Inequalities, assessment and computer algebra

Abstract

The goal of this paper is to examine single variable real inequalities that arise as tutorial problems and to examine the extent to which current computer algebra systems (CAS) can (1) automatically solve such problems and (2) determine whether students’ own answers to such problems are correct. We review how inequalities arise in contemporary curricula. We consider the formal mathematical processes by which such inequalities are solved, and we consider the notation and syntax through which solutions are expressed. We review the extent to which current CAS can accurately solve these inequalities, and the form given to the solutions by the designers of this software. Finally, we discuss the functionality needed to deal with students’ answers, i.e. to establish equivalence (or otherwise) of expressions representing unions of intervals. We find that while contemporary CAS accurately solve inequalities there is a wide variety of notation used.

Keywords:

• computer algebra
• inequalities
• reasoning
• automatic assessment

Notes

1. http://store.aqa.org.uk/qual/pdf/AQA-6360-W-SP-13.PDF

2. Perhaps this student used another CAS to answer the question, thus subverting the intention of the teacher and rendering the assessment invalid.

3. Maple is a registered trademark of Waterloo Maple Inc; GeoGebra is a registered trademark of GeoGebra Inc; WolframAlpha is a registered trademark of Wolfram Research Inc.

4. A package contributed by Prof. Barton Willis, University of Nebraska at Kearney.