“If you wish to forget anything on the spot, make a note that this thing is to be remembered.”
– Edgar Allen Poe
“The palest ink is better than the best memory.”
– Chinese proverb
This is part of a series offering my views on some problems with UK maths education. The first part looked at the state of affairs with regards to GCSE and PISA results, the second part looked at my attempt at a diagnosis, the third part looked at pre-existing maths education success stories, the fourth part looked at how textbooks offer the largest potential to improve pedagogy across the nation, and the fifth part examined the role of hard work and homework. This part looks at the problem of memory in maths education.
In my career as a maths teacher, I flip regularly between deep job satisfaction and mild despair.
Don’t get me wrong – I absolutely love my job. Most maths lessons I’m teaching pupils some sort of mathematical process. Most of the time pupils then perform that process with aplomb. Whiteboards with correct answers go up, I’m happy, the pupils are happy, I go around and mop up the remaining few pupils who weren’t quite 100%, put up some answers, and by the end of the lesson I and my pupils are feeling pretty pleased with ourselves.
But then comes the test. Even if it’s literally a few days later, and even if pupils face literally identical questions, their answers end up containing every confusion & misconception under the sun.
Whilst marking tests, I’ve often felt like Sisyphus – the mythical Greek figure condemned to roll a boulder up a mountain, watch it roll back down, and repeat forever. We strain and push our pupils up a mountain of mathematical understanding on a particular topic. After hours preparing pedagogy & teaching materials, then 60 minutes of communal graft in the lesson itself, it feels like we might have gotten somewhere with that topic. Then… fast-forward to tomorrow / the next week / the assessment, and those same pupils will literally deny having even heard of that topic before. ‘Gradient? What’s gradient?’
Yet I can’t write this solely as a complaint. After all, throughout my career, pupils have usually followed what I have told them. Lessons have gone well. I’ve explained things; pupils (seem to!) “get it” and show they can do what I just modelled for them; we move on. So, if pupils are doing what I teach them, their forgetfulness must partly stem from a defect in my teaching. (Of course, I’m written previously on how hard work and homework plays a huge role in maths learning, so I can’t take sole responsibility for this failing: I constantly talk about the importance of independent revision, and many of my most forgetful pupils are those who give in shoddy, low-effort homework and never revise.) Nonetheless, there must be more that I can do.
The problem in a nutshell? I can’t think of a better way to put it than in Bodil’s phrase: ‘a lesson is the wrong unit of time‘. Much of our UK educational culture is focused on lessons: lesson objectives, lesson grading, showing progress within a lesson. As a result, we plan topics in lesson-sized chunks (‘addition this lesson, subtraction next lesson’), and we judge our success in lesson-sized chunks (‘the exit tickets show me they all learnt how to answer the key question this lesson’). But if we’re solely focused on lessons, then of course very little gets retained beyond that. Of course pupils forget. After all, as teachers, all we usually aim and plan for is for the pupils to ‘get it’ in the hour itself. To put the problem in reverse: we don’t teach with an eye for long-term memory; therefore pupils naturally don’t remember over the long term.
How big is this problem? And what can we do about it?