# How to give your pupils a deeper understanding of maths

In the first episode of Tes' Mathematips podcast, Lucy Rycroft-Smith asks Margaret Brown about multiplicative reasoning

You may never have heard the name Professor Margaret Brown, but for several decades now she’s been working on researching aspects of maths education in the UK – not only trying to find out what the current picture is, but also crucially how to help make it better.

Her work has focused on multiplicative reasoning, one of the significant keys to mathematical understanding at all ages. (You pronounce it multi-PLIC-ative reasoning, for the record.  Margaret talks about pronouncing "matrix" wrongly – like "mattress" – for years until someone corrected her).

## Understanding maths

It is all about the deep understanding of multiplying and dividing, rather than just learning times tables or performing calculations, and starts with recognising when you actually need to use multiplication. It’s the basis for some very fundamental mathematical ideas, and can be a real sticking point for pupils who can’t then fully access other parts of the curriculum. It’s also "surprisingly under-researched".

Brown's background is originally in primary teaching. She remembers her first day: “I’d never really met a five-year old, when suddenly I was starting on Monday with 27 of them in Bootle.”

And she has stayed closely in touch with the classroom, regularly going back into schools to test new ideas and interventions with pupils (and get feedback from teachers).

## Practical approaches

So what is the key to developing good multiplicative reasoning in pupils?

A mixture of models, says Brown, and moving between different representations.

Often, pupils get "stuck" on a repeated addition model of multiplication, and it is remarkably hard to move them on.  Allowing pupils to play with arrays, area models, double number lines and scalings can help.

Brown has a research paper called "The struggle to achieve multiplicative reasoning 11-14" (although these ideas are also very important at all ages), which we discuss in this podcast.

You can also listen to hear more about when maths saved the day, and why we decided maths teachers should get some T-shirts printed (and what they would say).

## Listen now

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

In the podcast, Margaret mentions:

1. Patrick Barnby’s work on arrays

2. Julia Anghileri’s work

3. Dietmar Küchemann’s work

4. The ICCAMS project (investigating ways of raising students’ engagement with mathematics)

5. The IMAP project looking at low attainment in mathematics

Each week, Tes produces a magazine (available in print and online to subscribers) that gives you detailed, up-to-date teaching and learning guides, analysis and advice based on the latest research. It is essential reading for the informed teacher and school leader. You can subscribe here.

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

## Latest stories

### How to help students tackle prejudice post-Covid

A discussion about Covid-related prejudice helped to raise students' awareness of fake news, explains Jennifer Wilkinson
Jennifer Wilkinson 16 Jun 2021

### Exam cancellations save millions for second year

But – while the government has slashed funding to SQA – fees paid by schools and councils remain unchanged
Emma Seith 16 Jun 2021

### Revealed: What new £25m DfE tutor plan will deliver

Most tutoring under DfE's flagship NTP will be provided on a 1:3 basis to provide both 'value for money' and 'high impacts'
Amy Gibbons 16 Jun 2021

### GCSEs 2021: I back teachers on grades, says Williamson

Education secretary rejects speculation that teacher-assessed grades will not be an accurate reflection of abilities
Tes Reporter 16 Jun 2021

### GCSEs 2022: Ofqual lifts fieldwork requirement

Changes to non-exam assessment requirements carried over to 2022
Catherine Lough 16 Jun 2021

### Autumn 2021 phonics check to go ahead

Gavin Williamson confirms that autumn phonics check for Year 2 pupils will be repeated next academic year
John Roberts 16 Jun 2021

### Why a defibrillator was a priority for our school

The value of a school's campaign for a defibrillator was brought home by events at Euro 2020 last weekend
Johnny Lothian 16 Jun 2021

### GCSEs: 4 ways teachers want exams to change

Findings reveal majority of teachers favour assessment throughout the year
Catherine Lough 16 Jun 2021

### Today's school, education and teacher news: LIVE 16/6

The hub for specialist education news for those working in schools and everyone who is interested in them
Tes Reporter 16 Jun 2021

### GCSE English: Should we assess spoken language?

If we deem the GCSE spoken language assessment as important, it should contribute to the grade, says Kate Watts
Kate Watts 16 Jun 2021