Consistencies and inconsistencies in students' solutions to algebraic ‘single-value’ inequalities

Abstract

This paper describes students’ solutions to a commonly taught and not commonly taught inequality. The findings showed students’ difficulties. Participants implicitly and explicitly exhibited two intuitive beliefs: inequalities must result in inequalities and solving inequalities and equations are the same process. Following the analysis of students’ written solutions, individual interviews were conducted that gave a better insight into their reasoning and provided some ideas for teaching. The concluding section of the paper offers relevant educational implications.

Acknowledgment

A shorter version of this manuscript was presented at the 25th Annual Meeting for the Psychology of Mathematics Education in Utrecht, Holland in 2001.

Notes

 The students used in their classes either {x | x = 0} or x = 0 as the solutions to inequalities like x ² ≤ 0 or equations like x ² = 0, and we presented both options (either in writing or on the blackboard when distributing the questionnaires) in order to make sure that they understood what type of solution we have in mind. The two expressions are used in the paper as well.

 All names used in this paper are pseudonyms.