Teaching and Learning – Secondary Education
As a rule the tendency of curriculum designers for Mathematics at secondary level is to crowd the courses with too much material, instead of concentrating on basic ideas and including some significant motivational material. The recent National Curriculum is a case in point. The end result is a crowded, over-complicated curriculum that serves to do little more than frighten off average students. The question is whether we want more students completing mathematics at higher levels, perhaps with a slightly lower skill level but a sound understanding, or less students but with very high skill levels.
It would seem counter-productive and inefficient to create a very small group with high level skills. Our goal as educators should be to introduce as many students to the delights and uses of mathematics without frightening them off. There are many real, interesting applications that can be studied at high school level without over-complicating the material.
The end goal should be to create a system where students entering disciplines other than mathematics at University are not afraid, but enthused by its relevance and utility. A society in which Environmental Scientists, Biologists and Engineers are also competent mathematicians will be much stronger. The best maths students will still be able to reach the top of the field by doing a maths degree, but the exposure of students from other disciplines is likely to create a better research community across the board. Mathematics is now an integral part of all of the sciences and business and it should be our goal to create an atmosphere in which ALL students feel comfortable to proceed.
Success in producing a broader base of trained maths graduates would have a positive feedback into the quality of teaching. While there are some excellent teachers of mathematics, there is also a shortage that leads to many talented students losing interest or not having the opportunity, and weaker students becoming “afraid” and avoiding the subject completely.
Given that many Universities have now dropped the top pre-requisite Maths units for students entering degrees in the physical sciences and engineering from high school, the numbers doing the top level maths at school are dropping alarmingly. The solution to this is not simple, but most Universities now have some kind of bridging units to bring the larger part of the cohort up to the appropriate level to start University level training. The way forward is either to make these Secondary school units more attractive or, if numbers continue to drop, abolish them. The former is clearly preferable.
Recommendation: Implement measures that will produce a broader base of students with reasonable levels of mathematics training but a passion for the subject rather than a small group with high level skills. A broader base of students (if slightly less highly educated) will produce more able students entering all disciplines at University. Long term feedback through the school system will produce better teachers and a more educated community. This should be achieved by a less crowded but more applied secondary curriculum that introduces the fundamentals without unnecessary technical detail, and introduces significant motivational material.
Research Training and Breadth
Many Universities are moving toward PhD’s with a 2 year Master’s entry level rather than Honours. Further, some are also introducing postgraduate coursework as part of a PhD. This would seem to be out of the hands of staff in mathematics departments and is favoured by those in the older, more established, wealthier Universities. Those completing a PhD under this system will undoubtedly have a stronger mathematics training than the current crop of students, and may produce researchers of very high quality.
However, the price of this will be a concentration of PhDs into a smaller group of Universities and lower numbers overall. Given the shortage of people with this level of qualification I would hope that this step is reconsidered. It would seem to be an undesirable course of action if one wishes to create a broader pool of people with high level mathematics training. Students at poorer Universities will either have to move to the richer institutions or will not proceed. For many students from poorer backgrounds, the prospect of two years extra study as preparation is prohibitive, and they will simply leave the system. Furthermore, the abolition of Honours will potentially remove a whole cohort of students who wish to get some further training but do NOT wish to go on to a PhD. These graduates are invaluable in the work place and in disseminating mathematical knowledge outside of the higher education sector, but may disappear if the system continues on the present path.
Given that most of the current academics trained in Australia came through under the old system of Hons-PhD, including many of those who completed offshore, it seems somewhat churlish to force the current generation to take an extra year just to get started.
Recommendation: That Honours be retained as both a pathway to a PhD and an avenue for a year of further training in Mathematics/Statistics.
The broader intake of students to higher education means that the worst students are weaker, but I am yet to be convinced that the best students are any different to what they were 20 years ago. Narrowing of the field able to complete high level training will almost certainly create a negative feedback through the system with an increasingly narrow field.
Access of the broader academic community to highly trained mathematicians capable of interacting across a number of disciplines would seem to be crucial to the further development of science generally. Mathematics is used in an ever-increasing number of fields at the same time as many University disciplines are removing mathematics/statistics requirements from their degree. At my own institution, students in environmental and marine science, for example, once did 2 years of University level mathematics/modelling and a statistics unit. Now, they are only required to do a single statistics unit. This is not an uncommon situation and has arisen in spite of high quality, specialised units being designed for those students. While we cannot force these disciplines to include mathematics and statistics, we can produce graduates who are able to interact across multiple disciplines and make themselves available for collaborative studies. The positive vibes of these interactions will produce staff in other disciplines who are more willing to require further level quantitative skills training for their students.
The major goals of the mathematics community should be not only to increase the number of mathematicians doing research in mathematics, but to increase the number of people conducting high level research using mathematics in other fields. The increase in awareness of the utility and necessity of mathematics across all disciplines should have a positive feedback into future training. Encouragement for mathematicians to acquire the breadth of communication and applied mathematical skills required to interact with other disciplines should be part of all undergraduate training.
Recommendation: That mathematics/statistics students be given training in application of their discipline and interaction with others from different disciplines to improve the breadth of quantitative skills across all disciplines.