id: 06458045
dt: j
an: 2015e.00452
au: Sánchez, Ernesto; Orta, Antonio
ti: Levels of reasoning of middle school students about data dispersion in risk
contexts.
so: Math. Enthus. 12, No. 1-3, 275-289 (2015).
py: 2015
pu: Information Age Publishing (IAP), Charlotte, NC; University of Montana,
Department of Mathematical Sciences, Missoula, MT
la: EN
cc: E53 C33 K93 K43 K53
ut: risk; students’ reasoning; lower secondary; research; variation;
dispersion; risk-seeking; risk-aversion; problem posing; decision
making; uncertainty; SOLO model; variability
ci:
li: http://www.math.umt.edu/tmme/vol12no1thru3/21_Sanchez_and_Orta.pdf
ab: Summary: The aim of this research study is to explore students’ reasoning
concerning variation when they compare groups and have to interpret
dispersion in terms of risk. In particular, we analyze in this paper
the responses to two problems from a questionnaire administered to 82
ninth-grade students. The problems consist of choosing between two and
three groups of data by comparing them. The first one composed of
losses and winnings coming from a hypothetical game; the second is
about medical treatments. The results show the difficulty students had
in interpreting variation in a risk context. Although they identify the
data group with more variation, this is not enough for interpreting the
variation in terms of risk and making a rational decision. The
psychological categories of risk-seeking and risk-aversion are used to
explain the behavior of students who choose one group or another when
they identify correctly the risk in each situation. As a conclusion, it
is suggested that more risk context situations should be studied.
rv: