Research, Papers and Articles
Reports and Articles
- Supporting children's inhibitory control in mathematics learning: A participatory research study in classroom contexts - December 2025
- The Impact of the Teaching of Multiplication and the Multiplication Tables Check - Final report June 2025
- How Haylock and Cockburn and the connective model have shaped and inspired our thinking for 25 years - October 2024
- Adapting lesson study for early-years practitioners - July 2024
- Block Play Project Report - July 2024
- Maths is More - June 2022
- The Teaching and Learning of Multiplication Bonds: A Position Statement - May 2021
- Cardinality revisited: Recognising, understanding and trusting values - February 2020
- Learning from Variation - BCF Curriculum Investigation Grant Research Reports - BERA -January 2020
- What is 'variation' in early years mathematics? - BERA Blog Post - August 2019
- Understanding Structured Number Lines - Phase 1 Report July 2019
- Changing lives and providing equity through pre-teaching and assigning competence - July 2018
- Hearing the whistle: how children can be supported to be active and influential participants in mathematics lessons through effective use of assigning competence and preteaching - BCME proceedings [Page 183] - 2018
- Learning from the ICME international survey on teachers working and learning through collaboration - July 2017
- Supporting children to be active and influential participants in mathematics lessons through effective use of assigning competence and pre-teaching Final Report July 2017
- Teaching for mastery in mathematics in mixed-age classes - Final Report January 2016
- The Value of Two - Enrich - April 2015
- Think Maths - 1998
Video
Cardinality Counts: The Value of Two Revisited – Dr Ruth Trundley
Dr Ruth Trundley explores the importance of cardinality, drawing on the case study used for her doctorate (which followed two children from the age of 17 months to 5 years 7 months) and more recent research undertaken with Dr Helen Williams.
Understanding Structured Number Lines
Dr Ruth Trundley shares recent research, undertaken with Stefanie Burke and Helen Edginton, that ran in two parts from September 2018 to July 2020, with pupils from EYFS to Y6 focused on understanding structured number lines as a representation of the structure of the number system. Central to this is understanding the number line as a measurement model.
Supporting Active Participation in Maths Lessons Through Pre-teaching
Dr Ruth Trundley explores findings from the project which focussed on the research question: How can we support all children to access age-appropriate mathematics and be active and influential participants in maths lessons through effective use of pre-teaching and assigning competence?
The Use of Colour to Support Understanding in Mathematics
When maths is represented visually, colour can have a significant impact. It can both support and undermine understanding depending on how it is used. Dr Ruth Trundley shares research, undertaken with a group of teachers working with pupils from EYFS to post-16, that considered how colour can be used to enhance learning in three different contexts: Resources (manipulatives), Board work & Pupil recordings.
Solving Subtraction Problems by Means of Indirect Addition: findings from a Collaborative Lesson Research Cycle
Subtraction problems of the type a – b = ? can be flexibly solved by various strategies,. This includes the indirect addition strategy ("how much do I have to add to b to get at a?") which is particularly useful when a and b are close. However, often children do not choose this strategy. Dr Ruth Trundley will explore findings from a collaborative lesson research cycle which expose some of the reasons why this might happen and the challenges associated with addressing this issue.
Exploring computational fluency: connecting structures, strategies and symbols
Fluency is one of the aims of the National Curriculum in England, but is often unhelpfully associated with memorising facts. Drawing on work with primary schools, including the research project `Understanding Structured Number Lines' (2019), Dr Ruth Trundley explores the importance of connecting different representations of mathematics and in particular how the meaning attached to symbols is essential in supporting fluency. She uses one particular subtraction and one student's response to that subtraction as a vehicle for interrogating understanding, potential barriers to understanding and implications for teaching and learning mathematics.
Understanding Number in the Early Years
Dr Helen Williams and Dr Ruth Trundley have recorded a video in which they explore some key aspects of early learning in a way that might be used as a staff meeting. This involves maths teaching to Reception, Year 1 and Year 2 classes, and handles important topics for early maths understanding such as subitising, cardinality and composition. The recording lasts 40 minutes and asks you to pause in several places to allow staff to engage in activity.
Executive Function and Mathematics
In this half-hour recorded webinar Professor Camilla Gilmore, and Dr Ruth Trundley discuss executive function and mathematics, using observations of a child working on a maths problem to illustrate inhibitory control, working memory and attention shifting/cognitive flexibility.