id: 06476339
dt: j
an: 2015e.00450
au: Savic, Milos
ti: The incubation effect: how mathematicians recover from proving impasses.
so: J. Math. Behav. 39, 67-78 (2015).
py: 2015
pu: Elsevier, New York, NY
la: EN
cc: E50 C20 C40
ut: proving process; mathematicians; psychology of mathematics; proof-based
courses
ci:
li: doi:10.1016/j.jmathb.2015.06.001
ab: Summary: The literature on mathematicians’ actions during proving has,
thus far, been primarily anecdotal. This paper reports the observed
actions of nine mathematicians, six of whom came to an impasse while
constructing proofs alone on an unfamiliar topic, from a set of notes,
and with unlimited time. The existence of impasses and the actions
participants took to recover from them were either directly observed
from the real-time data collected (using an innovative technique) or
obtained from exit interviews or focus groups. Certain times could be
considered a period of incubation, which psychologists have defined as
a “temporary shift away from an unsolved problem that allows a
solution to emerge seemingly as if from no additional effort” [{\it
U. N. Sio} and {\it T. C. Ormerod}, “Does incubation enhance problem
solving? A meta-analytic review”, Psychol. Bull. 135, No. 1, 94‒120
(2009; \url{doi:10.1037/a0014212}), p. 94]. These actions to overcome
impasses, while naturally part of mathematicians’ proving processes,
could be discussed with students in a classroom setting to help
alleviate difficulties in proving.
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