FIRST YEAR UNDERGRADUATE STUDENTS’ ERRORS WHEN SOLVING INEQUALITIES

The purpose of this study was to investigate errors of first year undergraduate students when solving inequalities. Data were generated through a test and follow-up interviews. The inequalities include linear, quadratic, rational and absolute value inequalities. Findings reveal errors in expressing compound inequalities, errors in representing solutions as intervals, generalising equality to inequality, including a zero of denominator in the solution set of rational inequalities, generalising the definition of absolute value and incomplete solution processes. The results also show that there was one comprehension error and that the other errors occurred because of problems in transformation, process skills and encoding solutions. The findings suggest that the errors in expressing compound inequalities arose because the students did not understand underlying concepts. For instance, most students ignored the idea of numerical order implicit in inequalities. The results also show that the errors in expressing compound inequalities occurred because of the nature of the inequalities, the lack of a formal definition of absolute value and the lack of proofs for properties of absolute inequalities. The results suggest need for teacher educators to focus on these errors and the underlying concepts of inequalities in order to enhance students’ conceptual understanding of inequalities. The results also offer a valuable opportunity for deliberations on how to prevent, limit and deal with such students’ errors.