ASET-HERDSA 2000: Buttsworth - problems and solutions in Mathematical education

[ Abstracts ] [ Program ] [ Proceedings ] [ ASET-HERDSA 2000 Main ]

Problems and solutions in Mathematical education - a spectrum extremity

R. N. Buttsworth
School of Mathematics, Gardens Point Campus
Queensland University of Technology

When certain features of educational subjects are considered, the content of mathematics will quite readily be classified as extreme. However, the features in question do not isolate mathematics and so to varying extents problems and their solutions arising in that discipline may have quite a significant in other areas.

Important features where mathematics is extreme include:

The central role of accurate deductive reasoning
The very diminished role of opinions and "balanced" viewpoints

In this presentation, a number of major problems for mathematical education are considered. Included are what we may term:

The relevance credibility gap
The confidence potential gap
The prescription description gap
Butterfly mentality
Time and topics driving the tempo

Some discussion of these is central to the aim of this paper and in particular the objectives of the paper are

to clarify and illustrate these problems.
to argue that they are indeed major problems
to identify which or which aspects of these problems are addressable
to draw attention to the stability of much of the essential content of mathematics taught over many years and how this fact bears on educational research
to explain some useful concepts particularly relevant to mathematical teaching

In seeking to achieve the objectives, it will emerge that many of the concerns are not altogether new problems, but rather have been exacerbated by current climates thereby ensuring they are major not minor problems. Supporting evidence for all this is drawn from more than thirty years teaching in some seven tertiary institutions. This experience was mainly in two universities where over a decade was spent in each. the evidence itself is chiefly anecdotal, but some more objective data will be considered and analysed.

It is proposed that positive steps towards long term solutions can be taken if the relevant communities become aware of a number of pivotal distinctions. The distinction between:

Numeracy and mathematical literacy
Cultural diversity in elementary mathematics and cultural convergence in higher mathematics
Available flexibility and pedagogical rigidity
A logical presentation and a psychological presentation

A detailed successful method of teaching mathematics will be outlined and data from a few subjects over several years given as evidence of the method's success. A major ingredient is motivating students to make an effort learn. The conclusion will be drawn that it is possible to take steps to address some the major problems at least at a local level short term.

Contact person: Dr R. N. Buttsworth. Email: buttsworth@qut.edu.au
Voice: +61 (0)7 3864 5241 Fax: +61(0)7 3864 2310

Please cite as: Buttsworth, R. N. (2000). Problems and solutions in Mathematical education - a spectrum extremity. In Flexible Learning for a Flexible Society, Proceedings of ASET-HERDSA 2000 Conference. Toowoomba, Qld, 2-5 July. ASET and HERDSA. http://cleo.murdoch.edu.au/gen/aset/confs/aset-herdsa2000/abstracts/buttsworth-abs.html

[ Abstracts ] [ Program ] [ Proceedings ] [ ASET-HERDSA 2000 Main ]
Created 17 June 2000. Last revised: 23 June 2000. HTML: Roger Atkinson [atkinson@cleo.murdoch.edu.au]
This URL: http://cleo.murdoch.edu.au/gen/aset/confs/aset-herdsa2000/abstracts/buttsworth-abs.html