id: 06466677
dt: j
an: 2015e.00434
au: Stavrou, Stavros Georgios
ti: Common errors and misconceptions in mathematical proving by education
undergraduates.
so: Issues Undergrad. Math. Prep. Sch. Teach., J. 1, Content Knowledge, 8 p.,
electronic only (2014).
py: 2014
pu: Texas Tech University, Department of Mathematics and Statistics, Lubbock,
TX
la: EN
cc: D79 E59 F69 H49
ut: undergraduate students; error patterns; misconceptions; mathematical
concepts; proving
ci:
li: http://www.k-12prep.math.ttu.edu/journal/1.contentknowledge/stavrou01/article.pdf
ab: Summary: Ninety-seven education students majoring or minoring in
mathematics had their math homework examined in a Number Theory or
Abstract Algebra course. Each student’s homework was observed for the
purpose of identifying common errors and misconceptions when writing
mathematical proofs. The results showed that students collectively made
four recurring errors: assuming the conclusion in order to prove the
conclusion, proving general statements using specific examples, not
proving both conditions in a biconditional statement, and misusing
definitions. In the same courses taken subsequently by 91 new students,
we informed them about these common errors prior to assigning their
homework to see how the students’ proving processes would differ. The
results showed that more exercises were left blank with comments such
as “I’m not sure how to start the proof”, and that many students
provided unnecessary examples to supplement their valid proofs.
rv: