This message is not about maths, but I am going to use maths as the example, for reasons that I will explain later.
How do we help our students be better in Mathematics? More practice? Harder material? Further teaching? These are the most obvious, direct ways, for sure. We can trace a direct link from what we intend to do (maths tuition) to what we want to achieve (maths scores); that seems natural and obvious. In fact, if we want to improve maths, it might even seem a little perverse to do anything less obviously connected.
But that may not actually be the case; perhaps sometimes to pursue our goals most effectively, we may need to avoid pursuing them directly. In other contexts, that’s familiar – when, for example, the answer to a difficult, complex problem comes to you the day after you stop thinking about it. Sometimes, looking hard for something gets in the way of finding it. In school contexts, we know that teaching narrowly and mechanically may in the short term result in high test scores, but will not lead to long term educational gains.
The temptation is to go for the short-term solution; it’s understandable, and it happens because it’s easy to confuse the refined, finished, end products of inquiry – that is, the test scores, the perfect assignments, the quick answer – with the raw, crude inquiry which is, as I argued a few weeks ago, messy and difficult to control. Said another way, we need to guard against making the mistake of encouraging students to learn the solutions, rather than investigate the problems and engage in inquiry itself.
What does this mean in this case, for maths? Well, if mathematical knowledge and understanding is the pristine finished product, then perhaps we can retrain our focus on the process, and the inquiry. And if maths is about reasoning, implication and creativity, then perhaps looking at these qualities would be the best thing; and if that’s the case, it might mean that we can improve maths by doing no more maths at all. One school of thought has investigated the impact of doing philosophy for children. Philosophy is, after all, the art of thinking, and is explicitly about is about reasoning and implication. One project investigating the effect of a year of philosophy once a week on 2,000 students (Sharron and Coulter 1994) shows that compared with control children, large gains were made in Maths, in English and in reasoning. The results also indicated a significant improvement for formal reasoning and in creative reasoning (the capacity to generate new ideas, to discover feasible alternatives and to provide reasons) and the teacher’s appraisal was that children were markedly more curious, better oriented towards their work and better able to reason.
The results are quite astonishing (here’s a research paper and here’s quite a readable paper that digs into the ideas more discursively); and the message is a general one: that we need to take an expansive view of how to support learning. If we are helping students to think well, in ambitiously broad terms, then the knock-on effect will be great. Ideally, we will see the benefits right across the curriculum; and there is strong evidence that this approach works. It’s no coincidence that the factors identified in these papers are focussed around ideas like collaboration, communication and self-awareness – ideas that we consciously address across our Learning programme.
I chose maths as the vehicle for this message for several reasons. Firstly, I know it is a subject close to many parents’ hearts (myself included); secondly, because success in mathematics is less ambiguous and more easily measured than success in most other areas, but thirdly and most importantly, because it is precisely the distance between maths and philosophy that makes this research so compelling. If philosophy can improve maths, of all things, then there must be something in it! It’s one reason we have Theory of Knowledge as a compulsory Diploma Programme course, and we are thinking hard about what this might mean in other areas of the school.
