[Maths-Education] Big Mathematical Ideas

[Colin Foster]

Those working with teachers/pre-service teachers of mathematics might be interested in the entirely free website ’Teaching the Big Ideas in School Mathematics’ which I have just completed. It tries to show how school mathematics can be conceived of around five ‘Big Ideas’, which underpin everything and enable rich connections. It started out as a book, but at over 200k words it is too big to be a reasonably priced book, so I decided to put it all onto a website instead. It is all under Creative Commons licence, so please use any of it however you like: https://bigmathematicalideas.org/

With best wishes,

Colin.

Colin Foster
Professor of Mathematics Education
Department of Mathematics Education
Schofield Building
Loughborough University
Loughborough LE11 3TU

foster77.co.uk<http://www.foster77.co.uk/>
bigmathematicalideas.org<http://www.bigmathematicalideas.org/>

Editor-in-Chief of the International Journal of Mathematical Education in Science and Technology:tandfonline.com/tmes<http://www.tandfonline.com/tmes>
Director of the Loughborough University Mathematics Education Network (LUMEN): lboro.ac.uk/lumen<http://www.lboro.ac.uk/lumen/>
Director of the Loughborough University Mathematics Learning Support Centre: lboro.ac.uk/departments/mlsc<http://www.lboro.ac.uk/departments/mlsc/>
President of the Mathematical Association (2022-23): m-a.org.uk<http://www.m-a.org.uk/>

Recent publications
Inglis, M., Foster, C., Lortie-Forgues, H., Simms, V., & Stokoe, E. (2026). Psychology and research assessment in the United Kingdom. Cogent Psychology. Advance online. https://doi.org/10.1080/23311908.2025.2570100
Stannard, A., & Foster, C. (2025). Secondary school mathematics teachers’ accuracy at predicting student errors. School Science and Mathematics. Advance online. https://doi.org/10.1111/ssm.18404
Inglis, M., Foster, C., Lortie-Forgues, H., & Stokoe, E. (2024). British education research and its quality: An analysis of Research Excellence Framework submissions. British Educational Research Journal, 50(5), 2495–2518. https://doi.org/10.1002/berj.4040
Foster, C., Woollacott, B., Francome, T., Shore, C., Peters, C., & Morley, H. (2024). Challenges in applying principles from cognitive science to the design of a school mathematics curriculum. The Curriculum Journal, 35(1), 489–513. https://doi.org/10.1002/curj.249
Foster, C. (2024). Methodological pragmatism in educational research: From qualitative-quantitative to exploratory-confirmatory distinctions. International Journal of Research and Method in Education, 47(1), 4–19. https://doi.org/10.1080/1743727X.2023.2210063
Foster, C. (2023). Problem solving in the mathematics curriculum: From domain-general strategies to domain-specific tactics. The Curriculum Journal, 34(4), 594–612. https://doi.org/10.1002/curj.213

Please note that I send emails at various times, but I never expect you to reply outside of your normal working hours.