id: 06639209
dt: j
an: 2016f.00808
au: Zazkis, Dov; Villanueva, Matthew
ti: Student conceptions of what it means to base a proof on an informal
argument.
so: Int. J. Res. Undergrad. Math. Educ. 2, No. 3, 318-337 (2016).
py: 2016
pu: Springer US, New York, NY
la: EN
cc: E55 C35
ut: proof; informal argumentation; formalization; semantic reasoning; syntactic
reasoning
ci:
li: doi:10.1007/s40753-016-0032-3
ab: 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 studentsâ€™
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.
Studentsâ€™ 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.
rv: