id: 05628934
dt: j
an: 2009f.00147
au: Furinghetti, Fulvia; Morselli, Francesca
ti: Every unsuccessful problem solver is unsuccessful in his or her own way:
Affective and cognitive factors in proving.
so: Educ. Stud. Math. 70, No. 1, 71-90 (2009).
py: 2009
pu: Springer Netherlands, Dordrecht
la: EN
cc: C25 C35 E55 D25 F65
ut: affective factors; cognitive factors; beliefs; problem solving; proving;
elementary number theory; case studies; student observation; university
ci:
li: doi:10.1007/s10649-008-9134-4
ab: Summary: It is widely recognized that purely cognitive behavior is
extremely rare in performing mathematical activity: other factors, such
as the affective ones, play a crucial role. In light of this
observation, we present a reflection on the presence of affective and
cognitive factors in the process of proving. Proof is considered as a
special case of problem solving and the proving process is studied
adopting a perspective according to which both affective and cognitive
factors influence it. To carry out our study, we set up a framework
where theoretical tools coming from research on problem solving, proof
and affect are present. The study is performed within a university
course in mathematics education, where students were given a statement
in elementary number theory to be proved and were asked to write down
their proving process and the thoughts that accompanied this process.
We scrutinize the written protocols of two unsuccessful students, with
the aim of disentangling the intertwining between affect and cognition.
In particular, we seize the moments in which beliefs about self and
beliefs about mathematical activity shape the performance of our
students.
rv: