Visual representations in the primary classroom

Researchers: Dr Patrick Barmby | Dr David Bolden ...

Project overview


Knowing how to use external representations (diagrams, for example) of mathematical concepts is an important part of teachers’ specialised knowledge of their subject.

This project aimed to develop teachers’ use of visual representations, specifically for multiplication and fractions, two areas of difficulty for primary pupils. It involved eight primary mathematics coordinators who, with input from researchers, planned and implemented a teaching programme using visual representations of multiplication and fractions.

The impact of the teaching programme was measured through pupil tests, observations of teaching, interviews with teachers and interviews with pupils. Direct outcomes of the project are the development and evaluation of teaching programmes for the primary classroom utilising visual representations of multiplication and fractions. Broader outcomes include professional development for the teachers involved and the dissemination of findings to teachers throughout the UK through professional publications and the NCETM website.

Team


  • Dr Patrick Barmby
    Durham University
  • Dr David Bolden
    Durham University
  • Stephanie Raine
    Durham University
  • Lynn Thompson
    North East School Support
  • Dr Rosemary Cann
    Aberystwyth University
  • Dr Stephen Atherton
    Aberystwyth University

  • Director, Education
    Nuffield Foundation

Explore our projects

Young girl smiling and reading book on green sofa
In progress

Education | 2026 - 2028

Love to Read Phase 2: A large-scale evaluation

View project
New

Education | 2026 - 2027

The effects of permanent school closures on pupils’ outcomes

View project
Over-the-shoulder shot of a female secondary school teacher having a one-to-one conversation with a male teenage student. They are both sitting down and she is maintaining eye contact as she is talking. The teacher is smiling and sharing a positive interaction with the student.
In progress

Education | 2026 - 2028

The impacts of Relational and Restorative Practice in school

View project
In progress

Education | 2026 - 2028

The long-term impact of student loans in further education

View project
Young woman using a digital printing machine on an apprenticeship

Education | 2026 - 2027

Apprenticeship Pathways

View project
Early years professionals playing with children
In progress

Education | 2026 - 2028

Noise in early years settings for children from under-privileged backgrounds

View project
Female Student Standing Outside College Building

Education | 2026 - 2027

How do students with SEND fare in the transition to post-16 education?

View project
Parents with baby
In progress

Education | 2026 - 2028

Your Baby and You: Developing the home learning environment for babies

View project
A cheerful young man wearing a green apron and a grey hoodie. He is placing fresh baked goods outside a cafe, holding a bowl filled with freshly baked bread. The cafe is in the background.
In progress

Education | 2026 - 2027

Student employment and subsequent education and labour market outcomes 

View project
Pioneering study reveals teaching techniques which boost exam performance: a teacher sits on a desk among her secondary school pupils, all looking at the board
In progress

Education | 2026 - 2027

A study of multi-grade teaching in English primary schools

View project
In progress

Education | 2026 - 2027

Education pathways for unaccompanied asylum-seeking children

View project
In progress

Education | 2026 - 2028

School climate and pupil belonging, attendance and achievement

View project
New

Education | 2026 - 2027

The effects of permanent school closures on pupils’ outcomes

View project
Female Student Standing Outside College Building

Education | 2026 - 2027

How do students with SEND fare in the transition to post-16 education?

View project
Young woman using a digital printing machine on an apprenticeship

Education | 2026 - 2027

Apprenticeship Pathways

View project
Young girl smiling and reading book on green sofa
In progress

Education | 2026 - 2028

Love to Read Phase 2: A large-scale evaluation

View project
Pioneering study reveals teaching techniques which boost exam performance: a teacher sits on a desk among her secondary school pupils, all looking at the board
In progress

Education | 2026 - 2027

A study of multi-grade teaching in English primary schools

View project
Over-the-shoulder shot of a female secondary school teacher having a one-to-one conversation with a male teenage student. They are both sitting down and she is maintaining eye contact as she is talking. The teacher is smiling and sharing a positive interaction with the student.
In progress

Education | 2026 - 2028

The impacts of Relational and Restorative Practice in school

View project
Parents with baby
In progress

Education | 2026 - 2028

Your Baby and You: Developing the home learning environment for babies

View project
In progress

Education | 2026 - 2028

The long-term impact of student loans in further education

View project
In progress

Education | 2026 - 2027

Trialling an assessment protocol for LLM-powered careers advice 

View project
Teaching assistant plays with little boy at nursery
In progress

Education | 2025 - 2026

Room to Grow: School-based Nursery Places and the Disadvantage Gap

View project
In progress

Education | 2026 - 2028

School climate and pupil belonging, attendance and achievement

View project
Early years professionals playing with children
In progress

Education | 2026 - 2028

Noise in early years settings for children from under-privileged backgrounds

View project
Young girl smiling and reading book on green sofa
In progress

Education | 2026 - 2028

Love to Read Phase 2: A large-scale evaluation

View project
Pioneering study reveals teaching techniques which boost exam performance: a teacher sits on a desk among her secondary school pupils, all looking at the board
In progress

Education | 2026 - 2027

A study of multi-grade teaching in English primary schools

View project
Over-the-shoulder shot of a female secondary school teacher having a one-to-one conversation with a male teenage student. They are both sitting down and she is maintaining eye contact as she is talking. The teacher is smiling and sharing a positive interaction with the student.
In progress

Education | 2026 - 2028

The impacts of Relational and Restorative Practice in school

View project
Parents with baby
In progress

Education | 2026 - 2028

Your Baby and You: Developing the home learning environment for babies

View project
In progress

Education | 2026 - 2028

The long-term impact of student loans in further education

View project
In progress

Education | 2026 - 2027

Trialling an assessment protocol for LLM-powered careers advice 

View project
Teaching assistant plays with little boy at nursery
In progress

Education | 2025 - 2026

Room to Grow: School-based Nursery Places and the Disadvantage Gap

View project
In progress

Education | 2026 - 2028

School climate and pupil belonging, attendance and achievement

View project
Early years professionals playing with children
In progress

Education | 2026 - 2028

Noise in early years settings for children from under-privileged backgrounds

View project
In progress

Education | 2025 - 2026

Childminder-led structured language enrichment in the Early Years

View project
A horizontal image of two children outdoors using a big mental pan to make mud pies, while a young woman supervises. The children are both wrapped up warm in coats and are contently playing
In progress

Education | 2025 - 2028

Policy change and inequalities in early childhood education and care

View project
A cheerful young man wearing a green apron and a grey hoodie. He is placing fresh baked goods outside a cafe, holding a bowl filled with freshly baked bread. The cafe is in the background.
In progress

Education | 2026 - 2027

Student employment and subsequent education and labour market outcomes 

View project
New

Education | 2025 - 2025

Exploring Multi Academy Trust approaches to Artificial Intelligence

View project
SEND pupil drawing in classroom
New

Education | 2025 - 2026

The uneven distribution of pupils with SEND in mainstream schools

View project
Elevated view of students sitting and learning in computer room
New

Education | 2025 - 2027

Improving wellbeing-focused online media literacy in schools

View project
Young girl using an iPad at home
New

Education | 2024 - 2024

Early years digital media literacy review

View project
New

Education | 2024 - 2026

Spending across different stages of education

View project
Teenager hugging their mother
New

Welfare | 2023 - 2026

Juvenile onset rheumatic diseases: education, vocational readiness, & employment

View project
Pre-school students sitting in an art classroom being taught by a teacher. The classroom is colourful and the children are sat at a big table.
Reported

Education | 2024 - 2026

A comparative analysis of EY workforce policy in the four UK nations

View project
Sixth form student smiling in a classroom while a teacher helps a classmate in the row behind him
Reported

Education | 2023 - 2025

The Extended Project Qualification: An Opportunity for All?

View project
Two little boys and a little girl, all wearing primary school uniform, work together to solve a puzzle in their classroom.
Reported

Education | 2023 - 2025

What has ‘Free School Meals’ measured and what are the implications?

View project
Male and female apprentices looking at car engine
Reported

Education | 2022 - 2025

Work or study? Gender and the transition from school to work

View project
Teenage sixth form students taking notes in a lesson
Reported

Education | 2022 - 2025

Comparing inequality and outcomes across post-16 education in the UK

View project
Little girl watches TV on her own at home
Reported

Education | 2023 - 2025

Do same language subtitles help children learn to read?

View project
Reception class children using a parachute in a PE lesson
Reported

Education | 2022 - 2023

A movement and story-telling intervention for reception children

View project
Reported

Education | Welfare | 2022 - 2024

Understanding school attendance, education and labour market outcomes

View project
A classroom of children with their hands up to answer a question, with two teachers at the front of the classroom
Reported

Education | 2022 - 2024

Inspecting the inspectorate: new insights into Ofsted inspections

View project
Reported

Education | 2022 - 2025

The medium-term impact of the COVID-19 pandemic on pupils with SEND

View project
Side view of two female high school students in classroom working on laptops social distancing. Student in foreground is in focus and student in background is blurred
Reported

Education | 2021 - 2022

COVID-19 and disadvantage gaps in England 2020 and 2021

View project
Young boy draws and plays with a globe as part of nursery education
Reported

Education | 2020 - 2022

COVID-19 and childcare: local impacts across England

View project
Search projects

Profile