Sdrawkcab scitamehtam: The case for understanding mathematics backwards

Stephen Woodcock

Abstract


Despite the widespread acknowledgement of the need for graduates with quantitative problem-solving skills, many students enter university having relied heavily on pattern recognition techniques for high school mathematics. While these can often lead students to obtaining correct solutions for problems similar to those which they have practised, they do not lead to a deeper understanding of the material and, critically, may not develop more widely-applicable skills. Even when correct solutions are obtained, students can sometimes not understand or explain why their solution is indeed correct. Here, I present an argument in favour of avoiding predictability in question structures and, in particular, asking questions ``backwards'' to how they might traditionally be asked. Some mathematical topics readily lend themselves to such approaches --- the Fundamental Theorem of Calculus tells us that an integral problem is inherently linked to an antiderivative problem --- whereas other require much more care and subtlety to avoid routine or predictable assessments. I will discuss some preliminary results from a first year probability subject at the University of Technology Sydney (UTS) which suggest that student understanding of material can be increased when they feel that prioritising pattern recognition over problem solving is unlikely to be rewarded with high marks.

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Keywords


Mathematics Education; Assessment

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DOI: https://doi.org/10.21914/anziamj.v59i0.12640



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