Matthew Oldridge, a maths teacher on secondment to the Ontario Ministry of Education in Canada, has just published an Edutopia article on The Playful Approach to Math.
Interestingly, Ontario finds itself at a crossroads. For many years, it has been a standard bearer for fuzzy maths, eschewing the supposedly rote memorisation of procedures in favour of an approach where a basic arithmetic problem is over-intellectualised and performed in five different ways, all in the context of problem-based or inquiry learning. Predictably, this approach has coincided with a decline in maths performance.
In this context, it is therefore interesting that Oldridge rows back a little from the extremes of fuzzy maths. It is barely detectable among all the talk about how, “Play moves math instruction beyond rote memorization to a more expansive understanding of mathematics,” and yet, at one point, Oldridge does suggest the need to memorise multiplication facts. Well, at least as far as six times six. This limitation is because multiplication fact practice has to be performed by rolling two dice and dice only go up as far as six (Oldridge is clearly unfamiliar with Dungeons and Dragons).
The reason for the dice-rolling is Oldridge’s claim that, “Play is irrepressibly human, and we can play to learn”. This is true, up to a point. Play is perfect for learning what evolutionary psychologist David C. Geary refers to as ‘biologically primary knowledge’ – language, basic social skills, folk psychology and so on. This is knowledge we have needed to acquire since the dawn of humanity and so we have evolved mechanisms such as play as a means for acquiring it.
Maths is different. It is a far more recent cultural invention that Geary would term ‘biologically secondary knowledge’. This distinction is key to understanding cognitive load theory. When dealing with biologically secondary knowledge, we have to process every new item in our limited working memory. Presenting new biologically secondary knowledge alongside all the variables associated with a play situation is an obvious way to overload working memory.
To be fair to Oldridge, this does not preclude play from being used as a form of practice once students have grasped the relevant concepts. However, although Oldridge describes using play for practice, he does not make this distinction.
Oldridge is also ambiguous on the use of guidance. Briefly, when Kirschner, Sweller and Clark famously criticised approaches such as problem-based learning as deploying ‘minimal guidance’, adherents of these methods retorted that they use loads of guidance. For novices, a more guided approach will always be better than a less guided one, which is why fully guided, explicit teaching is the most effective approach of all (note that explicit teaching is a whole system and not just a bit of direct instruction here and there).
So when Oldridge promotes ‘guided play’ it can be seen as partly an attempt to preempt this criticism. However, we can get a sense of what he really means when he suggests, “There is a sweet spot, often about 30 minutes into working on an interesting problem, where ideas start to become solutions.”
This is an oddly faith-based approach. I would never let my students struggle without a solution to a problem for this amount of time. That’s my definition of ‘minimal guidance’. There is no reason to believe they will eventually figure it out or that there is something magical about 30 minutes. Instead, there are plenty of reasons to predict confusion, frustration, demotivation and distraction. And even if they do eventually figure it out, that’s 30 minutes of time wasted.
Being in favour of play is a lot like being in favour of peace and motherhood, and it will certainly get you published in Edutopia. However, when you examine it more closely, it’s merely a repackaging of the same bad ideas that have harmed students’ understanding of maths in Ontario and across the English-speaking world.
Let’s not play dice with our children’s futures.