The Construction of Meanings In and For a Stochastic Domain of Abstraction
unpublished Phd thesis, (1988)Abstract
This study takes as its focus young children's intuitive knowledge of randomness. Previous work in this field has studied the misconceptions that people, especially adults, hold in making judgements of chance (see, for example, the work of Kahneman & Tversky and Konold).
In contrast, I study how primitive meanings for randomness form a basis for new meanings, a process which the misconceptions approach fails to illuminate. The guiding principle for this study is that the observation of students' evolving thought in a carefully designed computer-based domain will provide a better understanding of how the specific features of the domain shape and are shaped by activities within it.
There are, then, two deeply connected strands to this thesis: the study of children's evolving meanings for randomness as expressed in a computer-based microworld, and the articulation of design principles which encapsulate pedagogic meanings for that microworld. More specifically, the thesis aims to shed light upon the answers to four crucial questions:
Meanings for the domain
What do formalisms of stochastic behaviour look like in a domain of abstraction?
What structures in the domain for stochastic abstraction optimise the articulation of intuitions and the construction of new meanings?
Meanings in the domain
What articulations of informal intuitions of stochastic behaviour do we observe?
How do the structures of the domain support the forging of situated meanings?
The study uses an iterative design methodology, which cycles between the design of computer-based tools and the observation of children, between the ages of 9 and 11 years, as they use these tools. The thesis identifies initial meanings for the behaviour of various stochastic phenomena and traces how new pieces of knowledge, especially relating to long term random behaviour, emerge through the forging of connections between the internal and external resources.