The NCETM's Five Big Ideas

The NCETM created the Five Big Ideas for Teaching for Mastery in maths classrooms. Further to my belief that we can all teach maths the same way, I invited a primary specialist to join me so that we covered primary and secondary ideas.

These hour-long sessions will cover each of the big ideas in turn and look at primary and secondary classrooms, as well as the research that supports each of the ideas.

They will be presented as an introduction into each of the ideas – if you want to learn more, then go to and have a look to see what support is being offered in your region by your local Maths Hub –

1 – Variation

Faye Glendinning and I discussed variation, and I particularly enjoyed Faye’s use of an elephant / rhino to demonstrate (worth watching!).

We discussed the importance of the standard/non-standard examples (as well as the non-example!) and a lot more too.

Thank you to Faye for taking part in this with me and excuse the edit in the middle (due to an error on my part!)

2 – Mathematical thinking

Helen Hackett joined me to consider mathematical thinking and how maths teachers can use certain types of questions regularly to ensure our pupils really do engage and think about the activities they undertake (“memory is the residue of thought” after all!)

Thank you to Helen for being willing to share her expertise in this fascinating hour.

3 – Fluency

Faye returned to discuss fluency with me and we both agreed quickly on the need to focus on efficiency, accuracy and flexibility to improve pupil’s fluency.

This video gave examples of tasks that teachers can set to target their fluency and a lot more too. This was the hour that suddenly we kept bouncing back and forth to the other big ideas also – they are all connected after all!

Thanks again, Faye!

4 – Coherence

Helen returned once more and her knowledge of this area far surpassed mine – some great ideas shared in this hour.

We discussed the importance of small steps when planning lessons and blocks of lessons, and explained how departments and staff can plan together to ensure that the misconceptions can be planned for in advance.

Again, thanks to Helen for this!

5 – Representation and Structure

Faye returned once more to look at the final of the 5 big ideas – probably the idea that maks the biggest difference when it comes to getting teachers engaged with Teaching for Mastery – representation

There are other videos on this website covering bar modelling and algebra tiles, so Faye and I tried to demonstrate the use of other manipulatives in this hour, and I found it fascinating, especially how much numicon can be used all the way up to key stage 3.

We also summarised some activities how teachers/departments could look at the the 5 ideas overall and decide how to move forward in their own journey to improve practice.