Educational Studies in Mathematics

, Volume 78, Issue 3, pp 275–305 | Cite as

Teaching absolute value inequalities to mature students

  • Anna Sierpinska
  • Georgeana Bobos
  • Andreea Pruncut
Article
First Online:

Abstract

This paper gives an account of a teaching experiment on absolute value inequalities, whose aim was to identify characteristics of an approach that would realize the potential of the topic to develop theoretical thinking in students enrolled in prerequisite mathematics courses at a large, urban North American university. The potential is demonstrated in an epistemological analysis of the topic. It is also shown that this potential is not realized in the way the topic is presently taught in prerequisite mathematics courses. Three groups of students enrolled in such courses were each exposed to one of three approaches we conceived for teaching the topic, labeled the procedural (PA), the theoretical (TA), and the visual (VA) approaches. The design of the three lectures was constrained by institutional characteristics of college-level courses, and informed by epistemological and didactical analyses of the topic. It was found that following the VA lecture, which proposed two equally valid mathematical techniques (graphical and analytic), one of which could be used to test the validity of results obtained by the other, students were more likely to engage in some aspects of theoretical thinking. They displayed more reflective and systemic thinking than other groups, and dealt more effectively with the logical intricacies of absolute value inequalities. VA students appeared to have a synthetic grasp of the inequalities, and a flexibility of thought not displayed by PA and TA students. However, without sufficient attention to tasks not easily solved by graphical means, VA approach provided students with a way to avoid the challenges of systemic and analytic thinking, some of which were more apparent in TA students. PA students expectedly behaved more as procedural knowers, but we saw interesting examples of engagement with theoretical thinking while dealing with the procedures proposed in the PA lecture.

Keywords

Absolute value inequalities Mature students Prerequisite mathematics courses Learning by example Theoretical thinking Teaching experiment 
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Notes

Acknowledgments

Research reported in this paper was funded by the Social Sciences and Humanities Research Council of Canada, grant number 410-2006-1911. We wish to thank the 18 students who agreed to participate in our research. We are indebted to the coordinating editor for our paper and the anonymous reviewers for their insightful comments and helpful suggestions.

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Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  • Anna Sierpinska
    • 1
  • Georgeana Bobos
    • 1
  • Andreea Pruncut
    • 2
  1. 1.Department of Mathematics and StatisticsConcordia UniversityMontrealCanada
  2. 2.Université de MontréalMontrealCanada

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