Linear Functions and Slope: How Do Students Understand These Concepts and How Does Reasoning Support Their Understanding?

Abstract

The aim of this study was to investigate eighth grade students' conceptual understanding and types of reasoning about linear functions and slope. This is a mixed method study. Quantitative data were collected with algebra test, and qualitative data were collected using clinical interviews. The participants for the quantitative part of this study included 103 students, and the qualitative part included 10 students selected from these 103 students who were high and middle achievers. Quantitative data were assessed based on the answer key, and their frequency scores were calculated and interpreted, too. Qualitative data were analyzed using the thematic analysis. The majority of the students counted on superficial knowledge of linear functions and slope, they mainly stuck to the slope formula and line equation, and they did not possess correct reasoning types. They also need to improve their use and interpretation of multiple representations.