Monthly Archives: January 2016

Swimming pool theory

Autistic people are often stereotypically described as being detail-focused or unable to see the big picture. But to me it’s always felt like an unsatisfactory description to call someone either detail-focused or “big picture”-focused. It’s impossible to do one without the other. I think the more significant factor is about how naturally or easily a person can go from one to the other, and how they use them to learn. Me and my dad have been working on a theory to describe the different learning styles that arise from this – it starts with an analogy.

The swimming pool

Imagine that the system of knowledge you want to learn (say, the rules and applications of a certain mathematical method) is a big, oddly-shaped swimming pool full of water. You get dropped in the middle of the pool, and the aim of learning is to map out the entire area – to find out where all the water is and where it ends. There are two main ways to go about this, which I’ll call the extrapolation method and the interpolation method.

Extrapolation
You start your map of the swimming pool by taking note of the spot you’re in when you start. You can map a certain distance around you that you can see – say, a few feet away from you in all directions. You start to paddle around, gradually mapping the new areas that you swim to. Your map grows from the place you started, in whatever shape you decide to paddle.

Gradually your map expands at the rate that you swim around. Eventually, you will have paddled around enough to have a pretty accurate map of the pool. You’ll probably have the odd patch which isn’t mapped, but you’ve got most of it recorded accurately.

Interpolation
The interpolation method is like being extremely short-sighted. You can’t just add the surrounding area to your map. You might be able to keep track of the path you take, but you can’t map a large enough area around you for that to be an efficient way to learn. You can barely “see” beyond the end of your nose. You’re not aiming to map whatever area you swim to. Instead, you have one clear goal: you swim around, looking for the edge of the pool.

Once you find the edge, you stick to it, and start making your way along. You carefully map out the line of the edge, all the way around. Eventually you get back to where you started – you’ve got the entire outline of the pool mapped. In one instant, your map of the entire pool fills in. You know that the pool is a solid body of water, so you immediately know exactly where the rest of the water is.

Beyond the swimming pool

In case it’s not obvious, the swimming pool part is largely irrelevant – it is nothing but an analogy. The point of the theory is that there are two main ways of learning. The difference is which “direction” a person can most easily move in – from details to general ideas, or from general ideas to specifics.

Extrapolaters are good at starting from one particular spot and finding nearby information (they can see a reasonable distance out across the water from wherever they are). They can create a fairly complete knowledge system just by moving from specific to specific, and example to example. But they have less ability to fill in gaps just from finding the edges of the system.

Interpolators can’t easily see from one specific to another or learn lots of details in one go. But they are good at finding the outlines of information and filling in from there. Their instinct is to find the edges of what they want to learn, which makes them good at getting systems of knowledge without any gaps.

Neither of these methods is better than the other, of course. They both have different perks. The extrapolation method increases your knowledge gradually as you go along – if you stop halfway through the learning then you have half of the knowledge. The interpolation method ensures that you have 100% of the knowledge once you’re finished – there’s no chance of any unmapped patches by the end.

But I don’t think the method a person generally uses is a just a choice every time. I think it’s mostly defined by innate traits like how much a person can “see” around the details they are focused on, and how easy they find it to fill in an area that they’ve outlined. Based on those abilities, each person will have an instinct for how they learn best – and might not even realise that other people do it differently.

There’s also no clear binary distinction between the two methods. Each person just has different preferences and tendencies – some people might have a strong drive towards one method, some people might find it easy to switch between the two. And I’m sure I’ve oversimplified my explanations of these learning styles, and not everything fits into them anyway.

Teaching and learning

Most teachers start a lesson by giving examples of the problem – challenging students to find the “big picture” themselves is supposed to be an effective way of teaching. And it must work well for a lot of people, otherwise it wouldn’t be so popular. Extrapolators can instinctively generalise from being given examples, and find it easy to add new knowledge in little chunks at a time.

But I’ve always found it difficult – if not impossible – to learn general concepts from examples. I can’t work out the “big picture” if all I’ve been given is specifics. When I’m taught in this way I end up frantically paddling around, barely able to see where I’m going, and desperately hoping I’ll find an edge that I can stick to in order to teach myself the rest – all while I’m expected to have already started filling in a map of the places I’ve passed through.

 

Extremes

I don’t know whether this is an autistic trait. My instinct tells me that it could be, but I also have a strong suspicion that my instinct will turn out to be wrong. Both me and my dad are extreme systemisers and extreme interpolators, and so my clearest idea of an autistic thinking style is based on that. But I have no idea whether it’s accurate for other autistic people, or if I’m just assuming there’s a connection because they happen to coincide within my family.

My secondary hypothesis is that the learning style (interpolation or extrapolation) is not the autistic trait in itself, but that it’s an autistic trait to have an extreme preference for one or the other. That would correspond with the way that autistic people often seem to be at one end of a bell curve or the other, in things like sensory preference and various other traits.

I’m really interested to hear input from other people on this. Are you an extrapolator or an interpolator (or maybe you think my distinction is meaningless)? Do you think a preference for one or the other is an autistic trait? Or that a strong preference in either direction is? Do I have completely the wrong idea trying to describe things this way?