Title: Statistics students' identification of inferential model elements within contexts of their own invention,
Abstract: Statistical thinking partially depends upon an iterative process by which
essential features of a problem setting are identified and mapped onto an
abstract model or archetype, and then translated back into the context of the
original problem setting (Wild and Pfannkuch 1999). Assessment in introductory
statistics often relies on tasks that present students with data in context and
expects them to choose and describe an appropriate model. This study explores
post-secondary student responses to an alternative task that prompts students
to clearly identify a sample, population, statistic, and parameter using a
context of their own invention. The data include free text narrative responses
of a random sample of 500 students from a sample of more than 1600 introductory
statistics students. Results suggest that students' responses often portrayed
sample and population accurately. Portrayals of statistic and parameter were
less reliable and were associated with descriptions of a wide variety of other
concepts. Responses frequently attributed a variable of some kind to the
statistic, or a study design detail to the parameter. Implications for
instruction and research are discussed, including a call for emphasis on a
modeling paradigm in introductory statistics.