
05239961
a
2008b.00439
Shaughnessy, J.Michael
Ciancetta, Matt
Canada, Dan
Types of student reasoning on sampling tasks.
Johnsen H\o ines, 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 1418, 2004. Bergen: Bergen University College. Part IV, 177184 (2004).
2004
Bergen: Bergen University College
EN
K43
K44
C43
C44
A63
A64
sampling
sample size
descriptive statistics
thinking skills
secondary school students
logical thinking
empirical investigations
emis:proceedings/PME28/RR/RR045_Shaughnessy.pdf
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.