id: 06418727
dt: j
an: 2015b.00860
au: Noll, Jennifer; Hancock, Stacey
ti: Proper and paradigmatic metonymy as a lens for characterizing student
conceptions of distributions and sampling.
so: Educ. Stud. Math. 88, No. 3, 361-383 (2015).
py: 2015
pu: Springer Netherlands, Dordrecht
la: EN
cc: K70 K40 C30 C50
ut: introductory statistics; statistical reasoning; distributions; samples and
sampling; informal statistical inference; informal inferential
reasoning; metonymy
ci:
li: doi:10.1007/s10649-014-9547-1
ab: Summary: This research investigates what students’ use of statistical
language can tell us about their conceptions of distribution and
sampling in relation to informal inference. Prior research documents
students’ challenges in understanding ideas of distribution and
sampling as tools for making informal statistical inferences. We know
that these ideas are complex and difficult for students, but little is
known about the ways in which students’ language mediates their
statistical problem-solving activities within the realm of
distribution, sampling, and informal inference. This study uses
examples from semi-structured interviews with eleven undergraduate
students from two universities. Interview tasks focused on (1)
distinctions between distributions of populations, samples, and sample
statistics; (2) properties of sampling distributions; and (3) how to
use sampling distributions to make informal inferences. Analysis
focused on students’ use of metonymy (i.e., the substitution of the
name of an attribute or adjunct for that of the thing or idea meant).
We observed two particular metonymies. The first was a paradigmatic
metonymy in which students applied the properties of the normal
distribution to all distributions. Second, we observed a proper
metonymy in which students talked about sampling distributions as
compilations of many samples. The potential impact of these metonymies
on students’ ability to solve problems and the implications for
teaching are discussed.
rv: