Our thanks go to the senior leadership, teachers and learners in participating schools and to friends and colleagues for their hospitality at Stanford. Steve Everhard, Greg Gomberg, Anne Haworth, Piers Messum and Tony Woodhouse helped devise and deliver professional development support.

We are indebted to the library staff at the University of Laval, Quebec, Bibliotheque Nationale de France, the National Library of Australia, the Moore and University Libraries, Cambridge University and Cubberley Library, Stanford University for their assistance in desk research on the place of Cuisenaire-Gattegno (Cui) in the research literature.

We acknowledge the valuable contributions of Jan Atkinson, Oliver Braddick, Justin Dimmel, Colin Foster, Dave Hewitt, Martin Hyland, Anna Vignoles and the anonymous reviewers who commented on earlier drafts of our research papers Sections 2.5 and 2.6.

Alexandre Borovik, Miles Berry, Jim Thorpe and the members of the Association of Mathematics Teachers Functional Programming and Computer Algebra Working Group have helped to assess the contribution that computer languages such as Mathematica, Scratch, Python and Haskell might bring to mathematics teacher professional development.

Melody Lang Drury, Bruce McCandliss and Nigel Marriott helped to analyse the Cuisenaire-Gattegno literature. The intervention design, delivery and analysis of the Cui longitudinal study was a partnership with teachers and senior leaders, Bruce McCandliss of the Stanford University Graduate School of Education Educational Neuroscience Initiative and Marriott Statistical Consulting.

Ian Benson is grateful for an equipment grant and advice from John Couch and Janet Wozniak at Apple Inc. We received guidance on outreach project design from Maisha and Bob Moses’ Algebra Project and John Chowcat of Prospect (formerly NAEIAC and Aspect), the UK union for school improvement consultants.

The work has been part funded by parents and a network of schools, the Ogden, Sutton and Shuttleworth Foundations, the Greg and Rosie Lock Charitable Foundation and Sociality Mathematics CIC. The UK government provided funding through the Maths Hubs of the Department of Education National Centre for Excellence in the Teaching of Mathematics, and the Department’s Primary Strategy Learning Networks. Funding also came from the UK Department of Trade and Industry Global Watch programme.

Cuisenaire is a UK registered trademark of Educational Solutions (UK) Ltd, Cuisenaire Company, Fishguard, Pembrokeshire, Wales. Sociality is a UK registered trademark of Ian Benson & Partners Ltd.

Benson, Ian. 2011. The Primary Mathematics: Lessons from the Gattegno School. Lambert Academic.
Catir, Zulie, and Caleb Gattegno. 1973. Notes on the Gattegno Approach to Mathematics. Educational Solutions.
Cheng, Eugenia. 2022. The Joy of Abstraction: An Exploration of Math, Category Theory and Life. Cambridge University Press.
Dehaene, Stanislas. 2020. How We Learn: The New Science of Education and the Brain. Allen Lane.
Gattegno, Caleb. 1986. Numbers in Colour Series. Educational Solutions.
———. 1987. Science of Education: Vols 1 and 2. Educational Solutions Worldwide.
Goutard, Madeleine. 1964,2017. Mathematics and Children. Educational Explorers, Fishguard.
———. 1974. Experiences with Numbers in Colour. Cuisenaire Company of America.
Winograd, Terry, and Fernando Flores. 1986. Understanding Computers and Cognition: A New Foundation for Design. Ablex.
Young, Roslyn, and Piers Messum. 2011. How We Learn and How We Should Be Taught. Duo Flumina.