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A comparison of trained and untrained science teachers' views about certain aspects of the nature of science
Citation
Boo, H. K., & Hoh, Y. K. (2006, November). A comparison of trained and untrained science teachers' views about certain aspects of the nature of science [Paper presentation]. Australian Association for Research in Education Conference, Adelaide, Australia.
Abstract
This tutorial-style paper aims to give a quick beginner’s introduction to the theory of continuous valuations – a domain-theoretic variant of measure theory tailored for topological spaces and ordered structures. Central to the theory of continuous valuations is the famous theorem of Claire Jones that asserts that the probabilistic powerdomain (i.e., the space of continuous valuations arising from the Scott topology of domains) ordered by the stochastic ordering is again a domain. Most existing proofs of Jones’ theorem are fairly technical and involved, and thus this paper aims to present an intuitive and self-contained proof that allows reader quick access to it with minimum mathematical overhead. Sifting through all the concepts and theorems leading up to Jones’ theorem, we make a judicious choice of a core essence – constituting those results that are featured prominently in the theory of continuous valuations – and expound on their proofs, focusing on the key techniques and reasoning methods while contracting on, or even omitting, other peripheral or burdensome intricacies.
Keywords
Date Issued
2006
Description
This paper was presented at the Australian Association for Research in Education Conference, held in Adelaide, Australia from 26 - 30 Nov 2006