Linearity and learning

March 8, 2013 - My learning

When I was a teenager, my stepdad taught me how to hit a golf ball. He was a humanities teacher for most of his career (and a bloody good one – speaking as one of his former students), and a single-figure handicap golfer (and still is). Being the impatient teen I was, I’d get frustrated with my perceived lack of progress as he taught me the techniques (physical and mental) that I needed to master if I wanted to get better. I’d feel like I was working as hard as I could, but that I wasn’t getting better. Then, every now and then, I’d ‘spike’, and my skill (or at least the measure of my skill, namely my scores around a course), would move to the ‘next level’ – dropping a few handicap strokes in a short time before plateauing again.

To my stepdad, this was completely normal. He’d be constantly reassuring me during my ‘flatline’ times to just stick at it. That learning was rarely linear. That I just needed to keep working on the right stuff, and eventually things would ‘click’ – until I reached a level where my natural abilities were at their limit (which for me was around a nine handicap – although some would have argued that my impatience just finally got the better of me – and other still would just say that I got distracted by other things that teenage boys tend to get distracted by). He used to call it the ‘S curve’, a term used to represent that rapid learning that occurs early on in a single, clearly defined learning process. He’d also argue that during some ‘plateau’ times a learner would sometimes even go backwards a little, which required even more faith to keep working at the learning process. Its also worth noting that his teaching method was more or less linear and holistic – it was rare that he’d drop some ‘big new concept’ on me, or that we’d be working on one isolated component, it was far more fluid – but my learning (or even more specifically, my skill building) progress was anything but linear.

I’ve been teaching my son how to bowl a cricket ball for the last three summers, and I’m seeing exactly the same thing. I’ve seen the plateaus, his frustration when he’s not improving, and then the rapid ‘spike’ in skill followed by the acceptance (as kids seem to be able to do) that the new level is now the new ‘normal’. I’ve watched it happen with his batting (cricket again), with how he hits a golf ball (shown below, just because I felt like it), and to a lesser extent with his reading and music. I’ve made sure that with his sporting stuff I’ve taken video so that during the times when he is plateauing I can play it back and say to him ‘Remember when this was your ‘normal’? See how far you’ve come? Stick at it – the next level will come as long as you keep working at it.’

So why this post?

Aside from allowing myself a little nostalgia and reflection, the bigger questions are:

  1. Is this an ‘accepted’ phenomenon, that learning (or skill building) does not happen in a linear fashion, but as ‘stepwise bursts’ in mathsy language – and if so, what is the name of this phenomenon? It is similar to the concept of an ‘S-curve’ described here, but on a longer spectrum, with bursts of improvement happening while working towards a longer term goal (rather than learning a single, simple, clearly defined skill).
  2. Is the phenomenon more common among skills that relate to ‘muscle memory’ (like sport), rather than purely mental skills?
  3. How much is this phenomenon taken into account by educators, curriculum designers and administrators when attempting to construct an effective learning environment?

I asked a short version of this question to my (normally outstanding) Twitter peeps, and got little more than smart arse responses back (which is fair – that’s what I usually give them), so I thought I’d ask here.

Responses of all kinds very welcome 🙂

PS sorry I’ve not blogged for so long. As life’s complexity increases, so does the challenge of me finding enough time to write.

PPS thanks to Lawrence and Jas for coming up with the best response, and the wikipedia link, to my Twitter musings. Yet again I think how blessed I am to work with clever people.

3 thoughts on “Linearity and learning


Drex, I think your step-father was onto something, but “S curve” still makes it sound smooth and flowing. Learning just ain’t like that, even if it feels like that. As a third and fourth year uni student, I could barely remember what I learnt in first year, but I do know it formed the very strong platform to be able to develop an honours thesis and a couple of abandoned Masters theses.

Muscle memory is not isolated from the mental activity of the brain but very strongly tied to it. That’s part of the reason why handwriting is such an excellent learning tool; it links the physical and cognitive (and sometimes, the emotional). It takes time for neural pathways to be laid down. Some are accomplished quickly, others more complex and time consuming in their creation. Some are laid down, then overwritten, or abandoned entirely. This is the lumpy bit. I shall call it Lumpy Learning. Unless of course someone else already has done so. Then I’ll just cite them.

Tim Hunt

This definitely happens with mental activities. The one I know best is the board game Go, where this is a recognised phenomenon. Interestingly there seem to be certain levels where people commonly get ‘stuck’. That is, there is a rating scale from about 30 kyu to 1 kyu (and beyond) and many people stick at around 10k, 4k and 1k for a while.

Mark Drechsler

Mental note to myself – read (as pointed out to me by my favourite librarian) for some insight into this concept from a sporting perspective.

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