In yesterday's department meeting, I decided that we might do some maths. The reasons for this were threefold:
- To share some resources for teaching an upcoming unit on trigonometry, and talk about question design (e.g. prompts, multiple-choice questions, problems, ...)
- To add some variety to our meetings, to gain a different perspective. Our meetings are more often about *teaching* maths (see here or here or here and here) instead of *doing* maths. A few members of the department have expressed a wish to do a bit more maths in our meetings.
- An ulterior motive: To try out some activities that I will be using for this ATM session next Saturday.
I made the following observations during the meeting:
- Some people in the group did not work on the mathematics with others (unless encouraged). One pair worked closely together, while other members of the department worked more or less separately for much of the time.
- There were some signs of competition not present in our 'normal' meetings. This was more pronounced when working on problems-to-be-solved than during the work on the 'prompt'; there were comments made, albeit jokingly, about not getting the 'right answers'.
Perhaps it should have been unsurprising that there would be competition, but nevertheless I was surprised. We have been meeting weekly for the whole year and there has been very little sign of competition - in fact, on thinking about it, only when we do some maths! Is this competition due to something inherent in solving mathematical problems (with a single answer), or perhaps more generally due to competitive conditioning learnt at school?
Why were the group reticent to share? I would say there is a very high level of trust in our group - although I may need to explore this assumption. It is more likely that some members of the group were insecure in their knowledge of this subject matter, and perhaps in their subject knowledge generally.
Working with others can offer support, but can also make deficits in knowledge more visible. A couple of members of the group had interesting insights into the problems but did not get the opportunity to develop them fully - perhaps due to perceived lack of status or confidence.
The excellent book Working Together by David Sturgess gives some further insight into what might be happening:
Depending on how well the group know one another the expectations that people have of each other are a very powerful element in a shared experience. If a group is asked to take part in some kind of learning experience to do with an area of the curriculum that members of the group are teaching, they will feel threatened by the degree of knowledge that they feel they are expected to display. If they feel that they are expected to 'know all the answers' they will feel inhibited from confessing any difficulty; if they feel that they know nothing about this area of the curriculum, then they will not wish to display their ignorance in front of others. It takes time for a group to realise that knowledge is relative, and that it is rare for anyone to know all the answers, and that the least knowledgeable can have insights denied to others. Knowledge should be part of the experience to be shared so that anyone who at any time has knowledge denied to others can share it if asked to do so.
It is very necessary that previous expectations do not divide a group into those who know and those who do not.
This suggests that our professional competence is examined when doing (curriculum) maths together, and I am inclined to agree. But I think it is important that we can talk about, and do, the mathematics that we teach.
What might we learn from this?
I am left with the uncomfortable feeling that some kind of division in mathematical status was created during the meeting. I plan to start the next meeting by reflecting on the passage above, considering the ideas of status and the relativity of knowledge.
This brings to mind something I have been pondering for a while. It is generally considered a good model for maths CPD to include an opportunity to *do* some maths. But might this do more harm than good, considering that we risk creating space for anxiety, competition, and divisions in status? [I would be interested to know whether other subjects *do* their subject as part of CPD.]
The next time we do maths together, I would strongly consider not presenting problems-to-be-solved, thus reducing the expectation-to-know. [Also, did the fact that I had selected and completed the problems in advance add to a possible perception of a 'test' of subject knowledge? This might be alleviated by varying who presents the mathematical activity]
Finally, and most importantly - how can we use this experience to inform our teaching? I would conjecture that what we experienced in this meeting is also how students feel when asked to work on problems-to-be-solved, and when encouraged to work in groups.
How might students' learning be affected by the types of problems we pose, and the methods of working we ask them to adopt?