Geoff Tennant - Promoting access to mathematics for all
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22/5/16: discussion as a teaching method

In my previous job as an initial teacher trainer working with secondary mathematicians, there were three sessions I ran very early in the year: debrief on the two weeks spent in primary schools before the course began, 'What is mathematics and why do we teach it?" and an introduction to teaching methods.

The first two I ran mainly by getting students to discuss the issues amongst themselves in small groups, then report back to the rest of the group for whole group discussion.  How would I justify discussion as  a good way of dealing with these issues?  Well, for the primary school debrief activity, the important point to make, both in the session and also the placement itself, is that children have 6 years compulsory schooling - and often pre-school as well - before arriving in secondary school, there needs to be a sense of continuing where they left off rather than starting all over again.  And experience teaches me that when people aligned to the secondary sector at all levels of seniority spend time in primary schools, they are amazed by the quantity and quality of the work they see children doing.  So in this debrief discussion, the starting point very much is students' own experiences over the last two weeks, the benefit is in the need to articulate them for the other group members, to listen to others and consider the similarities and differences in what people experienced in different schools.  The precise points made are not really the issue here, over and above the over-arching one which, once stated, is pretty obvious really - year 7 children have already been in years 1 through 6.

For the 'What is mathematics and why do we teach it?" I started with a bit of input - using this PowerPoint if you're interested! - but working with beginning mathematics teachers, the key point here is to start with their implicit views on what mathematics is and why we teach it and make them explicit.  Without going into details here, one can take a very purist, 'mathematics is beautiful for its own sake' view (which to some extent I buy into) or a more utilitarian 'mathematics is useful to the extent to which it can be used in everyday life and other school subjects' (which, again, to some extent I buy into).  There are legitimate alternative views which exist in a state of creative tension, the world of mathematics teaching is the stronger because not everybody involved sees things in exactly the same way.  It was my intention to get students to explore these issues, not to come to any particular definite conclusion.

For the introductory session I did not use discussion as the main way of conducting the session.  Arguably I could have done, starting with what methods they have seen as pupils themselves, voluntary teachers, parents, observers, etc.  But I knew that where I was heading to was the list as given in paragraph 243 of the Cockcroft report (either this means nothing to or you're thinking, "My goodness, yes, I remember paragraph 243!"  In brief, a major Government report published in 1982, from a committee chaired by Dr Wilfred Cockcroft, which had huge resonance in the mathematics teaching world, and still gets quoted now from time to time).  Somehow starting with a discussion when I knew that, whatever the students said, I was going to end up with that list seemed, at risk of overstating the case, deceitful.  Whatever they said I would then jettison in favour of my pre-prepared list.  I then proceeded to show, more-or-less by treating them as a (terribly well behaved!) class of children, how Pythagoras can be introduced using three different teaching methods (namely, using informal language: number investigation, cut-and-paste and chalk-and talk).

Coming away from the detail here, I want to suggest that discussion really comes into its own when two key factors are in place.  Firstly, when it is reasonable to suppose that participants have some knowledge, understanding, views on the topic in hand which can then be built on.  Secondly, when the facilitator of the discussion does not have in mind a definite fixed point to finish.

So, I can think of many times when I have been involved in discussions which have been frustrating because one or other of these two points have not been in place.  So, I remember on one occasion, again in my previous post (or previous but one) when we were in mixed subject groups doing micro-teaching exercises.  I can't now remember exactly what one particular student's slot was about, I do remember that it was an aspect of A level psychology and he set up a discussion saying something like, "Everybody's views are equally valid."  Really?  Your psychology degree counts for nothing, does it?  My views on psychology, a random collection of ill-thought out bits and pieces gathered over the years, can stand alongside the views of Jung and Freud?

Part of the confusion here, I think, is that it is considered good practice in teaching to give as much ownership of the process to the learners as possible, to think of the role of the teacher as the person to facilitate learning rather than to impose it autocratically.  The problem here is that, taken too far, we deny youngsters the benefit of knowledge and experience gained over considerable periods of time which could be beneficial to them.  So, coming back to Pythagoras, I can - and have - set up an activity which guides pupils towards coming up with the formula themselves.  Only an incredibly exceptional minority of people will ever get to Pythagoras unguided - Pythagoras himself being one of them, of course.

And similarly, I can think of many occasions in different contexts where somebody has apparently set up an open-ended discussion, somebody (often me with my big mouth) expresses a view which is then deemed to be 'wrong', as we then 'decide' what it was that the leader always had in mind at the beginning.  The idea that a genuine discussion had taken place was simply a sham.  Speaking personally, I have no problem with leaders taking a lead, deciding on a course of action and then communicating it, with explanation, to other members of the team.  I do have a problem when this happens under the heading of 'discussion' - 'facade' comes to mind.

So, where does this leave us?  Do what you need to do with boldness, clarity and honesty.  If you have knowledge on an area which other people can learn from, find ways of communicating this effectively and sympathetically.  If you are in a leadership role and have decided on a way forward, be clear that is what you have done and why.  Discussion is an invaluable teaching method - but like everything, it has its limitations and should not be used as a 'catch all'.


One final thing.  I decided I wanted to cook prawns in a creamy garlic sauce yesterday, not quite sure why but that is what I fancied.  So I went to the supermarket and bought a packet of frozen prawns which quite clearly said on the packet, "Cleaned and ready to cook".  Then to spend 1/2 hour before cooking deveining them all.  I would say that I've been here long enough that I wasn't surprised by this, but nevertheless.....  Thank you for reading, I'll be back again soon!

2 Comments to 22/5/16: discussion as a teaching method:

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Angurini Stephen on 23 May 2016 21:33
Thank you Dr Geoff for your views on discussion as a method.In active teaching and learning methods(commonly referred to as learner centred methods) introduced by BTC-TTE project in teachers' colleges in Uganda,discussion,demonstration, brainstorming,think-pair and share are regarded as techniques. Problem solving, learning stations, learning contract and project are considered as methods.What hasn't made sense to me is the difference between methods and techniques.I need your help.
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Geoff on 24 May 2016 00:01
Good to hear from you Stephen, great that you're reading my blog! Re: the difference between methods and techniques, to my knowledge there is no generally accepted, clear difference between these two things. If I'm understanding correctly, the underlying point being made by the trainers you have been working with is the moving from the general to the particular, from overall what we are trying to achieve to the precise mechanisms for achieving it. So, in the examples you give, techniques are more specific than methods. At least, I think this is the distinction they're making, meanwhile, trust you're well, Geoff

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