The first time that Professor Anne Watson had a meal at a Michelin-star restaurant, she did not commit to memory the taste of the whole meal or the ambience of the dining room. Instead, she focused on only one thing: the pea shoots scattered around her plate.

These shoots, Watson remembers, packed “pea flavour that was more intense than anything I could ever remember peas tasting like”.

“Goodness knows how he cooked the beef,” she adds. “I don’t remember that at all.”

Watson’s memory of the incident, recounted in the latest episode of the Tes maths podcast, Mathematips, illustrates an important question about maths teaching: how do we know what elements of an experience people will pay attention to and remember, and how can we try and direct that attention?  

In this episode, with these questions in mind, we pull apart the idea of variation theory - a way to look at tasks and examples that clarifies what is available to be learned.

Quick listen: How to give your pupils a deeper understanding of maths

Want to know more? Dispelling misunderstandings around variation theory

Maths: Variation theory

Watson, who is emeritus professor in the University of Oxford’s department of education is an expert in task design in mathematics teaching and learning from a variation theory perspective.

In the podcast, she talks about the “terrible mess” that she made of maths teaching as a new teacher, before studying variation theory gave her a better “lens and a language” through which to consider classroom task design in mathematics.

So where can teachers who want to know more about variation theory look for more information if they don’t know where to start? Watson suggests that this is one area where reading research might not be the best way in.

“There’s too much jargon [in research],” she says. “I don’t think it’s very helpful.”

Instead, teachers would be much better off familiarising themselves with variation theory in their own classrooms and developing a “growing awareness” of the teachable moments that arise there, she explains.

You can listen to hear more about variation theory, as well as one of Watson’s most emotional moments from her own days as a maths student and her suggestion that a linear relationship might just be a “degenerate quadratic”.

And, as always, there is a sprinkling of custom-written Macey and Rycroft-Smith jokes at the end.

Listen now

You can listen for free by downloading the podcast from your podcast platform (type “Tes - the education podcast”) or you can listen below.

Lucy Rycroft-Smith works in communications and research for Cambridge Mathematics 

Further reading

In the podcast, we mention:

• Watson’s article, written with her husband John Mason, ‘Seeing an exercise as a single mathematical object: using variation to structure sense-making’.
• Flatland by Edwin Abbott
• Walter and Brown’s ’The Art of Problem Posing’
• Ference Marton’s work
• Ulla Runesson’s work
• Piaget’s action schema