«Minus og minus blir pluss, det er bare sånn» : En kasusstudie av elever på 8. trinn og deres forklaringer og arbeid med oppgaver om negative tall

Abstract

Thisthesis studiesnegative numbers and how students explain their ways of thinking and methods in working with these numbers. Through literature studies and a case study of secondary school students in the 8th grade, the aim is to provide answers to the following research questions:•What characterizes four studentsin 8thgrade and their work on negative numbers?•In what ways do four8thgradestudents explain their approach to working on negative numbers?The theoretical framework of this thesis is based on a sociocultural learning theoryand the aspects for learning that this view is based on. The use of artifacts, mediation and the function of the language in learning is emphasized. Furthermore, the significance of gesticulation is drawn. A key term in this study is explanation.The theoryshows what a good explanation is in general, and how one can categorize explanations in mathematics in different ways. Negative numbersthrough the history of mathematics and the challenges students often encounter when working with negative numbers are also used as the basis for the discussion.To collect data, an observation was made of four students in the 8thgrade. These four all had high achievement in math. In each of the three observation sessions, the students worked with different task on negative numbers and explained the choice of procedure.The findings in the study show that lower secondary school students' work on negative numbers is characterized by the fact that they avoided negative numbers wherever possible. The studentssometimes had challenges to distinguish between the significance of the minus sign and were quickly confused when they received tasks with many computational operations. The use of debt as an example, gesturing the movements on a number line and «sign rules»such as justification characterized their work and their explanations. The explanations the students made use of were neither very advanced nor simplified.