# Could 'variation theory' improve your maths teaching?

In the latest episode of Tes' Mathematips podcast, Lucy Rycroft-Smith talks variation theory with Anne Watson

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

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

In the podcast, we mention:

It only takes a moment and you'll get access to more news, plus courses, jobs and teaching resources tailored to you

## Latest stories

### First dip in teacher training applicants since Covid

New UCAS data suggests teacher recruitment boom sparked by pandemic may already be coming to an end
Amy Gibbons 29 Jul 2021

### What happened when I didn't talk for an entire lesson

A sore throat led this music teacher to a novel idea: not talking for an entire lesson. The outcome was startling
Peter Simons 29 Jul 2021

### Only 46% schools on catch-up tutor scheme are poorest

Flagship National Tutoring Programme still short of target for pupils reached in 2020-21 by start of July, new stats show
Amy Gibbons 29 Jul 2021

### GCSEs 2022: Make geography exams fairer, Ofqual told

A lack of contingency plans for next year's exams is 'unacceptable and deeply disappointing', say heads
Catherine Lough 29 Jul 2021

### GCSEs 2020: How grading U-turn affected students

Ofqual reveals the impact of using grades produced by schools in last summer's GCSE and A levels
Catherine Lough 29 Jul 2021

### Magazine podcast: admissions, exclusions, finance

Join us for our weekly discussion about some of the hottest topics included in the latest issue of Tes magazine
Tes Reporter 29 Jul 2021

### Why teachers need research that works in the real world

Academics outline how they work to ensure research into best practice can actually work in a real classroom
Dr Jessie Ricketts, Eleanor Crow and Eleanor Gray 29 Jul 2021

### Lord Baker: Scrapping Btecs 'an act of vandalism'

Btecs are 'of particular help to disadvantaged young people', says former education secretary Lord Baker of Dorking
Julia Belgutay 29 Jul 2021

### Permanent exclusions up 5% before Covid school closures

But overall exclusions and suspensions fell in the year 2019-20 as schools closed to most students in March 2020
Claudia Civinini 29 Jul 2021

### 5 ways to introduce primary pupils to movie editing

Learning to use video editing software on tablets and smartphones with young learners may sound tough – but follow these simple steps, and you'll have a class of cinematic auteurs in no time