Published Resources Details Thesis

Author
Faull, D. J.
Title
Cognitive theory in the teaching of algebraic problem solving
Type of Work
EdD
Imprint
University of New South Wales, Kensington NSW, 2000
Url
http://primoa.library.unsw.edu.au/UNSWS:UNSW_ALMA21122660340001731
Subject
New South Wales
Abstract

Recent research has shown that integrated worked examples can reduce cognitive load and facilitate learning. The present research investigates these laboratory findings by replication and extension in a classroom setting. Cognitive load theory suggests that many conventional methods of instruction in mathematics are not effective because they deploy cognitive resources away from activities relevant to learning. Solving equations in algebra is a complex problem- solving task which imposes a heavy cognitive load. It is suggested that the conventional, multiple practice method in a classroom situation is one such method of ineffective instruction. The focus of the present research was based on the theoretical framework that students ability to solve algebra equations would be enhanced if cognitive load is reduced and a cognitive understanding approach is adopted as the dominant method of learning. Students exposed to this model of instruction were given worked - example models to study. Instructional emphasis was on understanding the process and the steps to solution, to facilitate cognitive understanding, rather than on the completion of large numbers of problems as multiple practice. All experiments were based on in class experience over a normal timetabled week. This involved the application of homework based on the instructional approach used in each class. In this way experiments were not simulated laboratory tests but were as close as possible to normal classroom environments. It is suggested, from these findings, that using a cognitive understanding approach can enhance the skills involved in solving some algebra problems. These findings reinforced previous laboratory based research and emphasise the importance of the theory of cognitive load, in classroom situations. Research results suggest that there is a need for changes in actual classroom practice in some aspects of the mathematics curriculum. Further research is needed to investigate issues raised as an outcome of the research encompassed in the present thesis.