Solving Polynomial Inequalities with GeoGebra: Opportunities of Visualization and Multiple Representations

The main purpose of the present study is to investigate the ways students' instrumentation of Computer Algebra System (CAS) can help promote their algebraic reasoning while solving polynomial inequalities. In addition, the relation between students' CAS techniques and paper-and-pencil (P&P) techniques are explored, together with the difficulties that students may face as they apply these techniques. Research participants are 33 tenth graders at a private mixed gender school in Mount-Lebanon, distributed among nine homogenous groups, five of which are selected as focus groups. The study is qualitative in nature. Data is collected from pretests, students' written solutions of four instructional activities, laptop screen recordings, video recordings of whole-class discussions, and audio recorded interviews with students in the focus groups. The findings of the study show that students' lack of prerequisite knowledge of the topic of functions and their low level of familiarity with GeoGebra software are determinant factors that hinder these students' instrumentation of CAS and hence their reasoning processes as well as their implementation of the solving techniques. High and middle-achieving students' solving techniques acquired little epistemic and some pragmatic values, whereas low achieving students' solving techniques acquired heuristic values.