• School Mathematics
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• 제18권3호
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• pp.647-666
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• 2016

This study investigates pre-service teacher's understanding of the concept and representations of irrational numbers. We classified the representations of irrational numbers into six categories; non-fraction, decimal, symbolic, geometric, point on a number line, approximation representation. The results of this study are as follows. First, pre-service teachers couldn't relate non-fractional definition and incommensurability of irrational numbers. Secondly, we observed the centralization tendency on symbolic representation and the little attention to other representations. Thirdly, pre-service teachers had more difficulty moving between symbolic representation and point on a number line representation of ${\pi}$ than that of $\sqrt{5}$ We suggested the concept of irrational numbers should be learned in relation to various representations of irrational numbers.

• Communications of Mathematical Education
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• 제12권
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• pp.249-264
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• 2001

학교수학을 가르치고 배우는 과정에서 교사의 역할은 기술 공학의 활용으로 변화하고 있다. 기술공학의 역할은 학생들로 하여금 수학에 대한 태도를 변하게 하여, 탐구적이며 창의적인 방법으로 수학을 공부하는데 열의를 갖도록 한다. 반면에 현재의 수학교수는 여전히 보수적이며 환경의 변화에 더디게 적응하고 있으나, 세상이 상당히 빨리 변하고 있으므로 기술공학을 활용하여 현재의 교수를 개선해 나가야 하겠다. 변화에 대한 인식과 갈망은 학습자료, 재정 상태, 그리고 기타 여러 가지 요인보다도 훨씬 중요하며 가장 중요한 것은 교수관점 및 교수견해의 변화에 대한 의지이다. 교사가 기호연산 실행 조작이 가능한 수학 학습용 컴퓨터 응용 소프트웨어와 이들을 탑재한 휴대용 수학학습 전용기를 중등학교수학에 적용할 경우, 수학교육에서 신중히 고려해야 할 것은, 첫째 모든 수준의 학생들을 격려하며, 둘째 대상 영역의 수학학습 내용을 이해하도록 기술공학을 활용한 새로운 교수 기법에 접근할 수 있어야 한다는 점이다.

• Communications of Mathematical Education
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• 제16권
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• pp.109-122
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• 2003

현재 초, 중, 고등학교의 수학교육 현실은 수학 개념의 정확한 이해에 초점을 맞추지 못하고 공식의 암기와 그것을 이용하여 단순한 문제 풀이에 시간을 많이 할애함으로써 수학의 기본적인 개념이나 기호의 정확한 사용법을 인지하지 못하고 계산 기능적인 면으로 치우치는 경향이 많이 나타나며, 문제 풀이의 창의적인 상황이 제시되지 않는 상태에서 교사 중심의 문제풀이 방법에만 의존하고 있다. 이러한 문제점 속에서 창의적인 문제 해결 방안을 구상할 수 있는 사고력의 배양에 소홀함이 있다고 볼 수 있다. 따라서 학생 스스로 의미를 파악하여 학습 할 수 있는 교수 방법이나 학습 방법에 대한 연구는 현실적으로 매우 시급한 상황에 처해있다. 이러한 상황에서 많은 수학교육자들은 학생들이 좀 더 쉽게 수학의 개념에 접근 할 수 있게 하기 위하여 많은 노력을 하고 있다. 그러한 노력 중의 하나로 테크놀러지를 이용한 수학교육을 말 할 수 있는데, 이는 실제로 수학교육에 긍정적인 영향을 준다고 알려져 있다. 본 논문은 현 고등학교 수학I의 등차수열에 관한 내용을 Mathematica를 이용하여 다각수(도형수)로부터 등차수열의 개념을 유도하였다.

• Journal for History of Mathematics
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• 제21권3호
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• pp.53-66
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• 2008

The concepts of ratio and proportion are familiar with students but have difficulties in use. The purpose of this paper is to identify the meanings of the concepts of ratio and proportion through investigating the historical development process of the meanings and representations of them. The early meanings of ratio and proportion were arithmetical meanings, however, geometrical meanings had taken the place of them because of the discovery of incommensurability. After the development of algebraic representation, the meanings of ratio and proportion have been growing into algebraic meanings including arithmetical and geometrical meanings. Through the historical development process of ratio and proportion, it is observable that the meanings of mathematical concepts affect development of symbols, and the development of symbols also affect the meanings of mathematical concepts.

• Education of Primary School Mathematics
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• 제25권4호
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• pp.459-475
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• 2022

The equal sign and equivalence are the most basic and core concepts in elementary mathematics, but there has been lack of research on how to teach these concepts with textbooks. Given this, this study analyzed elementary mathematics textbooks in terms of three instructional elements (i.e., emphasizing the meaning of the equal sign as a relational symbol, dealing with an equation as an object for reasoning, and using an equation with a missing value). In particular, this study analyzed 10 different mathematics textbook series that are newly used in 2022 and examined the overall trends and characteristics for teaching the equal sign and equivalence. The results of this study showed that the activities emphasizing the meaning of the equal sign as a relational symbol were most noticeable but the activities dealing with an equation as an object for reasoning or using an equation with a missing value were relatively rare. Based on the results of the analysis, this study provides textbook writers with implications on what to further consider in covering the equal sign and equivalence.

• Communications of Mathematical Education
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• 제24권2호
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• pp.365-384
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• 2010

This paper is an analysis study where we surveyed how well pre-service teachers understand the mathematical concepts taught in elementary school. We analyzed the results focusing on the following: First, what are the pre-service teachers' understandings of the equal sign and variables? Secondly, how exact are their understandings of other elementary school mathematical concepts? The survey was done on the students in Teachers College of Jeju National University. We hope that the results of this study will help the improvement of mathematical education for elementary pre-service teachers.

• School Mathematics
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• 제16권4호
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• pp.803-825
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• 2014

From the early stages of learning algebra, literal symbols are used to represent algebraic objects such as variables and parameters. The concept of parameters contains both indeterminacy and fixity resulting in confusion and errors in understanding. The purpose of this research is to compare the beginners of algebra and pre-service teachers who completed secondary mathematics education in terms of understanding this paradoxical nature of parameters. We recruited 35 middle school students in eight grade and 73 pre-service teachers enrolled in a undergraduate course at one university. Using them we conducted a survey on the perception of the nature of parameters asking if one considers parameters suggested in a problem as variables or constants. We analyzed the collected data using the mixed method of qualitative and quantitative approaches. From the analysis results, we identified several difficulties in understanding of parameters from both groups. Especially, our statistical analysis revealed that the proportions of subjects with limited understanding of the concept of parameters do not differ much in two groups. This suggests that learning algebra in secondary mathematics education does not improve the understanding of the nature of parameters significantly.

• Journal of the Korean School Mathematics Society
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• 제13권3호
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• pp.345-356
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• 2010

Variables and expressions are essential for doing mathematics. Especially abbreviations of the multiplication sign ${\times}$ and the division sign ${\div}$ are current rules that we usually follow. In this paper, we devised a Card-Game for exercising abbreviations of the multiplication sign ${\times}$ and the division sign ${\div}$ in calculating expressions, designed a teaching unit for the calculation of expressions using the Card-Game in the variables and expressions strand, and discussed the implications of using the Card-Game for motivating students, cooperative learning, diagnosis and correction of errors, and so on.

• New Physics: Sae Mulli
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• 제68권12호
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• pp.1364-1373
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• 2018

A recognizable form having meaning is called a sign in semiotics. The sign is transformed into a physical counter form in this work. Its internal structure is restricted on the linguistic concept structure. We borrow the concept of a mathematical function from the utility function of a rational personal in the economy. Universalizing the utility function by introducing the consistency of independency on the manner of construction, we construct the probability. We introduce a random variable for the probability and join it to a position variable. Thus, we propose a physical sign and its serial changes in the forms of stochastic equations. The equations estimate three patterns (jumping, drifting, diffusing) of possible solutions, and we find them in the one-day stock-price flow. The periods of jumping, drifting and diffusing were about 2, 3.5, and 6 minutes for the Kia stock on 11/05/2014. Also, the semiotic sign (icon, index, symbol) can be expected from the equations.

• Communications of Mathematical Education
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• 제18권1호
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• pp.45-60
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• 2004

수학텍스트의 한 부분인 식은 일상 언어, 시각적 표현, 상징 등의 여러 기호와 함께 학생들에게 다양한 수학을 경험을 제공한다. 그러나 이러한 수학텍스트의 다양성은 수학시험 채점시 4+3인가, 4+3=7인가 혹은 부분점수를 줄 것인가의 이슈로서 변질되어 등장한다. 따라서 본 연구에서는 초등학교에서 다루는 식의 의미, 초등학교 아동에게 지도되는 식의 형태, 초등학교 1학년 아동의 식에 대한 이해, 초등학교 교사들의 식에 대한 이해 형태를 서울시 소재 한 초등학교의 1학년 담임교사 9명과 1학년 1 개 학급에 속한 아동과의 면담 및 설문 조사를 통하여 알아보았다. 아울러 제언에서는 수학텍스트의 한 부분인 식의 실제 교육현장에서 어떻게 반영되고 있는가에 대한 탐색을 통하여 식의 의미를 올바르게 전하기 위한 지도 방법, 교사 인식에 대한 방향을 제시하였다.