Journal of the Korean School Mathematics Society (한국학교수학회논문집)
- Volume 11 Issue 1
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- Pages.97-115
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- 2008
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- 1229-0890(pISSN)
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- 2713-4350(eISSN)
On the Role of Intuitive Model for Teaching Operations of Integers in the Middle School Mathematics Class
중학교 수학 수업에서 정수의 사칙계산 지도를 위한 직관적 모델의 역할에 관한 연구
Abstract
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.
고등학교 수학 수업에서는 실수 전체의 집합에서 뺄셈은 빼는 수의 덧셈의 역원을 더하고 나눗셈은 나누는 수의 곱셈의 역원을 곱하는 형식적인 관점으로 다룬다. 본 논문에서는 정수의 사칙계산 지도에 있어서 중학교 수학 수업에서 사용되는 직관적 모델(수직선 모델, 셈돌 모델)과 고등학교 수학 수업에서 제시되는 형식적 관점과의 연계에 대하여 논의하고자 한다. 직관적 모델을 이용하여 정수의 뺄셈을 덧셈을 이용하여 나타내는 방법의 의미를 재조명하고 이를 바탕으로 (음수)
Keywords