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Student conceptions of what it means to base a proof on an informal argument. (English)
Int. J. Res. Undergrad. Math. Educ. 2, No. 3, 318-337 (2016).
Summary: In this paper we explore how students construe what it means for an informal argument to be the basis of a proof. We use students’ attention as a proxy for their conceptions and document what they pay attention to when assessing whether a proof is based on an informal argument. The data illustrate that some undergraduate mathematics students pay attention to only a limited cross section of the connections that exist between informal arguments and proofs. This indicates that their conceptions of what it means to base a proof on an informal argument involve relatively superficial similarities. Students’ attention to only a small cross section of what can be carried forward from an informal argument toward the goal of creating a proof can account for some student difficulties with, and avoidance of, using their own informal arguments as a basis for proof construction.
Classification: E55 C35
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