id: 05239961
dt: a
an: 2008b.00439
au: Shaughnessy, J.Michael; Ciancetta, Matt; Canada, Dan
ti: Types of student reasoning on sampling tasks.
so: Johnsen Høines, Marit (ed.) et al., Proceedings of the 28th international
conference of the International Group for the Psychology of Mathematics
Education, PME 28, Bergen, Norway, July 14‒18, 2004. Bergen: Bergen
University College. Part IV, 177-184 (2004).
py: 2004
pu: Bergen: Bergen University College
la: EN
cc: K43 K44 C43 C44 A63 A64
ut: sampling; sample size; descriptive statistics; thinking skills; secondary
school students; logical thinking; empirical investigations
ci:
li: emis:proceedings/PME28/RR/RR045_Shaughnessy.pdf
ab: Summary: As part of a research project on students’ understanding of
variability in statistics, 272 students, (84 middle school and 188
secondary school, grades 6 - 12) were surveyed on a series of tasks
involving repeated sampling. Students’ reasoning on the tasks
predominanly fell into three types: additive, proportional, or
distributional, depending on whether their explanations were driven by
frequencies, by relative frequencies, or by both expected proportions
and spreads. A high percentage of students’ predominant form of
reasoning was additive on these tasks. When secondary students were
presented with a second series of sampling tasks involving a larger
mixture and a larger sample size, they were more likely to predict
extreme values than for the smaller mixture and sample size. In order
for students to develop their intuition for what to expect in
dichotomous sampling experiments, teachers and curriculum developers
need to draw ‘explicit’ attention to the power of proportional
reasoning in sampling tasks. Likewise, in order for students to develop
their sense of expected variation in a sampling experiment, they need a
lot of experience in predicting outcomes, and then comparing their
predictions to actual data.
rv: