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This episode of the Mr Barton Maths Podcast is kindly supported by Arc Maths.

You can find more information about their app for helping students remember those crucial maths skills – and register for a free trial – at arceducation.co.uk/for-schools/

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Hello, and welcome to another episode of the Mr Barton Maths Podcast, with me Craig Barton.

This time around I spoke to Dan Draper

I have been a big fan of Dan’s work for a few years now. Along with last episode’s guest, Paul Rowlandson, Dan’s blog is one of the few I have notifications on for new posts because I find it essential reading. I love the way Dan reflects on his thinking from the ideas he tries out in his lessons. The About section of the blog sums this up perfectly:

This blog is primarily a space to tease out ideas about education generally and secondary mathematics education specifically. By writing down my ideas I find it easier to bring them into some kind of coherence in my own mind.

This blog is not meant to be informative and authoritative, but speculative.

The conversations and debate started by posting ideas here has been immensely valuable to my growth as a classroom practitioner, so please get in touch if you disagree or if you’re doing something brilliant that gets to what I’m trying to articulate in my ham-fisted way.

When planning the discussion, Dan and I decided to focus on two key areas: overlearning and conceptual leaps, and then chucked on a bit on curriculum sequencing at the end for a bonus! I thoroughly enjoyed this conversation, and learned loads – Dan is brilliant to chat to.

The examples Dan shares are here:

1) What does ‘overlearning’ look like? Not teaching integration by parts to year 7… but how can you take a concept/representation and stretch it, almost to absurdity to make sure it remains robust enough to do what we need to do – for example using grid method with operations with integers and fractions (14×52 and two thirds for example)

Taking the most basic definition and STILL providing examples for depth like the examples below:

when does the gif below go from being 32 to 3 squared?

even ‘simple’ graph work:

this example with vectors

2) Conceptual leaps: like how the top four images here represent a square number but three of them are shown with CUBES!? No wonder kids get it wrapped round their neck when we look at three dimensional properties etc.

Trying to isolate the actual thing you want kids to focus on like the VT Bearings task I set too:

making meaning out of y=mx+cME: It’s DEAD good that four variables can generate ANY straight line on a 2D plane!!!!! m is the slope and c is the intercept like we’ve painstakingly derived every so carefully.
ME, internally: Oh ayup hang on, negative symbols in these equations contribute to completely different meanings, with a negative m ‘flipping’ and a negative c translating.

just nice BITS: So the huge difficulty my top set 11s had with seeing that I’d done (45/46)x9 non-algorithmically and instead done 9-(9/46). So we unpicked it and linked it to mental calculations with integers (anything multiplied by 19 as 20x-x) and expanding brackets ( 9(1-(45/46)) ) etc. stunning rich depth stuff that does not and cannot fit into a scheme of learning.
This as a structural appreciation:

On Twitter Dan is: @MrDraperMaths
Dan’s blog is: mrdrapermaths.wordpress.com

My free course all about the Ultimate Scheme of Work 2.0 is here and the massive spreadsheet is here.
My new course, Supercharging worked examples using variation and self-explanation, is here

Dan Draper’s Big 3
1. Spurious correlations
2. Gapminder
3. Interactive live stats

My usual plugs:

• You can help support the podcast (and get an interactive transcript of all new episodes) via my Patreon page at patreon.com/mrbartonmaths
• If you are interested in sponsoring an episode of the show, then please visit this page
• You can sign up for my free Tips for Teachers newsletter and my free Eedi newsletter
• My online courses are here: craigbarton.podia.com
• My books are “Tips for Teachers“, “Reflect, Expect, Check, Explain” and “How I wish I’d taught maths”