Page 210 - Contributed Paper Session (CPS) - Volume 8

CPS2254 Dan C.

Improving middle school students’ expectations
of variability in a two-dimensional context
Dan Canada
Department of Mathematics, Eastern Washington University, Cheney WA 99004 (USA)

Abstract
The purpose of this paper is to report on the emerging results of a project that
used an instructional intervention designed to improve middle school
students’ informal expectations of variability in a two-dimensional context.
Specifically, one aim of the project was to compare how students reasoned
about variability to make informal inferences both before and after modelling
a task physically and then via computer simulation. A simultaneous goal was
to have students pursue their own additional questions, beyond the initial
prompts given, that were prompted by an analysis of the data they had
gathered.

Keywords
Statistics; Education; Probability; Variation; Teaching

1. Introduction
The underlying task in this project, based on work by others (e.g. Engel &
Sedlmeier, 2005; Green, 1982; Piaget & Inhelder, 1975), posits raindrops just
beginning to fall across a patio of sixteen square tiles in a 4 x 4 array: Where
might the first sixteen drops land? In Engel and Sedlmeier’s work, using falling
snowflakes as a context, their “objective was to find out how children decide
between random variation and a global uniform distribution of flakes” (2005,
p. 169). Using a framework that considered the degree to which student
responses reflected a perspective of randomness versus determinism, those
researchers found evidence across a range of tasks and grade levels that
students’ ability to coordinate randomness and variability seems to deteriorate
with age.
Of particular interest was the call by the researchers for instructional
interventions that would leverage technology (such as computer simulations)
to bolster gathering experimental data in a quest to develop “students’
intuitions about chance variation” (Engel & Sedlmeier, 2005, p. 176). In fact, as
detailed in the next section covering methodology, the intervention in the
current project reflects the first four aspects of Engel’s (2002) five-step
procedure: Making initial conjectures or observations of a given phenomenon,
developing a model for the purposes of simulation, gathering data, and
comparing subsequent results to initial predictions. The fifth step, involving

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