id: 06310366
dt: a
an: 2014d.00795
au: Ejersbo, Lisser Rye; Leron, Uri
ti: Revisiting the medical diagnosis problem: reconciling intuitive and
analytical thinking.
so: Chernoff, Egan J. (ed.) et al., Probabilistic thinking. Presenting plural
perspectives. Dordrecht: Springer (ISBN 978-94-007-7154-3/hbk;
978-94-007-7155-0/ebook). Advances in Mathematics Education, 215-237
(2014).
py: 2014
pu: Dordrecht: Springer
la: EN
cc: K50 M60
ut: cognitive challenge; dual process theory; intuitive thinking; analytical
thinking; mathematical tasks; task design; statistical thinking;
medical diagnosis problem
ci:
li: doi:10.1007/978-94-007-7155-0_12
ab: Summary: A recurrent concern in mathematics education ‒ both theory and
practice ‒ is a family of mathematical tasks which elicit from most
people strong immediate (“intuitive") responses, which on further
reflection turn out to clash with the normative analytical solution. We
call such tasks cognitive challenges because they challenge cognitive
psychologists to postulate mechanisms of the mind which could account
for these phenomena. For the educational community, these cognitive
challenges raise a corresponding educational challenge: What can we as
mathematics educators do in the face of such cognitive challenges? In
our view, pointing out the clash is not enough; we’d like to help
students build bridges between the intuitive and analytical ways of
seeing the problem, thus hopefully creating a peaceful co-existence
between these two modes of thought. In this article, we investigate
this question in the context of probability, with special focus on one
case study ‒ the medical diagnosis problem ‒ which figures
prominently in the cognitive psychology research literature and in the
so-called rationality debate. Our case study involves a combination of
theory, design and experiment: Using the extensive psychological
research as a theoretical base, we design a new “bridging" task,
which is, on the one hand, formally equivalent to the given
“difficult" task, but, on the other hand, is much more accessible to
students’ intuitions. Furthermore, this new task would serve as a
“stepping stone", enabling students to solve the original difficult
task without any further explicit instruction. These design
requirements are operationalized and put to empirical test.
rv: