Solving polynomial inequalities with GeoGebra. (c2017)

Abstract

„Polynomial inequalities‟- a particular form of „Inequalities‟- is an important topic that interweaves with most mathematical topics. Polynomial inequalities are treated by the Lebanese curriculum as a purely algebraic and abstract topic where graphs and visualization are not fully invested when solving them. Hence a resource for deepening students‟ conceptual understanding of polynomial inequalities is being neglected. It is conjectured that Computer Algebra Systems (CAS), as a tool package with different views and mathematical environments, can offer a suitable medium for solving polynomial inequalities and promoting students‟ algebraic reasoning. The purpose of this research is to study the ways students‟ instrumentation of CAS can help them promote their algebraic reasoning while solving polynomial inequalities. In addition, the relation between students‟ CAS techniques and paper-and-pencil (P&P) techniques is explored, together with the difficulties that students face in this respect. Participants are 33 tenth graders at a private 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 a pretest, students‟ written solutions for 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 with the topic of functions and their low level of familiarity with GeoGebra were determinant factors that hindered their 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.