• Communications of Mathematical Education
• /
• v.13 no.1
• /
• pp.287-304
• /
• 2002

현재 시행되고 있는 6차 교육과정이나 2002년도부터 새로이 시행되는 고등학교 7차 교육과정에서는 수열의 극한을 직관적으로 지도하도록 하고 있다. 그러나 기존의 연구들을 살펴보면, 수열의 극한에 관한 학생들의 인지 장애의 원인 중 하나가 이러한 직관적인 이해로부터 기인한다고 볼 수 있다. 이에 본 논문에서는 다른 나라에서 수열의 극한을 다루는 법을 살펴보고, 그것을 바탕으로 수열의 극한 개념을 교수 ${\cdot}$ 학습하는 방법을 제시하고자 한다.

• Journal of the Korean School Mathematics Society
• /
• v.21 no.2
• /
• pp.113-139
• /
• 2018

There is no doubt about the importance of teacher knowledge for good teaching. Many researches attempted to conceptualize elements and features of teacher knowledge for teaching in a quantitative way. Unlike existing researches, this article suggests an interpretation of preservice teacher knowledge in the field of geometry using the Shulman - Fischbein framework in a qualitative way. Seven female preservice teachers voluntarily participated in this research and they performed a series of written tasks that asked their subject matter knowledge (SMK) and pedagogical content knowledge (PCK). Their responses were analyzed according to mathematical algorithmic -, formal -, and intuitive - SMK and PCK. The interpretation revealed that preservice teachers had overally strong SMK, their deeply rooted SMK did not change, their SMK affected their PCK, they had appropriate PCK with regard to knowledge of student, and they tended to less focus on mathematical intuitive - PCK when they considered instructional strategies. The understanding of preservice teachers' knowledge throughout the analysis using Shulman-Fischbein framework will be able to help design teacher preparation programs.

• Communications of Mathematical Education
• /
• v.33 no.3
• /
• pp.335-354
• /
• 2019

The purpose of this study is to explore alternative ways of teaching derivatives in a way that emphasizes intuition. For this purpose, the contents related to derivatives in Korean curriculum and textbooks were analyzed by comparing with contents in Singapore Curriculum and textbooks. Singapore, where the curriculum deals with derivatives relatively earlier than Korea, introduces the concept of derivatives and differentiation as the slope of tangent instead of the rate of instantaneous change in textbook. Also, Singapore use technology and inductive extrapolation to emphasize intuition rather than form and logic. Further, from the results of the exploration of other foreign cases, we confirm that the UK and Australia also emphasized intuition in teaching derivatives and differentiation. Based on the results, we discuss the meaning and implication of introducing derivatives and teaching differentiation in a way that emphasizes intuition. Finally, we propose the implications for the alternative way of teaching differentiation.

• 한국정보교육학회:학술대회논문집
• /
• 2008.01a
• /
• pp.192-197
• /
• 2008

초등학교 수학과 도형 학습은 매우 추상적인 분야로 직관적인 이해를 돕기 위해 다양한 구체적인 조작이 요구되는데, 그 중에서 컴퓨터를 활용한 도형 학습은 학생들의 구체물을 이용한 학습의 한계를 극복할 수 있는 장점이 있다. 특히 Flex와 Flash를 이용하면 입체도형의 가상물의 제작 및 동적인 학습은 물론 사용상의 제약이 적어 시,공간의 한계를 극복할 수 있다. 본 연구에서는 초등학교 수학과 제 7차 교육과정의 입체도형 영역을 분석하여 학습요소를 추출하고 플래시의 드로잉 메서드를 바탕으로 학습요소별로 속성과 메서드를 정의하고 클래스를 설계하여 입체도형 객체를 생성하고 플렉스의 컴포넌트로 구성된 학습 어플리케이션의 틀을 설계하여 입체도형 객체가 플렉스의 어플리케이션 내에서 사용이 가능하도록 설계 개발하였다. 본 연구가 갖는 의의는 첫째, 초등학교 수학과 수준에 맞는 속성과 메서드를 갖도록 개발한 입체도형 객체를 활용하여 학습자의 입체도형에 자유로운 탐구활동 기회를 제공하여 보다 직관적이고 구체적으로 도형학습을 할 수 있도록 돕는다. 둘째, 플렉스를 활용함으로서 학습자의 쉬운 접근을 돕고 학습 어플리케이션 틀을 활용하여 기존에 개발되어 있는 수학과 플래시 파일들을 활용한 다른 수학과 영역의 학습 어플리케이션 설계 및 개발의 시간과 노력을 단축시키는데 있다.

• Journal of the Korean School Mathematics Society
• /
• v.10 no.1
• /
• pp.91-111
• /
• 2007

This study investigated how high school students predict the rule, the sum of sequence for the concept of sequence, for the given patterns based on inductive approach using computers that provide dynamic functions and materials that are visual. Students for themselves were able to induce the formula without using the given formula in the textbook. Furthermore, this study examined how these technology and materials affect students' understanding of the concept of actual infinity for those who have the concept of the potential infinity which is the misconception of infinity in a infinity series. This study shows that students made a progress from the concept of potential infinity to that of actual infinity with technology and materials used I this study. Students also became interested in the use of computer and the visualized materials, further there was a change in their attitude toward mathematics.

• Journal for History of Mathematics
• /
• v.24 no.4
• /
• pp.45-59
• /
• 2011

Constructionists believe that mathematical knowledge is obtained by a series of purely mental constructions, with all mathematical objects existing only in the mind of the mathematician. But constructivism runs the risk of rejecting the classical laws of logic, especially the principle of bivalence and L. E. M.(Law of the Excluded Middle). This philosophy of mathematics also does not take into account the external world, and when it is taken to extremes it can mean that there is no possibility of communication from one mind to another. Two constructionists, Brouwer and Dummett, are common in rejecting the L. E. M. as a basic law of logic. As indicated by Dummett, those who first realized that rejecting realism entailed rejecting classical logic were the intuitionists of the school of Brouwer. However for Dummett, the debate between realists and antirealists is in fact a debate about semantics - about how language gets its meaning. This difference of initial viewpoints between the two constructionists makes Brouwer the intuitionist and Dummettthe the semantic anti-realist. This paper is confined to show that Dummett's proposal in favor of intuitionism differs from that of Brouwer. Brouwer's intuitionism maintained that the meaning of a mathematical sentence is essentially private and incommunicable. In contrast, Dummett's semantic anti-realism argument stresses the public and communicable character of the meaning of mathematical sentences.

• The Mathematical Education
• /
• v.44 no.4 s.111
• /
• pp.535-546
• /
• 2005

We study on intuitive verification and rigor proof which are in geometry of Korean and Russian $7\~8$ grade's mathematics textbooks. We compare contents of mathematics textbooks of Korea and Russia laying stress on geometry. We extract 4 proposition explained in Korean mathematics textbooks by intuitive verification, analyze these verification method, and compare these with rigor proof in Russian mathematics textbooks.

• The Mathematical Education
• /
• v.47 no.3
• /
• pp.373-386
• /
• 2008

In highschool probability education, this study analyzed conflicts between intuitive concept and formal definition which originates from the process of establishing the concept of statistical independence. In judging independence, completely different types of problems requiring their own approach was analyzed by dividing them into two types. By doing so, this study researched a way to view independence as an overall idea. That is purposed to suggest a solution to a conflicts between intuitive concept and formal definition and to help not to judge independence out of wrong intuition. This study also suggests that calculation process which leads to precise perception of sample space and event be provided when we prove independence by expressing events with assembly symbols.

• Journal of the Korean School Mathematics Society
• /
• v.11 no.1
• /
• pp.97-115
• /
• 2008

In high school mathematics class, to subtract a number b from a, we add the additive inverse of b to a and to divide a number a by a non-zero number b, we multiply a by the multiplicative inverse of b, which is the formal approach for operations of real numbers. This article aims to give a connection between the intuitive models in middle school mathematics class and the formal approach in high school for teaching operations of negative integers. First, we highlight the teaching methods(Hwang et al, 2008), by which subtraction of integers is denoted by addition of integers. From this methods and activities applying the counting model, we give new teaching methods for the rule that the product of negative integers is positive. The teaching methods with horizontal mathematization(Treffers, 1986; Freudenthal, 1991) of operations of integers, which is based on consistently applying the intuitive model(number line model, counting model), will remove the gap, which is exist in both teachers and students of middle and high school mathematics class. The above discussion is based on students' cognition that the number system in middle and high school and abstracted number system in abstract algebra course is formed by a conceptual structure.

• Communications of Mathematical Education
• /
• v.15
• /
• pp.23-28
• /
• 2003

실수계와 n-차원 벡터 공간을 대수적 특성, 순서적 특성 그리고 위상적 특성을 중심으로 전개하고, 실변수 실가 함수와 n-차원 벡터 공간을 정의역으로 하는 실가함수를 연속성 (미분가능성), 단조성 그리고 볼록성을 중심으로 내용을 다룬다. 특히 실생활과 관련하여 이론을 전개하여 학습을 지도할 수 있는 교육과정을 개발하고, 직관적인 사고와 수리 논리적인 사고의 적절한 배합을 통해 학습자들이 적극적으로 학습에 임할 수 있는 교수 학습 방법을 개발하는 것을 목적으로 한다.