With the increasing professionalization of teaching in HE it is timely to consider how we might establish it on a more formal, principled, perhaps even scientific, basis. We have to remember that the professionalization of teaching in schools has only taken place in the last couple of centuries. Since modern higher education has evolved primarily through the research route and has until recently recruited students from the top few percent of ability (or income), there was never much need to concern oneself too much with the quality of the teaching. So it is no surprise that we are a long way behind school teaching in the training and education of our HE teachers. However, things have changed rapidly in the last couple of decades or so. Specifically:
· Universities now recruit over 40% of the eligible age group
· The world economy is now highly ‘information – based’ requiring high levels of good education at every level to ensure international competitiveness
· Students are now paying directly for their higher education, accumulating vast debts in
the process
· HE teaching is under increasing scrutiny from government and the taxpayer
For such reasons formal teacher training for academics is essential if they are to retain credibility as a profession. The question is, what form should it take? One could argue that it should be every bit as lengthy, rigorous and theoretically founded as school teaching, but this is neither affordable nor necessary. But we do need something that is rigorous, theoretically informed and discipline led.
In Mathematics we are fortunate in that we have a long established discipline of Mathematical Education on which to draw – a great deal of work has been done at the HE level. But there are a number of problems. Practical HE mathematics teachers have little time for the study of pedagogy, and find it difficult enough just keeping up with the demands of day to day class contact partly because the pressure . On the other hand Mathematical Educators are obliged, to focus their efforts on theoretical questions that are often too far removed from the chalk face to appear useful to the practitioner. And of course the language of the typical mathematics education paper will of necessity be almost impenetrable for the average lecturer. There may also be a deep seated distinction between Mathematics and Mathematics Education (Weber, 20007) purely in the way they approach problems and communicate ideas. Mathematicians tend to be analytical, focused, convergent thinkers, constantly aiming for ‘the solution’. Mathematics Educators on the other hand tend to be empirical, broad based, divergent thinkers, aiming more for ranges of solutions to meet differing circumstances and often satisfied with less than perfect evidence base for their actions. But in fact the latter is more the nature of the teaching activity itself. None of this is new. The same applies to schoolteachers in relation to mathematics education at their level, but because of their longer training they have more opportunity to digest the theoretical foundations which are made more accessible for them during their training. And as mathematicians we should be used to the distance that often exists between the theoretical and practical aspects of a discipline.
For example there are whole swathes of Mathematical Physics that have little actual use in Physics. But eventually theory does catch up with practice, and can eventually lead it. In the early days of the industrial revolution theoretical fluid dynamics was often far removed from (but admittedly driven by) practical ship building and civil engineering which were largely craft based. But eventually advances in theory began to make an impact on the practical aspects of engineering and now no one would entertain launching a new vessel or building a substantial bridge without extensive prior mathematical modelling and simulation It will be the same in Mathematics Education. Certainly, much that has been done so far has limited relevance to day to day teaching, but increasingly there will be a greater need for theoretical underpinning of teaching and, combined with the craft basis existing amongst practicing teachers, Mathematics Education has probably already produced most of this that will be required. In order for all of our graduates, whatever their innate ability, to compete effectively at the international level the quality of our teaching needs to be first class there is no room for a minimalist approach to teaching in HE. The use of IT, web, and other technological advances now provides unprecedented opportunities for investigating and delivering education, not just as a mode of delivery, but as an investigative tool for advancing our knowledge of how students learn. One can imagine that in a decade or so incoming students will take some kind of psychological test that will be used to design the curriculum to suit each of them and enable them to fulfill their individual potential. And in future lecturers will learn, as part of their training, ideas about student learning that are scientifically evidence based.
So, how can we train, educate and support lecturers for their teaching, while recognizing at the same time the practical and political realities within which we all have to work? How would I do such a thing in my mathematics teaching – that is how would I give the students the best education in a limited time? Would I give them a list of quick ‘top tips’ on group theory – the top ten theorems? Would I show them rules of thumb designed to get the job out of the way quickly, thereby confirming its lowly status? Would I give them a recipe book, a troubleshooting manual? Encourage them to learn by rote and blindly follow algorithmic processes? Do we train them as we would call centre personnel?
Or would I teach them the fundamental principles, illustrate how one can build on these using one’s own independent intellectual resources, how to use and apply them to inform practice? Would I teach them the basic ideas of reasoned and rigorous argument – with examples from the key proofs? Would I teach them to adapt theorems and techniques to new circumstances? And would I try to instill attitudes commensurate with their professional duties and the values of their discipline and scientific inquiry, generating a love and respect for the subject, an intellectual honesty and integrity that will guide them through their careers? I think the latter would be better. So I reject the ‘top tips for teaching’ approach. Such teaching approaches, often adopted by generic courses teach teaching in exactly the opposite way to how one would teach anything properly. Top tips, teaching tips, 1000 tips, etc try to get the teacher to accept bite sized chunks without underlying unity and coherence – would we teach algebra like that? Certainly, we use menomics such as BODMAS, but these are just reminders that trigger what we hope is fundamental understanding that the student can apply to particular circumstances. I believe that practical teaching should be underpinned by sound evidence based theoretical frameworks. These will only evolve gradually over extensive and intensive debate, controversy and practice. Since we have to start somewhere, in this paper I suggest eleven basic principles of teaching that are evidence based and can be used to build most good teaching practice. My claim is that any set of ‘2000 Teaching Tips’ can be derived as applications or consequences of these by any thoughtful teacher. The term ‘principle’ is used loosely here. These are intended to be used as guidance for actual practice in the classroom, and so they are phrased precisely at this level. Also, they are not meant to be ‘principles’ in the sense of say Newton’s Laws of motion, experimentally founded to high orders of accuracy within their context. Nor are they meant to be ‘axioms’ as we might understand them in the mathematics sense, immutable and divorced from requirements of external reality, satisfying only logical consistency.
They are however meant to be founded on convincing evidence which will be a composite of findings from Mathematics Education theory, widespread practitioner consensus and plain common sense. Their main function will simply be as a start for continual critique, improvement, replacement and so on. The object is that if the lecturer learns and continually applies these principles then they will be a good practical guide for effective teaching. Many authors on pedagogy already attempt such a thing – Krantzs’ ‘Guiding principles’ (1999) or Baumslag’s Rules of Good Teaching (2000). In the eleven given here I have tried to be more theoretically–based, more comprehensive and more rigorous. Some of them may be wrong, some may be unnecessary, they may be incomplete, they may be ill informed, they may be unfashionable. But, they are there for anyone so inclined to critique and hopefully improve. There is always the danger that such principles will appear bland, trite, vacuous, anodyne. But this is often the case with fundamental principles of any kind. Such principles only really come to life when they are put together, their consequences explored, and they are applied to particular situations.
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