Eighth grade students' ways of conceptual understanding and algebraic reasoning

Algebra, which has an extensive coverage in mathematics education programs, is one of the most important and challanging branch of mathematics. In order to reduce the difficulties encountered in understanding algebra and improve the development of algebraic reasoning, it is essential to develop a solid algebra foundation from an early grade. Therefore, development of basic algebra concepts and algebraic reasoning in students is highly-related to a teaching of concepts and algebra in primary school. The aim of this study is to identify the conceptual understanding and algebraic reasoning of eighth grade students using linearity and slope concepts. Data were collected with algebra test and clinical interview techniques. The study was conducted in two primary schools in Eskişehir city center participating 103 eighth grade students. The algebra test was applied to all participants to form a metric for the selection of students for clinical interviews. Test results were evaluated by two independent experts so as to increase the reliability. Ten students, five high-level and five midlevel, were subjected to clinical reviews. The reviews were recorded using a video camera with the permission of teachers, students and parents. The collected data were analyzed through mix method technique. The results show that considerable majority of the participants exhibit misconception about linear functions, graph and slope of a line. It is also deduced that, most of the concepts adopted by students rely on the knowledge acquired by rote. In addition to that, participants, in general, were not successful in building satisfactory arguments about slope, linearity and linear function concepts. Moreover, it is found out that, they could not support their arguments well enough. As a conclusion, this study shows that the algebraic reasoning skills of the participants are inadequate. Keywords: Algebra, algebraic reasoning, conceptual understanding, eighth grade,linear functions, slope.