id: 05648596
dt: j
an: 2010a.00427
au: Ko, Yi-Yin; Knuth, Eric
ti: Undergraduate mathematics majorsâ€™ writing performance producing proofs
and counterexamples about continuous functions.
so: J. Math. Behav. 28, No. 1, 68-77 (2009).
py: 2009
pu: Elsevier, New York, NY
la: EN
cc: I25 E55
ut: counterexamples; proofs; continuous functions
ci:
li: doi:10.1016/j.jmathb.2009.04.005
ab: Summary: In advanced mathematical thinking, proving and refuting are
crucial abilities to demonstrate whether and why a proposition is true
or false. Learning proofs and counterexamples within the domain of
continuous functions is important because students encounter continuous
functions in many mathematics courses. Recently, a growing number of
studies have provided evidence that students have difficulty with
mathematical proofs. Few of these research studies, however, have
focused on undergraduatesâ€™ abilities to produce proofs and
counterexamples in the domain of continuous functions. The goal of this
study is to contribute to research on student productions of proofs and
counterexamples and to identify their abilities and mathematical
understandings. The findings suggest more attention should be paid to
teaching and learning proofs and counterexamples, as participants
showed difficulty in writing these statements. More importantly, the
analysis provides insight into the design of curriculum and instruction
that may improve undergraduatesâ€™ learning in advanced mathematics
courses.
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