Category Archives: Learning

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?

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Change of direction

Last year, I wrote a post about what I wanted from my academic future. I cockily ended that post with “I’m sure I won’t change my mind!” – I should have spotted the potential for irony. Although arguably, I’m not changing my mind. I’m not regretting the decision I made at the time. It’s just that new information and experiences have arisen, and now I am making a new, different decision.

I’ve almost finished the first year of my distance-learning degree, which means it’s time to choose the modules for my second year. A few weeks back, I was in a bit of a crisis about the decision. I was torn (as I have been for most of my life) between psychology and physics/maths.

I say physics/maths, because they are in the same category to me. They fit together and they belong together, and it’s the combination of the two that I’m interested in. Psychology, on the other hand, does not fit together with them. They are two very incompatible subject areas. And don’t bother trying to find a compromise, either. I don’t care about “the psychology of the universe” or “the statistics behind psychology”. I am interested in them in two extremely different, separate, and irreconcilable ways.

Then I had something of an epiphany. I realised that, while I am interested in both areas, I only feel a need to contribute to existing knowledge of psychology. I want to gain new information about autism, and improve the way that people understand it. Whereas I just want to learn about physics. Seeing as my ideal career (in either subject) involves higher study and eventually research, it makes sense that I should choose the one I feel the need to contribute to.

But, then, not long after that epiphany, I had another one – sort of. I watched The Theory Of Everything (the film about Stephen Hawking). And I was overcome with the urge to be a physicist. Everything about the film just made me think “this is the kind of life I should have” and “those are the people I belong with” and “these are the things I need to learn about”. I was reminded just how strongly I feel about physics, in a way that I’ve never felt about psychology. I realised that there’s no point in going with a ‘practical’ choice if it goes against the way I actually feel about the options.

There’s also the fact that it’s possible for me to spend time contributing to psychology without getting a PhD and being a researcher. I’m doing that right now! I am blogging, surveying, working on a book, and I’m about to become an assistant presenter for educational courses about autism. By virtue of my own autisticality, I am already a kind of psychology expert. I don’t need to worry about losing touch with my interest in psychology. I’m always going to be autistic and it’s always going to be relevant.

Whereas I have been reminded that it is worryingly easy for me to lose touch with my interest in physics. My science module this year finished slightly earlier than my psychology module. And in the few weeks since I finished studying it, I am already missing it! But it’s difficult to stay involved in science at the level I am interested in, without formally studying it. I am going to carry on blogging and writing and thinking about autism no matter what else I’m doing with my life. But if I really want to be involved in physics, then I have to actually make it happen.

So, I’m making it happen! I’m switching to a specific Maths + Physics joint honours degree, and I’m going to be a physicist.

…I think.

 

Choices

Recently I’ve been thinking about my academic future. I started a distance-learning degree in October, and I quite quickly decided to switch from part-time to full-time. Which means deciding which course/s to add to my workload, because the degree is totally open – so every course is optional.

The course I’m already doing is in science. The main things I was torn between for my next course were maths and psychology. Maths has always been my best and favourite subject. But psychology is important to me because I want to learn about how people – and especially autistic people – work.

At first glance, it seems like maths should be the first choice. It’s been my strongest subject since before I can remember. Anyone who knew me as a kid would always say maths is what I “should” be doing. And I can understand that. It’s even what I think instinctively. But when I think about it a bit more carefully, that’s not the case.

Maths is really important to me. It’s pretty much the first language of my brain. When I reach for an analogy, I reach for mathematical concepts without even noticing. When I’m trying to find a way to understand something, I’m really finding a way to turn it into maths so that it can fit in my brain.

But that doesn’t actually mean that I should be studying maths, or that it’s necessarily my favourite or most important subject. A person who thinks in words does not assume that they want to study language. They use language to process whatever they do study. It’s the same for me, with maths. No matter what I learn or think about, I will be using maths constantly. So I don’t need to worry that, if I don’t study maths, I might lose one of my favourite subjects.

Whereas that is more likely to be the case with psychology. I think about autism a lot, but it’s the subject of my thoughts – not the language of my thoughts. Which means that if I do want to think about autism, I have to actively decide to.

So, I’ve decided on a psychology module. Part of the reason I’m posting this is so that I can read back over it if I start doubting my decision again. But I don’t think I will!

Learning in patterns

I wrote a post about ways of thinking a while ago, referencing Temple Grandin’s “thinking in pictures” quote. Since then, I’ve read her book, The Autistic Brain. I was really excited to find there was a section about thinking styles. She mentioned that lots of people had criticised her claim about all autistic people thinking in pictures. Then she went on to talk about a third thinking style. Words, pictures, and patterns. Patterns is very clearly the way I think – I’m really excited to find that I independently came to the same conclusion as a well-respected researcher! (albeit using slightly different words).

I’ve talked before about how I’m not very good at generalising. I can’t learn from examples, because I can’t turn the example into an overall concept in my head. I either need lots of examples (and I mean, an impractical amount of examples: too many to be reasonable), or I need the overall idea explained first. Examples are a way for me to check that I’m understanding right, but nothing more than that.

The combination of these two things: thinking in patterns, and having trouble generalising, means I learn in a bit of a strange way compared to some other people. Other people’s understanding will gradually increase in little steps as they gain more examples and information. Whereas my understanding will stay at absolutely nothing for a long time, and then suddenly jump up to ‘completely understanding everything’. There isn’t any in-between. If I there’s even one small element of a topic that I don’t understand, then it means I don’t understand any of it.

This has confused teachers (as well as other people), because I can seem to get irrationally upset when I don’t understand something very minor. Because for me, it’s not just “I don’t quite get how to do this specific type of equation, but I have the general idea of most of the rest of the topic”. It’s more like “I don’t get this specific type of equation, so I have no overall system which encapsulates everything, so I have no way of understanding any of it”. It’s not me being over-dramatic or exaggerating, it’s a genuine difference in the way I learn. I am unable to understand something bit by bit, it’s all or nothing.

This does have its benefits when I want to explain something to someone else. If I understand the whole topic, then I have it fixed in my head. There’s a complete system which contains every part of it connected together. So I can give an overview of the ‘shape’ of the whole system, and I can also focus on smaller parts if someone has trouble with a specific bit. And I can look at it from different perspectives to try and find new ways of putting it if someone doesn’t understand at first.

I have only known a few of people who explain things in the way that works for me. Those I can remember: my secondary school science teacher, my A-level maths teacher, and my dad. They are all people who either ‘get’ that I need patterns to understand, or who naturally think in patterns themselves. Any time I’ve tried to learn something that hasn’t been from these people, it has involved me working desperately hard to process all of the information at once and distil a pattern from it myself. It’s inefficient compared to the way most people learn things, but I’m pretty good at it by now.

Education

I recently had a disappointingly familiar experience. I was referred to a group CBT course – not group therapy, but more of a series of small group lectures to learn some techniques and exercises.

After a few of the weekly sessions, a recognisable feeling started to creep over me. The content was interesting enough, and the course was not run particularly badly. But I absolutely knew that it was not providing anything for me. I could learn the information much more efficiently, quickly, and enjoyably, if I was at home alone and not in the lecture itself.

I suppose a lot of NT people find it helpful to learn in groups. At the CBT course, the other participants seemed to enjoy telling and listening to stories and ideas from each other. But all I could think when they were talking was “When do we get back to the point? I’m not learning from this.”

This is an experience I have had repeatedly throughout education of all kinds. Initially, I can see the appeal of interacting with people who have similar interests, and of being able to directly interact with the educators themselves. But that appeal is extremely short-lived and soon runs dry when I’m faced with the exertion required to keep it up.

I have to push myself to go out, travel to wherever it’s happening, find my way into the right room to settle in, interact with my fellow learners, interact with the educator, keep up with verbal explanations, keep still throughout the lesson, concentrate solidly with no chance of a break, then lots more interaction followed by finding my way out and back home again! And all of this in exchange for learning something which I could understand much more quickly and easily if I just read written/visual information alone and in my own time.

I can understand the appeal of a social situation involving a certain subject, but not when I’m learning the subject. For me, those two things have to happen separately in order to be efficient or enjoyable. If I’m in a situation which has both, I have to just pick one to focus on (generally the learning), and I still find it much harder because I’m distracted by the other element (i.e., the people socialising around me).

I’m starting a distance-learning degree soon. It will be an interesting experience, because it seems like it will be the perfect learning style for me. But I’m wary of getting my hopes up too much. Maybe I actually need something that’s in-between traditional classroom learning and completely solitary learning? I guess I’ll find out.

Educational accommodations

I’ve recently found myself in an interesting situation. I’m about to start a distance-learning degree, and it’s the first time I’ve entered education with a formal diagnosis behind me. Suddenly I’m being inundated with help and accommodations that I don’t know what to do with!

It’s strange. The only experience I have with education is that when I have zero accommodations, it’s clearly not enough. But I don’t actually know what kind of accommodations I do need, or how much will be enough. So I’m having to try and imagine what things might help me, when I don’t actually have any evidence for it. Most people my age who are starting a degree will have plenty of history to rely on: “In college, they gave me an extra week on all my assignments”, for example.

But I don’t have that. All I have is a history of a few desperate attempts to get me to attend my exams by offering me the chance to sit in a smaller room or take a break. None of which were particularly effective by themselves.

The other complicating factor is that distance-learning is already very different from any education I’ve had before, so I can’t directly compare it to my previous experiences. Usually the most stressful aspect of education is sitting in lessons themselves – and there won’t be any lessons this time.

I’m left doubting whether I will actually need any accommodations at all  – or whether the different experience will be enough to help me cope. Only time will tell, I suppose.

Ways of thinking

There’s often a lot of talk about the way autistic people think. Anyone who’s heard of Temple Grandin has probably heard that she describes ‘thinking in pictures’ – her thoughts flick through her mind like photographs. Other autistic people say they think in words – with no visual element at all.

I’ve thought about this a lot, because I wasn’t sure whether I was a words or pictures thinker. I eventually decided that the reason I had trouble figuring it out was because I’m not a words or pictures thinker. I know that I don’t think in pictures, because I don’t visualise photo-real images of things. Not every thought has a visual element attached. I know I don’t think in words, because I have to translate my thoughts in order to communicate using words  – which is sometimes difficult to do.

I guess the best way to describe my thoughts would just be… concepts? My thoughts take the form of maths, logic, spatial relationships, sets, diagrams, graphs, and other non-verbal things. They aren’t visual in the sense of being perfectly accurate or precise images. The visual element (when it’s there) is just a way of representing the relationships between things.

This is why my thoughts are sometimes easy and sometimes difficult to translate. Certain types of concept are a lot easier to express in words. For example, we can easily say something like “there is more of this than of that”. Others are almost impossible to translate – at least not with any language I know (perhaps if I was fluent in advanced mathematical logic I would be able to express myself better!).

When I was first talking to my dad about autism and the inaccuracy of the linear spectrum, I ended up drawing endless graphs and diagrams to try and make my point. It took weeks before I was able to find the words to really explain myself, and even now I’m not sure I’ve quite said what I wanted to.

I often resort to using diagrams to express myself. Sometimes it works well enough to communicate my point to someone. Other times, just making the diagram concrete allows me to ‘read’ it and form a verbal description. And sometimes the thoughts are so abstract that I can’t find a way to visually represent them – it would require a four-dimensional graph or a moving animation or something else I can’t do with a pen and paper.

Generalising

For a person that’s supposed to be really smart, I sometimes seem to miss the exceedingly obvious.

I am usually surprised by the twist at the end of a children’s film. I never realised that an episode with two separate storylines is supposed to draw attention to the parallels between them. When I learn a new technique in a video game, I often fail to identify future situations which require the same technique – even though I probably learnt it very quickly in the first place.

I guess I have problems with generalising. This often looks like problems with learning in the first place, but it’s very different. I’m a fast learner, and it usually only takes me one ‘try’ to get something into my memory. My difficulty comes in recognising future situations where that new knowledge is relevant or useful.

My brother and cousin found it hilarious when I played the game Antichamber. Every time the game demonstrated a new technique, I would learn it quickly. And then completely fail to use it in the challenge that came immediately afterwards. They’d ask “Don’t you remember that thing you just learnt to do using eight blocks?!”, and I’d answer “Yes, I remember! But there are ten blocks here, so obviously I don’t need to use it now.”

During the climax of every children’s film I ever watch, I am convinced that the main character is about to fail. If you stopped at that point and asked me suggest how the story would be resolved, it would take a lot of concentrated effort for me to make a guess. Never mind that every other children’s film in existence has the protagonist succeed with a ‘happy ever after’.

In fact, it’s difficult for me to even identify the ‘climax’ or ‘build-up’ or ‘resolution’ of a story of any kind. I learnt about the basic story arc in primary school when we were taught how to write our own stories. But it’s very hard for me to actually apply that information to other experiences. Even now, I can do it – but it doesn’t come instinctively. Unless I am actively prompted or reminded to try and consider a story in that way, I am unlikely to do it.

Maths is my absolute favourite – and strongest – subject. But I’d often have trouble with the mixed tests that came at the end of a chapter. Suddenly I was no longer doing exactly the same process with different sets of numbers. Now I was expected to look at a question and somehow figure out which processes needed to be done. I have frequently had to ask a teacher for help on a question only to be told something along the lines of “Just use Pythagoras’ theorem… you learnt about that years ago.” And of course it’s obvious when they point it out. But if the question was in a chapter that made no mention of Pythagoras, then my brain simply would not make the link to tell me what information was relevant.

This is also why I often forget things which should be easy to remember.  “Don’t forget to empty the dishwasher tomorrow”, and I nod and agree as mum tells me it when I’m going to bed. Then the next day, the knowledge is just gone. If someone asked me “What did your mum ask you do last night when you were going to bed?”, I would remember immediately. But of course no-one does ask me that, so the information never gets recalled. I can walk past the dishwasher overflowing with plates and still not process the fact that I have an important piece of information about that.

And this is why lists, notes, and reminders are what keep me on track. Without external help to recall and use the right information in the right situations, I would never get anything done.