account arrow-down-linearrow-down-small arrow-downarrow-download arrow-left-small arrow-leftarrow-link arrow-rightarrow-upaudio-less-volume audio-not-playing audio-plus-volume audio awarded books calendar close-modal closedate document education emailevent Facebookhamburger impact instagramjustice linkedin location-outline location opinion page phonepinterestplay pluspost preview project reports search-bigsearch-old search share startime twitterwelfare youtube zoom-in zoom-out

Visual representations in the primary classroom

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

By Nuffield Foundation

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.


  • 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
By Nuffield Foundation

Explore our projects

Search projects

We aim to improve people’s lives by funding research that informs social policy, primarily in Education, Welfare and Justice. We also fund student programmes that give young people skills and confidence in science and research.

We are an open, collaborative and engaged funder that offers more than money. Through connecting the individual projects we fund, we strengthen their collective impact and give voice to an overarching narrative.