id: 06310383
dt: a
an: 2014d.00827
au: Sánchez, Ernesto; Landín, Pedro Rubén
ti: Levels of probabilistic reasoning of high school students about binomial
problems.
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, 581-597
(2014).
py: 2014
pu: Dordrecht: Springer
la: EN
cc: K64 K54 E54
ut: hierarchy; SOLO levels; probabilistic reasoning; binomial distribution
ci:
li: doi:10.1007/978-94-007-7155-0_31
ab: Summary: In this chapter, some aspects of the process in which students
come to know and use the binomial probability formula are described. In
the context of a common high school probability and statistics course,
a test of eight problems was designed to explore the performance of
students in binomial situations. To investigate the influence of
instruction to overcome some common cognitive bias or their
persistency, the first three problems are formulated in a way that may
induce bias. Each one is structurally equivalent to another problem
phrased to avoid any bias that was included in the test. Also, the
second and third problems were administered before and after the course
to assess the changes produced by instruction. A hierarchy of
reasoning, designed in a previous study, was adapted and used to
classify the answers of the students in different levels of reasoning.
The classification of these answers points out that the components of
knowledge, the classical definition of probability, the rule of product
of probabilities, combinations, and the binomial probability formula,
are indicators of transitions between levels. The influence of the
phrasing of the problems is strong before instruction, but weak after
it.
rv: