Developing Materials for Addition and Subtraction of Integers

Abstract

The set of integers emerged in mathematics after natural numbers, with the need for negative numbers. Students, encountering integers for the first time, often face difficulties in addition and subtraction. With the aim of addressing this issue, the study aims to develop a different method for addition and subtraction of integers. Three number lines are utilized in developing a new method for addition of integers. These number lines are parallel to each other on a plane. The top and bottom number lines form a classic number line where integers are located. The middle number line consists of intervals half the size of the intervals between the top and bottom number lines. The selected numbers on the top and bottom number lines will be the ones to be added. The middle number line represents the resulting integer sum. For subtraction, the top number line is a classic number line with integers. The bottom number line has negative integers to the right of zero and positive integers to the left of zero. The middle number line is again similar to the addition ruler. The number chosen on the top number line is the subtrahend, the number chosen on the bottom number line is the minuend, and the integer that corresponds on the middle number line is the difference. The three-dimensional design of the ruler was drawn in the Tinkercad program and printed using a 3D printer. Additionally, the developed method was designed on the dynamic software Geogebra. It was also created on the Scratch program in a way that the student could interact with. For the effectiveness of the developed method, a qualitative study was conducted with 20 6th-grade students who were diagnosed with special abilities and attended the Science and Art Center. The method was implemented with students using both the Geogebra and Scratch programs, as well as the printed ruler from the 3D printer. A semi-structured interview form was applied to the students. Descriptive analysis was performed with the data obtained from the observation form. The research results showed that students easily learned addition and subtraction operations with integers and actively participated in the lesson in an enjoyable manner. The developed method's digital content was found to be intriguing and useful. Geogebra was indicated as the most suitable digital content for the developed method.