• 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.

• The Mathematical Education
• /
• v.51 no.4
• /
• pp.429-453
• /
• 2012

The purpose of the study were to analyze teaching models of arithmetic operations of integers in Korean middle school mathematics textbooks of the first grade and Americans', from which we compare and analyze standards for choice of models of middle school teachers and preservice mathematics teachers. We also analyze the effect of the choice of teaching models for students to understand and appreciate number systems as a coherent body of knowledge. On the basis of that, we would like to find the best model to help students understand and reason the process of formulate the arithmetic operations of natural numbers and integers into the operation of the real number system. Furthermore, we help these series of the study to be applied effectively in the middle school mathematics class in Korea.

• Proceedings of the Korea Information Processing Society Conference
• /
• 2007.05a
• /
• pp.259-262
• /
• 2007

수학, 물리학, 전자전기공학에서 취급하는 수치 자료는 매우 크거나 정밀도가 높을 수 있고, 이 경우 계산과정에서 흔히 오버플로우나 언더플로우가 발생한다. 본 연구는 이런 현상을 최소화하기 위하여 겁수(Kalpa Number) 표현 방법을 제안하고, 정수형 겁수의 사칙연산과 논리연산을 구현하였다. 겁수를 이용할 경우 실행속도는 느리지만 매우 큰 수의 연산이 가능하다.