strand in the Nether-lands as follows: counting numbers, contextualization, positioning, structuring, progressive algoritmization based on levels, estimation and insightful use of a calculator. Finally, discussing Points for improving our primary mathematics curriculum and textbook series development are described.

• Education of Primary School Mathematics
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• v.1 no.1
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• pp.45-58
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• 1997

초등학교 아동은 교육과정을 이수하면서 수 영역에서 자연수, 정수, 그리고 양의 유리수까지 학습하게 되어 있다(교육부, 1992). 초등학교에서의 유리수는 분수ㆍ소수를 의미하는 소박한 의미의 유리수를 의미한다. 여기서 유리수는 자연수와 정수를 포괄하는 수 체계적 의미로서 포함관계가 강조되지는 않는다.(중략)

• Education of Primary School Mathematics
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• v.15 no.1
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• pp.31-40
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• 2012

In this paper, we developed teaching learning models using a numeral operation for the mathematical gifted focused on the design of a circle using GSP and investigated effects of this models. This model gave gifted-students to be able to produce creative outputs with mathematical principles and practicality and beauty of mathematics. We found following facts. Firstly, a developed teaching-learning model improves a mathematical gifted student's mathematical creativity as analytic thinking and deductive inference. Secondly, a circular design using GSP helps gifted students to understand the abstract rules because mathematical patterns was represented visually by a circular design. Lastly, a circular design using a numeral operation is helpful to gifted students revealing to creativity and beauty of mathematics.

• Communications of Mathematical Education
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• v.6
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• pp.257-273
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• 1997

• School Mathematics
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• v.14 no.2
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• pp.191-212
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• 2012

In the field of arithmetic in mathematics education, there has been lack of fine-grained investigations addressing the relationship between students' construction of division knowledge with fractional quantities and their whole number division knowledge. This study, through the analysis of part of collected data from a year-long teaching experiment, presents a possible constructive itinerary as to how a student could modify her unit-segmenting scheme to deal with various fraction measurement division situations: 1) unit-segmenting scheme with a remainder, 2) fractional unit-segmenting scheme. Thus, this study provides a clue for curing a fragmentary approach to teaching whole number division and fraction division and preventing students' fragmentary understanding of the same arithmetical operation in different number systems.

• 한국HCI학회:학술대회논문집
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• 2008.02a
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• pp.91-96
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• 2008

증강현실(Augmented Reality)을 위한 효과적인 비전 기반 인터페이스 개발은 꾸준히 진행되어 왔으나, 대부분 환경적 제약을 받거나, 특수한 장비 혹은 복잡한 모델을 요구한다. 예를 들어, 마커를 이용하면 구현 상의 편의성과 정확성을 보장하지만, 일반적으로 마커는 환경과 대비되는 모양을 가지기 때문에, 사용자에게 거부감을 줄 수 있으며 무엇보다 복잡한 인터랙션에는 적용되기 힘들다. 한편, 손동작을 이용할 경우, 자연스럽고 다양한 인터랙션을 수행할 수 있지만, 색을 이용한 손동작 인식은 복잡한 환경에서 인식률이 크게 저하되고, 3 차원 모델 기반의 손동작 인식은 많은 연산량을 필요로 한다는 문제점을 가진다. 이로 인해 지금까지 제안된 방법을 증강현실 시스템에 적용하는 데는 한계가 있다. 본 논문에서는 기본적으로 손동작을 이용한 인터페이스를 제안하는데, 손동작 인식을 위한 알고리즘을 효율적으로 개선함으로써, 복잡한 환경에서 적은 연산량으로 자연스러운 인터랙션을 제공하고자 한다. 제안방법은 손목에 컬러 밴드를 착용하고, 색 정보를 이용하여 손을 포함하는 최소 영역을 용이하게 검출함으로써, 손 동작 인식률이 좋아지도록 하였다. 제안된 인터페이스는 손의 자연스러운 움직임을 감지해서 손의 모양과 동작에 따라서 가상의 물체를 자연스럽게 제어할 수 있도록 해 준다. 예를 들어, 손이 지정한 위치에 가상의 물체를 나타내고, 가상의 물체를 잡고 다양한 조작을 하는 등의 제어를 할 수 있다. 다양한 환경에서의 실험 및 사용자 평가를 통해 제안된 인터페이스의 유용성을 검증하였다.

• Korean Journal of Logic
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• v.6 no.2
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• pp.49-67
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• 2003

조합논리는 기본적으로 정해진 해석이 없는 순수한 형태만을 가지고 추상적으로 연산하는 관점에 관한 논리로서, 논리학을 기호학적 관점에서 볼 수 있는 토대를 제공해 준다. 조합논리의 특징은 연산자가 피연산자도 될 수 있다는 사실에 있으며 그래서 동일한 연산자가 그 자신의 피연산자도 될 수 있다. 이 논문에서 우리는 기본연산자들의 직관적 개념과 형식적 개념을 소개하고 연산자 대수에 내해 검토하고 나서 조합논리와 $\lambda$-연산의 번역가능성에 다해 알아보겠다. 조합논리에 유형의 개념을 추가하면 자연언어 분석에서 아주 효율적인데 기본유형인 대상자 명제 이외의 어떤 요소라도 함수자로 나타낼 수 있는데 이들은 조합자의 특수한 경우로서 파생유형들이다.