id: 06388988
dt: j
an: 2015a.00810
au: Kapon, Shulamit; Ron, Gila; Hershkowitz, Rina; Dreyfus, Tommy
ti: Perceiving permutations as distinct outcomes: the accommodation of a
complex knowledge system.
so: Educ. Stud. Math. 88, No. 1, 43-64 (2015).
py: 2015
pu: Springer Netherlands, Dordrecht
la: EN
cc: K53 E53 C33
ut: probability; reasoning; conceptual change; knowledge in pieces; secondary
school
ci:
li: doi:10.1007/s10649-014-9570-2
ab: Summary: There is ample evidence that reasoning about stochastic phenomena
is often subject to systematic bias even after instruction. Few studies
have examined the detailed learning processes involved in learning
probability. This paper examines a case study drawn from a large corpus
of data collected as part of a research project that dealt with the
construction of knowledge of probability at the junior high level while
working on specifically designed activities. We discuss the dynamic
construction of knowledge of a student who, while working on the task
with a fellow student, learned to correctly predict the probability of
getting a particular event in a two-dimensional sample space, although
his initial intuitive take on the situation clearly conflicted with
mathematical theory and empirical evidence. The studentâ€™s learning is
analyzed from the knowledge in pieces (KiP) epistemological
perspective. We identify key knowledge elements, extend the Piagetian
notion of accommodation through the activation and deactivation of
these knowledge elements, and discuss the accommodation of a particular
knowledge system that informs the perception of real-world situations
as instances of a simple event in probability theory.
rv: