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maths
variation theory
7th February 2025
Variation Theory in Maths: The Key to Better Maths Understanding
Rachael Welsh
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by Shotton Hall Research School
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In my role as Director of Shotton Hall Research School I am in the privileged position of visiting many schools, as well as working with them to improve reading across the curriculum. We know that a robust vocabulary plays a vital role in a child’s cognitive and academic development. We also know that vocabulary is the building block of reading, writing, listening, speaking- and thinking. Yet, one of the most common areas for improvement we identify is around the explicit teaching of vocabulary. Most of the time, we are met with the response ‘we already do that’. To which our response should always be – ‘how well do you do it?’
There is no doubt in my mind that you know that words are important. You’ve probably read the EEF guidance reports, you may have read books, listened to podcasts and watched webinars. You know that we need to ‘have targeted vocabulary instruction in every subject’.1
So, you’ve spent hours selecting tier 2 and 3 vocabulary, chosen ‘Word of the Week’ and ‘Word of the Day,’ – you might even have laminated them, confident they will never be wiped away at the end of the day (and in fact, will outlive us all). You’ve created word lists and booklets, spent a fortune on printing them, and added them to all platforms (so there’s no excuse!). Yet, no one’s vocabulary knowledge or usage is really improving.
So what do we do? What does excellent vocabulary instruction look like? Put simply, teaching vocabulary isn’t a one-off event. While ‘Word of the Week’ is an admirable nod in the right direction, it quite simply isn’t enough to ensure our students develop a rich and robust vocabulary. As a linguist, I’ve built a career on teaching vocabulary – and made many mistakes along the way. Here are my thoughts on what not to do – as well as some helpful (evidence-informed) ideas and resources on what great vocabulary teaching might look like.
What does this look like in practice?
It’s easy to tell you what to do and what not to do. It’s far more challenging to exemplify this. To support teachers with this, we teamed up with Bedlington Academy to create a 5 minute video showcasing their seven step approach when teaching vocabulary.
1. Practise pronunciation;
2. Give a definition;
3. Explain, using morphology;
4. Build word families;
5. Model an example sentence;
6. Pupils use the vocabulary in their own sentence;
7. Revisit and reward.
To support you with using this video in staff training, we’ve also produced a scaffold with questions to prompt discussions, linked here.
QA shows us repeatedly, that schools are increasingly good at the early parts of the ‘select’ phase. Words are selected – but, if at the end of a unit or phase, the pupils don’t know the carefully selected vocabulary – something is not working and therefore, something needs to change.You can read more about this in our ‘5 minutes on vocabulary’ guide, linked here.In our next blog, we’ll look at how you can get it right in the ‘select’ phase.
References
Improving literacy in Key Stage 1 (2021) EEF. Available here.
Improving literacy in Secondary Schools (2021) EEF. Available here.
Improving Literacy in Key Stage 2 (2021) EEF. Available here.
Quigley, A. (2022) Closing the writing gap. Abingdon, Oxon: Routledge, Taylor & Francis Group.
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