The use of graphic calculators to address errors first-year university students make with the solution of quadratic inequalities

Abstract

This study aimed at analyzing students' errors in quadratic inequalities and examining whether instruction using graphic calculators would result in building critics in students. Seven students participated in the task-based interviews and a test related to quadratic inequalities was administered to eight students. The students' final answers and intermediate steps for each of the test and interview items were analyzed. Those items identified as having incorrect responses were analyzed to infer probable error behaviours leading to those responses. These inferences were coded to form error categories and error types. Two error categories and three error types were subsequently identified. The categories were overgeneralisation errors and errors due to rules creating rules. Errors were called overgeneralisation errors when students seemed to overgeneralise rules for solving quadratic equations in order to solve quadratic inequalities. This category consisted of generalisation over equality errors and generalisation over number errors. Students created a rule from several rules. Errors of this type were called additive inverse errors.