id: 06571523
dt: j
an: 2016c.00575
au: Lee, KoSze
ti: Students’ proof schemes for mathematical proving and disproving of
propositions.
so: J. Math. Behav. 41, 26-44 (2016).
py: 2016
pu: Elsevier, New York, NY
la: EN
cc: E53
ut: proof; proof schemes; mathematical reasoning; counterexamples; examples;
mathematical proving
ci:
li: doi:10.1016/j.jmathb.2015.11.005
ab: Summary: Classification of students’ proof schemes offers insights into
students’ mathematical proving. However, previous studies revealed
little about finer progressions in students’ proving and barely
examined their proof schemes involving counterexamples. This study
examined students’ proof schemes through their considerations of
examples and counterexamples and reasoning in Proof Constructions. From
480 proofs constructed by 60 Singapore secondary three (14‒15 years
old) students, classifications of schemes for Deductive-proof
Construction and Proof-by-counterexample Construction were established
as a progression through four phases. The former consisted of seven
levels, spanning from irrelevant inferences to deductive proofs using
formal representations. The latter consisted of six levels, spanning
from irrelevant inferences to construction of a general set of
counterexamples. The refined classifications revealed students’
progression through their sophisticated use of examples,
counterexamples, and deductive inferences and that Proof Construction
was knowledge-driven. Comparisons to previous classifications and the
role of counterexamples in Proof Construction were discussed.
rv: