Mathematician’s Lament – Paul Lockhart

So – I put out the call to see if there were any voices of inspiration from #mathchat for my assignment and sure enough, I was rewarded. David Wees (@davidwees) pointed me in the direction of this paper and it was more than a little unsettling.

Paul Lockhart is lamenting the state of Mathematics education world-wide which, it would seem, has no redeemable characteristics at all. It’s variably compared to painting by numbers and music without an instrument, presenting what we know as school-based mathematics as “an empty husk”.

Reading the article, I could see what he means and agreed in many places but felt it was a little over egged. I’ve explored the area of the triangle as he states it, we think about puzzles and strategies in my classroom – I try to make students appreciate the process as much as the final result. I know that isn’t the whole story, but neither I think is Lockhart’s presentation. And I’m not alone.

The new GCSE curriculum has an increased focus on “functional mathematics”. The fear of some of the maths departments I’ve been in touch with about this is palpable – just how much are the students going to be expected to do on their own? We are trying to allow our students to look at a problem and apply some of the strategies they have developed. We don’t really have a very clear concept of how this will look on a potential exam paper nor do there seem to be a lot of resources available.

Is this preparing them for the real world? I don’t know. Lockhart argues that when we make things ‘relevant’ we have a danger of making them ‘irrelevant’. For example, do kids really care about compound interest? Rather, we should be asking engaging questions and exploring mathematics for it’s own sake. I think ‘functional mathematics’ has helped me do this more in the high-stakes classes but I think I’d have done most of it anyway.

Maybe I’m being blindly naive but I think there are chinks of this shining through. In the UK there has been major curriculum reform in Maths every two or so years for the past 10. In the midst of all of that, I have been part of groups of teachers who have been passionate about engaging and enthusing their students – in teaching for understanding rather than utility – in deep and meaningful learning.

I’m going to read Lockhart again and think about it more. I think for my question – Are we teaching the right stuff? – it adds a really interesting flavour and distinctive voice. It challenges the issue to be more “Are we even teaching Mathematics?” I’m going to be taking part in a conversation on this article this next Thursday with people I’ve never met in Canada and elsewhere. Exciting!

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Subject content – why do we teach what we teach?

For my current MA module – Contemporary Issues in Mathematics – I have to do this:

Assessment: A written report which provides a critical reflection of the chosen issues or concern, discussing the impact and suggesting ways to overcome areas of professional concern. (4000 words).

On the last taught day, I became quite interested in why our curriculum subject content is the way it is.  I couldn’t find much work previously done on this.  I found the work of Geoffrey Howson – he has compared the curricula as they stood in the early 90s of a wide range of European countries.  My problem is I can’t decide what issue I’d like to focus on.

I have a thought to analyse what we teach (subject content) and explore the impact of this on student engagement.  Does the subject content affect engagement?  Are we adequately preparing students for future lives and careers?  For example, should there be more on probability and risk? I can compare this with other countries and come to some kind of conclusion.  Hard to think about gaining data on ‘engagement’ – maybe post-16 take up?  [I’m considering this as a separate issue than how it is taught – I know this is a difficult separation to make but I need to think about manageable questions for this – I only have 2 months!]

I’m also concerned with curriculum reform in and of itself … how often it happens – how effective it is – how much impact it has in the typical mathematics classroom – whether it is done for the ‘right’ reasons or for gaining political capital – whether it is done with research involved or without it – who is involved in the process and are these the right groups.

I feel they are two distinct questions … the second one seems more meaty but not sure how much work has been done on it.

Does anyone have any thoughts or research that might be useful for this?