Time to be serious.

Recently, a colleague of mine point-ed (damnit) out two things about my blog in recent times:

1) It has become very AI-centred

2) It always has a pun in the title.

Well, I do like to be consistent... but, at the same time, a change is as good as a rest. So, this week I thought I'd take a break from the AI-spam (especially since, spoiler alert, my Differential Equations applet is still moribund) and talk about something else.

I recently purchased Craig Barton's "Tips for Teachers guide to.... Atomisation". I specifically used the word 'purchased' there, as finding time to read it has so far been beyond me. It's high up on my to-do list... the problem is that 'high-up' is relative to the length of the list, which is becoming so long that it seems ever-further out of reach to read it myself. If only I could ask AI to read it for me and... no, wait, I'm not allowed to talk about that.

So, what have I gleaned from it so far? Well, firstly (spoiler alert) - Atomisation is incredibly powerful. The idea of breaking up a concept into its "smallest meaningful parts", and understanding how best to communicate each of these, link them together etc... of course it is. But also, how easy it is to get this wrong - and to get it wrong in a way which a) makes you think you're getting it right, and b) actually creates even more issues than you could imagine.

I'm stuck on such a simple issue, and one which I've genuinely never considered seriously in all my years of teaching (or, at least, not considered to be an issue). Consider the following questions:

• I invest £4000 into an account paying 3% compound interest per annum for three years. Calculate...

• Solve 2x + 2 = 8

They're perfectly sound questions in their own right. We'd all know as maths teachers how to explain them to our students. But... they have the potential to create misconceptions. Let's think about example two and how we'd explain our first step... we're telling them to take away 2 from both sides, yes? Of course!

Except... which 2 is that?

We know it's the one being added. We know we're using the inverse order of operations. We know what we intend. That is the expert paradox in a nutshell - we perceive no difficulty, and perhaps don't even smell any danger, we see no way for the learner to perceive a difficulty. But we've actually created the danger for them - it's akin to stopping our students in the middle of a busy road to lecture them on their behaviour crossing roads and how they need to be more careful!

I do this all the time (make up poor examples, that is, not lecture students on road safety mid-dual-carriageway). Sometimes I even do it deliberately - thinking that if I show them the danger, they'll inherently understand better what to do, how to avoid it... and it's utter poppycock.

It's an implied arrogance that I think I can generally create a good "I do" example off the top of my head. Maybe more often than not I can. But those times I don't... I create so many potential perils that needn't exist for my students in the knowledge-acquisition phase of a lesson.

So, the TLDR here - think carefully about what makes a good example. We need to do everything we can to ensure our students can focus - entirely focus - their limited working memory and cognitive capacity on understanding what is being demonstrated, not trying to untangle poorly-chosen values and decipher which two is the two to use and why there's a two there, too.