• Journal for History of Mathematics
• /
• v.18 no.2
• /
• pp.9-22
• /
• 2005

Natural numbers have not yet been studied adequately on the aspect of its historical development in spite of its mathematical and educational importance. This article studied the historical development of natural number concept, that is, its historical meaning in the mathematical development process and influence of cultural and social element in relation with way of understanding number. From these examinations, we identified some characteristics in the history of natural number concept.

• Journal of Elementary Mathematics Education in Korea
• /
• v.21 no.1
• /
• pp.195-214
• /
• 2017

The standardized algorithm of natural number multiplication simplify the procedure of arithmetic. In the case of multiplication algorithm with regrouping, we write small the carrying number on the multiplicand. But, teachers and students have to make their own way about the case of two digits multipliers, because Korean elementary mathematics textbooks just deal with the case of the one digit multipliers. In this study, we investigated Korean current elementary mathematics textbooks related to multiplication algorithm with regrouping, and analyzed the result of research on the real condition about marking the carrying number. Besides, we reviewed the guidance contents of algorithm of natural number multiplication in Finland's math textbook and literature. By conclusions, we suggest several implications as followed; First, we need some examples of the way to mark the carrying number in teacher's guidance books and textbooks. Second, teachers try for students to feel the good points of the systematic ways to mark the carrying number. Third, teachers understand algorithm of natural number multiplication and the alternative ways about marking the carrying number.

• School Mathematics
• /
• v.5 no.3
• /
• pp.385-399
• /
• 2003

In our present elementary mathematics curriculum, natural numbers are taught by using the a method of one-to-one correspondence or counting operation which are not related to measurement, and fractional numbers are taught by using a method which is partially related to measurement. The most serious limitation of these teaching methods is that natural numbers and fractional numbers are separated. To overcome this limitation, Dewey and Davydov insisted that the natural number and the fractional number should be taught by measurement of quantity. In this article, we suggested a method of teaching the natural number and the fractional number by measurement of quantity based on the claims of Dewey and Davydov, and compare it with our current method. In conclusion, we drew some educational implications of teaching the natural number and the fractional number by measurement of quantity as follows. First, the concepts of the natural number and the fractional number evolve from measurement of quantity. Second, the process of transition from the natural number to the fractional number became to continuous. Third, the natural number, the fractional number, and their lower categories are closely related.

• Communications of Mathematical Education
• /
• v.26 no.2
• /
• pp.205-220
• /
• 2012

In this article convergent sequences with natural number terms are investigated and the behaviors of tails and limits of these natural number sequences are explored. Firstly this study showed how the pre-service teachers response to the intuitive limit definition using "getting closer" for constant sequences. As a case of convergent natural sequences, the sequences in which the latter term is determined by the sum of digit squares of the former term are considered. To exploring these sequences the computational and charting capabilities of spreadsheets are utilized and some mathematical findings are obtained. Spreadsheet can be instrumentalized by teachers or students to provide a laboratory-like environment to explore a mathematical problem.

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

• Journal of Elementary Mathematics Education in Korea
• /
• v.17 no.3
• /
• pp.395-411
• /
• 2013

There are two concepts of division: measurement division and partitive or fair-sharing division. Students are expected to understand comprehensively division algorithm in both contexts. Contents of textbooks and teachers' guidebooks should be suitable for helping students develop comprehensive understanding of algorithm for whole-number division in both contexts. The results of the analysis of textbooks and teachers' guidebooks shows that they fail to connect two division contexts with division algorithm comprehensively. Their expedient and improper use of two division contexts would keep students from developing comprehensive understanding of algorithm for whole-number division. Based on the results of analysis, some ways of improving textbooks and teachers' guidebooks are suggested.

• Journal of Educational Research in Mathematics
• /
• v.17 no.3
• /
• pp.309-331
• /
• 2007

Mathematics education starts from learning the concept of number. How the children at the beginning of school age learn the concept of natural number is therefore important for their future mathematics education. Since ancient Greek period, the concept of natural number has reflected various mathematical-philosophical points of view at each period and has been discussed ceaselessly. The concept of natural number is hard to define. Since 19th century, it has also been widely discussed in psychology and education on how to teach the concept of natural number to the children at the beginning of school age. Most of the works, however, were focused on limited aspects of natural number concept. This study aims to show the best way to teach the children at the beginning of school age the various aspects of natural number concept based on activistic perspective, which played a crucial role in modern mathematics education. With this purpose, I investigated the theory of the activistic construction of knowledge and the construction of natural number concept through activity, and activistic approaches about instruction in natural number concept made by Kant, Dewey, Piaget, Davydov and Freudenthal. In addition, I also discussed various aspects of natural number concept in historical and mathematical-philosophical points of view. Based on this investigation, I tried to find out existing problems in instructing natural number to primary school children in the 7th National Curriculum and aimed to provide a new solution to improve present problems based on activistic approaches. And based on activistic perspective, I conducted an experiment using Cuisenaire colour rods and showed that even the children at the beginning of school age can acquire the various aspects of natural number concept efficiently. To sum up, in this thesis, I analyzed epistemological background on activistic construction of natural number concept and presented activistic approach method to teach various aspects of natural number concept to the children at the beginning of school age based on activism.

• Proceedings of the Acoustical Society of Korea Conference
• /
• spring
• /
• pp.87-90
• /
• 2000

문-음성 합성기의 자연감을 높이기 위해 주로 자연음에 존재하는 운률 법칙을 정확히 구현해 주어야 한다. 일반적으로 언어학적 정보를 이용하거나 자연음으로부터 추출한 운률 정보를 추출한 운률 법칙을 합성에 이용하고 있다. 이와 같이 구한 운률 법칙이 자연음에 존재하는 모든 운률 법칙을 포함할 수 있으면, 자연스러운 합성음을 들을 수 있겠으나, 실질적으로는 모든 법칙을 구현한다는 것은 어려운 실정이고, 자연음으로부터 추출한 운률 법칙이 잘못 구현되는 경우 합성음의 자연성이 떨어지는 것을 피할 수 없을 것이다. 이런 점을 고려하여 우리는 자연음에 내재하는 운율 법칙을 훈련을 통해 학습할 수 있는 인공 신경망을 제안하였다 운률의 세 가지 요소는 피치, 지속시간, 크기 변화가 있는데, 인공 신경망은 문장이 입력되면, 각 해당 음소의 지속시간에 따른 피치 변화와 크기 변화를 학습할 수 있도록 설계하였다. 신경망을 훈련시키기 위해 고립 단어군과 음소균형 문장군을 화자로 하여금 발성하게 하여, 녹음하고, 분석하여 운률 데이터베이스를 구축하였다. 자연음의 각 음소에 대해 지속시간과 피치변화 그리고 크기 변화를 구하여 곡선 적응 방법을 이용하여 각 변화 곡선에 대한 계수를 구해 데이터베이스를 구축한다. 이렇게 구축한 데이터베이스를 이용해 인공 신경망을 훈련시켜 평가한 결과 훈련용 데이터를 계속 확장하면 좀 더 자연스러운 운률을 발생시킬 수 있음을 관찰하였다.

• Proceedings of The Korean Society of Health Promotion Conference
• /
• 2009.05a
• /
• pp.83-83
• /
• 2009

본 연구는 한국인 노년층이 대표적으로 섭취하는 강도별 음식을 조사하고 각 음식별로 씹어 먹을 수 있는 음식들이 무엇인지를 조사하여 자신이 보유하고 있는 자연치아수와의 상관관계를 알아보아 자연치아의 건강도를 유지, 관리, 예방하는데 하나의 지표로 사용하고 더 나아가 국민구강건강향상에 이바지 하고자 실시되었다. 전국의 60세 남 녀 586명을 대상으로 치과의사와 치과위생사가 구강검사와 면접법으로 설문내용을 기록하는 방식으로 진행하였다. 수집된 자료는 SPSS WIN 14.0 프로그램을 이용하여 분석하였다. 분석기법으로는 잔존치아수와 저작능력간의 관계를 상관계수와 회귀분석으로 분석 검증을 실시하여 다음과 같은 결과를 얻었다. 1. 저작능력과 구강상태와는 치석, 동요도, 충전점수, 우식경험점수, 발거치아수, 임플란트 수, 자연치아수와 나이, 고혈압, 당뇨병, 기타질환, 흡연이 유의한 것으로 나타났다(p<0.05). 2. 회귀분석 결과 나이가 높을수록 저작능력이 감소하며, 자연치아수가 많을수록 저작능력이 높은 것으로 나타났으며 회귀방정식은 저작능력=79.417-(연령$\times$0.281)+3.813$\times$치아수와 같았다(p<0.05). 3. 회귀분석결과 저작능력점수와 자연치아수와의 관계가 가장 높은 것으로 나타났고 회귀방정식은 저작능력=3.817$\times$자연치아+58.694와 같았다(p<0.05). 4. 자연치아로 식사를 하기 위해서는 한국 노인의 주식인 밥과 김치정도를 잘 씹어 먹으려면 잔존 자연치아수가 18개 정도는 있어야 아주 잘 씹어 먹을 수 있고, 잘 먹으려면 12개의 자연치아가 있어야 하며, 육류를 잘 먹기 위해서는 최소한 18개는 있어야 잘 먹을 수 있고, 25개가 있으면 아주 잘 씹어 먹을 수 있다는 연구결과가 나왔다.

• Journal of The Korean Association of Information Education
• /
• v.19 no.4
• /
• pp.525-532
• /
• 2015

Unplugged has been widely used as an instrument for teaching the basic principles of Computer Science. This study presents the teaching contents developed for the children without any knowledge of binary numbers. which successfully guided them to understand the natural number binary system. The level of the pre-lesson for this learning requires counting numbers, matching numbers with cards, and arranging numbers. The activity-based learning is provided for describing natural numbers with the binary system and finding out them in everyday life. To check the adequacy of these materials on their organization and assessment they were tested at the classroom, which showed effective about the knowledge, the attitude and the generalization.