January 08, 2018

Mind the Gap! (between what is taught and what is learned) – Jeremy Burrows

I had three Latin teachers. Between them they taught me everything I know about Latin … and a whole lot more besides. It is this “whole lot more” which concerns me right now. We have taught something to a class, but that doesn’t necessarily mean that all of them (or even any of them) have actually learned it. In my previous career with HMRC I was concerned with closing the “tax gap”: the difference between the amount of tax which was owed and the amount of tax which was actually collected. In my new career as a teacher I am concerned with closing the “learning gap”: the difference between the things we teach and the things our pupils actually learn.

In mathematics, this problem is particularly acute. Children do not like learning mathematics. Boaler (1996, 1997, 1998) and Nardi & Steward (2003) have conducted studies which offer some very keen insights as to why this is: it’s all down to the way in which we are teaching them. When I learned woodwork at school, they didn’t just show me how to use a drill, tell me to drill 16 holes in a piece of wood, and then move on to the next skill as soon as they judged that I had mastered drilling holes (or move on even if they didn’t judge that I had mastered drilling holes). They taught me woodworking skills in context, and I actually used them for a purpose. I made a box, with dovetailed corners and a hinged lid. I veneered a chess board on the top and a backgammon table on the inside. I never finished it, but that doesn’t matter: I learned the skills and what they were for. I used the skills in order to make something. I have not forgotten those skills.

In mathematics, we just seem to teach the skills, without any context, and then move on. We cannot take time to explore how those skills are used in practice, to set them in context, because then we wouldn’t have time to get through the whole syllabus. And we must teach the whole syllabus, mustn’t we?

Must we?

In Boaler’s comparative study, the pupils who were taught the traditional way covered the whole syllabus. The pupils whose teaching consisted of open-ended mathematical investigations did not. There were gaps in their teaching. But … they performed better in their examinations, because the “learning gap” was smaller. They were taught maths with a purpose. They “made boxes”, rather than just “drilling holes”. At the end of the day there was a closer identity between the maths they had been taught and the maths they had learned, and they understood how to use what they had learned.

Maybe we need to spend more time in the mathematics classroom “making boxes”, and not be afraid if this results in a “teaching gap”. It is, after all, the “learning gap” that matters.


Boaler, J. (1996) Learning to lose in the mathematics classroom: a critique of traditional schooling practices in the UK. International Journal of Qualitative Studies in Education 9 (1), 17 – 33

Boaler, J (1997) Experiencing School Mathematics: Teaching styles, sex and setting. Maidenhead (Open University Press)

Boaler, J. (1998) Open and Closed Mathematics: Student Experiences and Understandings. Journal for Research in Mathematics Education 29 (1), 41 – 62

Nardi, E. and Steward, S. (2003) Is Mathematics T.I.R.E.D? A Profile of Quiet Disaffection in the Secondary Mathematics Classroom. British Educational Research Journal 29 (3) 345 - 367

- One comment Not publicly viewable

  1. Jeremy Burrows

    As soon as your work is published, you spot an error which you didn’t pick up at the proof-reading stage. So … in the second paragraph, in the brackets on the third line, delete the word “not”.

    02 Mar 2018, 18:44

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