id: 06430634
dt: j
an: 2015c.00511
au: Komatsu, Kotaro; Tsujiyama, Yosuke; Sakamaki, Aruta
ti: Rethinking the discovery function of proof within the context of proofs and
refutations.
so: Int. J. Math. Educ. Sci. Technol. 45, No. 7, 1053-1067 (2014).
py: 2014
pu: Taylor \& Francis, Abingdon, Oxfordshire
la: EN
cc: E53 G43
ut: proof; proving; discovery function; refutation; counterexample
ci:
li: doi:10.1080/0020739X.2014.902135
ab: Summary: Proof and proving are important components of school mathematics
and have multiple functions in mathematical practice. Among these
functions of proof, this paper focuses on the discovery function that
refers to invention of a new statement or conjecture by reflecting on
or utilizing a constructed proof. Based on two cases in which eighth
and ninth graders engaged in proofs and refutations, we demonstrate
that facing a counterexample of a primitive statement can become a
starting point of studentsâ€™ activity for discovery, and that a proof
of the primitive statement can function as a useful tool for inventing
a new conjecture that holds for the counterexample. An implication for
developing tasks by which students can experience this discovery
function is mentioned.
rv: