When I was still teaching in the traditional way (by which I mean pre digital media network technology based way), the scope of what I imagined the effects of my teaching might be on the world was largely constrained by the operational principles of the educational system in which I worked. One teacher in one place can be assumed to make no real difference to the way that the world goes. The inspirational teacher story, based on real events (I am not sure how closely), of Freedom Writers is a pretty striking counterexample to this fatalism, but this story very starkly highlights just how much a teacher who wants to really redress the failures of the system they work in must be prepared to sacrifice to do so, and for a victory that may be tremendous in terms of the lives affected by it first hand, but which is in the end a drop in the ocean. I chose to work in EdTech because of the possibility of building functionally superior education systems that could offer people hopeful possibilities that the world’s failing educational systems and institutions increasingly could not.
In vastly more concrete and functional terms, I had ideas about how technology could help make learning mathematics and related subjects much more accessible, so that learning such subjects successfully could be a realistic aim for a majority rather than merely for a minority. This goal, and how it might be achieved, has two appealing qualities; firstly, it is tremendously rich and deep, and secondly, it seems obvious that it is a worthwhile endeavour. So obvious in fact does the worthiness of the undertaking seem that until recently it had never occurred to me in any properly conscious way to even wonder if it actually was as important as I supposed. What reasons do I have then for thinking it good that mathematical understanding become much more widespread?
Giving some conscious deliberation to this question fairly rapidly made it clear to me that I was considering mathematical understanding as a proxy for the better use of a more general kind intelligence, something like Khaneman’s System Two thinking. A world of people in the grip of System One thinking is a world where everyone makes only unreflective decisions based on being convinced that what they know is by definition the only thing that they need to know. This is a world in which people only learn things the hard way, and anything too hard to learn is never learned. A pessimist might say that this is the world we actually live in, and there is some truth to that, but it is hardly the whole truth.
Accepting a healthy dose of pessimism, I must concede that learning mathematics (and physics, statistics, logic, etc…) does not ultimately drive out the demons of System One thinking even a little distance beyond the context in which these things are learned. As learning is detached from life in general, so are the fruits of that learning. One of the enduring themes in (some) EdTech dreaming is the notion of embedding learning in the broader pattern of living. Quite recently, this was a fairly prominent theme. M-Learning (both mobile and micro), lifelong learning, and learning on demand were popular buzz-terms. More recently, educational institutions (and the funds that they represent) have become more EdTech enthusiastic. Project based learning, based around hubs that map conveniently to existing educational infrastructure, has taken more of a foreground position since then. PBL could be a way of merging the world of work with the world of education; schools becoming makerspaces promoting design thinking and STEM skills.
When I was teaching, I would stress to my tutees preparing for higher education or employment, that they needed to be giving major consideration to what they could learn to do that would not be easily automatable in the near future. Jack Ma took this idea to something of an extreme in the speech where he argued that students should not be learning anything that a machine could do, because machines will outsmart them soon enough. Ma’s extreme statement does not perhaps go very much farther than Ken Robinson’s ideas on individuality and creativity. Robinson is critiqued rather well in this blog post, and I concur that Ma and Robinson are wrong to say that we can avoid being outsmarted by machines purely by doing different things than they do, because if we do not understand what machines do, then how do we know what would be different to that? I should have said to my tutees (not that they believed my warnings) that they should anticipate that in their future they would be competing for jobs with a computer, and that like in any other competition, they should want to know anything about their competitor that they could find out in case something in that would help them to win the contest.
The question that bubbles up from these insights (hopefully) is the question of what kind of skill and/or intelligence is really going to be helpful for most people, now and looking ahead. In the twentieth century there was almost no question that what basically mattered was IQ. The dominance of the importance of IQ has been such that it has become uncontroversial for people to see IQ as a synonym for intelligence. I would argue that IQ is more properly a particular kind of intelligence, but the only kind that can effectively be systematically measured, and the kind that generally mattered most in a world overwhelmingly organised along systematic approaches to solving problems. Human evolution, and the ways of learning that come most easily to most humans, are not particularly systematic, they’re far more heuristic. Heuristics can be very effective in many situations, but they don’t tend to travel well or to scale well. The effectiveness of heuristics in the particular niches in which they apply can easily act as a disincentive to painstakingly learning systematic alternatives to the heuristics, as the heuristics so often work better (up until the point where they don’t).
The clash between the short-term gains versus the long-term opportunity costs of relying on heuristics is something that I think could be ameliorated in two main ways.
The first way would be to teach the heuristic and systematic approaches to learning things in parallel, only making connections when learners are interested in making them. There exists a qualification called “Use of Maths”. The name is misleading, the course content is barely any different from applied maths, but what if “Use of Maths” did exactly what it said on the tin? What if it was a subject that taught people heuristics that would be helpful in their lives, things that were mathematically derived but didn’t need to be understood systematically. People do not need to know how to calculate compound interest to be taught and to remember that a 25% APR on a loan is not a particularly good thing to be offered. The collection of useful facts that people can know about dealing with money, and more generally with risk, as well as how to better recognise manipulation and deception relating to quantifiable events, are things that can be learned pretty much in isolation from their systematic underpinnings, by whatever heuristic methods people find helps them to remember the key facts.
The second way of aligning heuristic learning with the painstaking effort of systematic learning would be to make systematic learning less painstaking. One way of doing this would be through interacting with artificial environments in which heuristics applied that taught things which corresponded rather than clashed with what systematic approaches to learning would teach, such as games that were constructed to teach mathematical procedures while also being enjoyably playable; your brain would like them even if you didn’t.
What I’ve more and more come to realise is that no one really knows with much surety what the important things are for people to learn to prepare them for the future. I do still think though that whatever approaches reduce the insight lag between people’s System Two and System One thinking ought to be worth trying.