Research areas and publications

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Research areas and publications

In this section we present our research in curriculum design and reform, professional learning in mathematics education and educational technologies in mathematics education, along with reports on our methods, use cases and emerging technologies in education.

We publish our work for several reasons:

contributing to standards, expectations and practices in mathematics curriculum and professional learning design and in mathematics education research
providing transparency in our methods and outputs to demonstrate and increase trustworthiness and the value of our work in various mathematics education communities
stimulating feedback on and refinement of our work.

We contribute articles, proceedings papers and book chapters to peer-reviewed journals and other external publications, and publish our own reports.

Research areas

Curriculum design and reform in mathematics education

Our synthesis of research on learning progressions in mathematics enables us to explore and analyse subject coherence and sequencing, and alignment between curricula, assessments, resources and teacher professional learning. This informs our curriculum design and consultancy work. Our publications in this area help us develop, share and refine our perspectives and approaches.

Macey, D., & Rycroft-Smith, L. (2025). Developing guidelines for assessment and resource design in mathematics education to support equity, diversity, inclusion and belonging. Educational Designer.

Jameson, E., & Bobis, J. (2023). Modelling curriculum reform: A system of agents, objects and processes. In Y. Shimizu & R. Vithal (Eds.), Mathematics curriculum reforms around the world: The 24th ICMI study (pp. 431–443). Springer.

Jameson, E., Sullivan, P., & Arzarello, F. (2023). Conclusion: Implications for active curriculum reform work and future research. In Y. Shimizu & R. Vithal (Eds.), Mathematics curriculum reforms around the world: The 24th ICMI study (pp. 469–474). Springer.

Jameson, E., Sullivan, P., & Arzarello, F. (2023). Introduction. In Y. Shimizu & R. Vithal (Eds.), Mathematics curriculum reforms around the world: The 24th ICMI study (pp. 397–400). Springer.

Jameson, E., Macey, D., & McClure, L. (2022). Implementing research in the practice of curriculum designers: Barriers and an example approach. In J. Hodgen, E. Geraniou, G. Bolondi, & F. Ferretti (Eds.), Proceedings of the Twelfth Congress of the European Society for Research in Mathematics Education. ERME/Free University of Bozen-Bolzano.

Shaw, S., Rushton, N., & Majewska, D. (2022). Tracing the trajectory of mathematics teaching across two contrasting educational jurisdictions: A comparative analysis of historical and contemporary influences. International Education Journal: Comparative Perspectives, 21(1), 41–60.

Jameson, E. (2021). Evaluating the Cambridge Mathematics Framework: Perspectives and approaches. Cambridge Mathematics, Cambridge University Press & Assessment.

Jameson, E., Whitney-Smith, R., Macey, D., Morony, W., Benson-Lidholm, A.-M., McClure, L., & Leigh-Lancaster, D. (2021). Curriculum development and use of a digital framework for collaborative design to inform discourse – a case study. In Y. H. Leong, B. Kaur, B. H. Choy, J. B. W. Yeo, & S. L. Chin (Eds.), Proceedings of the 43rd annual conference of the Mathematics Education Research Group of Australasia. (pp. 235–242). The Mathematics Education Research Group of Australasia.  

Johnson, M., Horsman, R., & Macey, D. (2021). Design for learning in uncertain contexts: Developing a maths curriculum framework for emergency situations. Educational Designer, 4(14).

Koch, M., Confrey, J., Clark-Wilson, A., Jameson, E., & Suurtamm, C. (2021). Digital maps of the connections in school mathematics: Three projects to enhance teaching and learning. In A. Clark-Wilson, A. Donevska-Todorova, E. Faggiano, J. Trgalová, & H.-G. Weigand (Eds.), Mathematics education in the digital age: Learning practice and theory (pp. 121–137). Routledge.

Majewska, D. (2021). Using the Cambridge Mathematics Framework to map the Common Core to HOTmaths [Case study report]. Cambridge Mathematics, Cambridge University Press & Assessment.

Jameson, E., & Horsman, R. (2020). Using the Cambridge Mathematics Framework to refine the UNICEF-Cambridge Curriculum Progression Framework [Case study micro-report]. Cambridge Mathematics, Cambridge University Press & Assessment.

Jameson, E., Horsman, R., Macey, D., Gould, T., Rushton, N., Rycroft-Smith, L., Majewska, D., Stevens, B., & McClure, L. (2020). Ontology: Structure and meaning in the Cambridge Mathematics Framework [Research report]. Cambridge Mathematics, Cambridge University Press & Assessment.

Jameson, E., & McClure, L. (2020). Agreeing to disagree for the sake of formative evaluation: A Delphi panel deliberates on mathematical thinking and doing. In M. Gresalfi & I. Horn (Eds.), The interdisciplinarity of the learning sciences, 14th International Conference of the Learning Sciences (ICLS) 2020 (Vol. 3, pp. 1753–1754). International Society of the Learning Sciences.

Koch, M. J., Confrey, J., Jameson, E., & Clark-Wilson, A. (2020). Facilitating the design and enactment of mathematics curricula through digital mapping. In A. Donevska-Todorova, E. Faggiano, J. Trgalova, Z. Lavicza, R. Weinhandl, A. Clark-Wilson, & H.-G. Weigand (Eds.), Proceedings of the tenth ERME topic conference (ETC 10) on mathematics education in the digital age (MEDA) (pp. 61–68).

Jameson, E. (2019). Background for the case study micro-report series. Cambridge Mathematics.

Jameson, E. (2019). Mapping MathemaTIC tasks to the Cambridge Mathematics Framework [Case study micro-report]. Cambridge Mathematics, Cambridge University Press & Assessment.

Jameson, E. (2019). Methodology: Building the research base. Cambridge Mathematics, Cambridge University Press & Assessment.

Jameson, E. (2019). Methodology: Formative evaluation. Cambridge Mathematics, Cambridge University Press & Assessment.

Jameson, E. (2019). Methodology: Research-informed design. Cambridge Mathematics, Cambridge University Press & Assessment.

Jameson, E., & Horsman, R. (2019). Writing a textbook chapter using the Cambridge Mathematics Framework [Case study micro-report]. Cambridge Mathematics, Cambridge University Press & Assessment.

Jameson, E., & Lai, R. P. Y. (2019). Designing a framework for computational thinking with Arm [Case study micro-report]. Cambridge Mathematics, Cambridge University Press & Assessment.

Jameson, E. M., McClure, L., & Gould, T. (2018). Shared perspectives on research in curriculum reform: Designing the Cambridge Mathematics Framework. In Y. Shimizu & R. Vithal (Eds.), ICMI Study 24 conference proceedings (pp. 531–538). ICMI.

Macey, D., Jameson, E., Horsman, R., Kathotia, V., McClure, L., & Rycroft-Smith, L. (2018). Towards a research-based framework for statistics education. In M. A. Sorto (Ed.), Looking back, looking forward. Proceedings of the Tenth International Conference on Teaching Statistics. International Statistical Institute.

Jameson, E., Horsman, R., & McClure, L. (2017). Exploring the development of a mathematics curriculum framework: Cambridge Mathematics. In G. Kaiser (Ed.), Proceedings of the 13th International Congress on Mathematical Education (pp. 665–666). Springer International Publishing.

Professional learning in mathematics education

Through our research synthesis work we have built insights across many sources that we feel could make positive contributions directly to teacher professional learning. Our publications in this area aim to report on ways we are helping to translate research into teaching practice.

Jameson, E., Li, X. (2025). JourneyMaths: Deepening teachers' specialized content knowledge through exploration of mathematical connections. In P. Seitamaa-Hakkarainen & K. Kangas (Eds.), General proceedings of the 5th annual meeting of the International Society of the Learning Sciences 2025 (pp. 52–56). International Society of the Learning Sciences.

Gould, T., Jameson, E., & Watson, F. (2024, July 7–14). Designing professional development activities to support pedagogical content knowledge [Workshop]. The 15th International Congress on Mathematical Education, Sydney, NSW, Australia.

Rycroft-Smith, L. & Watson, F. (2024). The big picture: Designing infographics in mathematics education. In Fujita, T. (Ed.), Proceedings of the British Society for Research into Learning Mathematics (Volume 44, No. 1). BSRLM.

Jameson, E., Gould, T., & Rycroft-Smith, L. (2022). Designing for teacher reflection and engagement with research on connected mathematical ideas. In C. Fernández, S. Llinares, Á. Gutiérrez, & N. Planas (Eds.), Proceedings of the 45th conference of the International Group for the Psychology of Mathematics Education (Vol. 4, p. 240). PME.

Rycroft-Smith, L., & Stylianides, A. J. (2022). What makes a good educational research summary? A comparative judgement study of mathematics teachers’ and mathematics education researchers’ views. Review of Education, 10(1), e3338.

Baldry, F., Mann, J., Horsman, R., Koiwa, D., & Foster, C. (2022). The use of carefully planned board work to support the productive discussion of multiple student responses in a Japanese problem-solving lesson. Journal of Mathematics Teacher Education. 26(2), 129–153.

Rycroft-Smith, L. & Macey, D. (2021). Deep questions of evidence and agency: How might we find ways to resolve tensions between teacher agency and the use of research evidence in mathematics education professional development? In R. Marks (Ed.), Proceedings of the British Society for Research into Learning Mathematics (Vol. 41, No 2). BSRLM.

Digital technology, including AI, in mathematics education

Our synthesis of research on interconnected ideas in mathematics learning has led us to represent them as a web rather than the straight line of a curriculum. In the publications below we explore how digital technologies, including AI, might open up different pathways for learning.

Li, X., & Zaki, R. (2026). Empowering early educators and learners: Integrating AI in mathematics education. In S. Papadakis (Ed.), AI applications in preschool and primary education: Teaching with artificial intelligence (pp. XX – XX). Springer Nature.

Li, X., Fadel, C., & Zaki, R. (2025). Beyond chatbots: Improving intelligent tutoring systems with better data and assessments. In L. G. Chova, C. G. Martínez, & J. Lees (Eds.), Proceedings of the 19th Annual International Technology, Education and Development Conference, INTED (pp. 5789–5798). IATED.

Li, X., Morley, F., & Zaki, R. (2025). AI tutors: From promise to practice in primary and early education. In S. Papadakis (Ed.), Teaching with artificial intelligence: A guide for primary and elementary educators. Routledge.

Li, X., Morley, F., & Zaki, R. (2025). Mind the knowledge gap: Evaluating AI tutors’ ability to detect mathematical prior knowledge and misconceptions. EasyChair Preprint 15939.

Li, X. (2024). Engaging with artificial intelligence in research and writing (Engaging with emerging technologies in education, Issue 2). Cambridge Mathematics, Cambridge University Press & Assessment.

Li, X. (2024). Extended reality (XR) in mathematics assessment: A pedagogical vision. Research Matters: A Cambridge University Press & Assessment publication, 37, 6–23.

Li, X., Blackwell, A., & Ge, H. (2024). Harnessing the power of artificial intelligence in mathematics education: The potential of probabilistic programming languages in the teaching and learning of Bayesian statistics. In L. G. Chova, C. G. Martínez, & J. Lees (Eds.), Proceedings of the 16th International Conference on Education and New Learning Technologies (pp. 8074–8083). IATED.

Li, X., Gould, T., & R. Zaki. (2024). The impact of artificial intelligence on learners and teachers: A mathematics education perspective. In S. Papadakis & M. Kalogiannakis (Eds.), Education, development and intervention: Toward participatory and integrated solutions (pp.133–148). Springer.

Li, X., & Zaki, R. (2024). Harnessing the power of digital resources in mathematics education: The potential of augmented reality and artificial intelligence. In S. Papadakis (Ed.), IoT, AI and ICT for educational applications: Technologies to enable education for all (pp. 191–223). Springer.

Li, X. (2023). Bridging the literature gap: An innovative framework for understanding secondary school students’ emerging technology use in out-of-class mathematics learning contexts. In P. Drijvers, C. Csapodi, H. Palmér, K. Gosztonyi, & E. Kónya (Eds.), Proceedings of the Thirteenth Congress of the European Society for Research in Mathematics Education (pp. 2983–2984). Alfréd Rényi Institute of Mathematics and ERME.

Li, X. (2023). Engaging with artificial intelligence in research and writing (Engaging with emerging technologies in education, Issue 1). Cambridge Mathematics, Cambridge University Press & Assessment.

Li, X. (2023). Transformative implications and evidence-based principles for creating content for mathematics learning in the metaverse. In L. G. Chova, C. G. Martínez, & J. Lees (Eds.), Proceedings of the 15th International Conference on Education and New Learning Technologies (pp. 1994–2003). IATED.

Series: Cambridge Mathematics Framework documentation

The design of the Framework is influenced by our assumptions, theories and methods. In this section we record our decisions, both for ourselves and so that others can understand our journey. Here you will find fully referenced articles describing different aspects of the design, and a linked summary of each report.

View documentation

Series: Use case reports

Our use case reports describe what we’ve learned from observing and supporting the use of the Framework in real curriculum and resource development projects.

View reports

Series: Engaging with emerging technologies in education

In this series we present guidelines on how to engage ethically and responsibly with emerging technologies in education.

View guidelines

Team authors

Information about publication authors for Cambridge Mathematics can be found on Our team page.

Advisors

As part of our aim of trustworthiness, we have collected feedback on our methods and content from people in our various stakeholder communities over the years. These advisors are listed here.