Complete thesis - Murdoch University

simple (Fuson (1992) provides a review of this area). Even when the same procedural knowledgewould seem to be called for, the mastering of different classes of the same problemdoes not occur at the same time. As a consequence, success in the application of a givenprocedure, or its use in a given problem context, does not ensure the recognition of the procedure’srelevance to a problem when the construction of different mental models in responseto different types of problems is called for (Gobet and Wood, 1999). A consequence of thisis that the theoretical interpretation and explanation for both success and errors is not simplewhere there are one-to-many mappings between procedural performance and conceptualunderstanding.Problem solving skills appear to be related to many other aspects of cognition (Frederiksen,1984), such as schemata, pattern recognition and creativity (developing new solutions).Problem solving itself may also be viewed as a creative process, as well as requiring creativity.Grundy (1987), in describing a Creative Problem Solving Model identifies five major steps:fact-finding; problem finding; idea finding; solution finding; acceptance finding. Mumfordet al (1998) point to evidence that the ability to solve problems creatively is based on thefollowing key processes: definition and structuring of the problem situation (e.g., restatementof the problem); information acquisition or encoding in order to select and organise relevantinformation; and combination and reorganisation of knowledge to address the problem.In all of this, the issue of transfer is highly relevant, while the effectiveness of even generalproblem-solving skills appears to improve when students learn self-regulation metacognitiveskills (Hannafin et al, 1996):Declaration 3 metacognitive self-regulation training helps students transfer learning tomore difficult problems within the same domainIn describing a computational representation for problem solving, Goldstein (1980) suggeststhe problem solving task requires multiple perspectives on its subject matter, achievedthrough playing the following roles:mathematician a set of mathematical and probabilitistic skills (eg argument by elimination,sets to represent hypotheses, sequential organisation of a set of heuristics) are appliedto theorems of a domain (the rules that apply). Problem solving has an element oftheorem provinghistorian the use of analogies, generalisations, corrections and refinements, to construct newknowledge based on the relationships between knowledge elements already possessedepistemologist data and hypothesis representation: insight into the breadth of knowledge115