Journal Articles

Alcock, L., Davies, B., & Inglis, M. (in press, August 2026). Logical Reasoning in Mathematics Students: Conditional Inference with Mathematical, Abstract and Everyday Content. Journal of Research in Mathematics Education.

Bokhove, C., Davies, B., Cen, J., Spakula, J. & Gammack, D. (in press, August 2026). The interplay of Task Difficulty, Precision, and Feedback in Online Maths Environments.

Cronin, A. & Davies, B. (under review). Comparative Judgement as a means to authentic student engagement with proof writing in a specialist linear algebra course. Problems, Resources, and Issues in Mathematics Undergraduate Studies.

Kinnear, G., Jones, I. & Davies, B. (2025). Comparative Judgement as a Research Tool: A Meta-Analysis of Application and Reliability. Behavior Research Methods, 57(8), article 222. https://doi.org/10.17605/OSF.IO/M5WTZ

Davies, B. (2025). The Summary Task and its potential for Proof Comprehension. In Savic, M. and Weber, K. (Eds) New Directions in University Proving: Honoring the Legacy of John and Annie Selden. 10.1007/978-3-031-85004-2_8

Davies, B., Smart, T., Geraniou, E. & Crisan, C. (2024). A Department-wide Transition to a New Mode of Computer-Aided Assessment Using STACK. International Journal of Research in Undergraduate Mathematics Education. 10.1007/s40753-024-00251-5

Kinnear, G., Iannone, P. & Davies, B. (2024). Student approaches to generating mathematical examples: comparing e-assessment and paper-based tasks. Educational Studies in Mathematics. https://doi.org/10.1007/s10649-024-10361-1

Jones, I. and Davies, B. (2023). Comparative judgement in education research. International Journal of Research & Method in Education, 1-12, doi.org/10.1080/1743727X.2023.2242273

Tanswell, F., Davies, B., Jones, I. & Kinnear, G. (2023). Comparative Judgement for Experimental Philosophy: Assessing Ordinary Meaning in Vehicles in the Park Cases. Philosophical Psychology. https://doi.org/10.1080/09515089.2023.2263036

Kinnear, G., Jones, I., Sangwin, C., Alarfaj, M., Davies, B., Fearn, S. et al. (2022). A collaboratively-derived research agenda for e-assessment in university mathematics. International Journal of Research in Undergraduate Mathematics Education. doi.org/10.1007/s40753-022-00189-6

Miller, D., Case, J., & Davies, B. (2022). Students’ beliefs on empirical arguments and mathematical proof in an ‘introduction to proof’ class. International Journal of Mathematics Education in Science and Technology. https://doi.org/10.1080/0020739X.2022.2086082

Davies, B. & Jones. I. (2021). Assessing proof reading comprehension using summaries. International Journal of Research in Undergraduate Mathematics Education. https://doi.org/10.1007/s40753-021-00157-6

Davies, B., Jones. I, and Alcock, L. (2021).  What do mathematicians mean by proof? A comparative judgement study of students’ and mathematicians’ views. Journal of Mathematical Behaviour. https://doi.org/10.1016/j.jmathb.2020.100824

Davies, B, Infante, N., & Miller, D. (2021). The role of authorial context in mathematicians’ evaluations of proof. International Journal of Mathematics Education in Science and Technology. https://doi.org/10.1080/0020739X.2021.1966531

Davies, B., Alcock, L. & Jones, I. (2020). Comparative judgement, proof summaries and proof comprehension. Educational Studies in Mathematics. 105, 181–197. https://doi.org/10.1007/s10649-020-09984-x

Davies, B., Yoon, C., Moala, J. G., and Maciejewski, W. (2016). Principles for designing invention tasks for undergraduate mathematics. In 13th International Congress on Mathematical Education. https://www.researchgate.net/publication/312130794

Conference contributions

Davies, B. (2026). Whose job is it now? Agentic AI, STACK, and the changing dynamics of question authoring. British Society for Research into Learning Mathematics, Summer Day Conference, June 2026

Alcock, L. & Davies, B. (2024). Believability in Mathematical Conditionals: Generating Items for a Conditional Inference Task. In Proceeding XXVI C-RUME, Nebraska, USA. https://hdl.handle.net/2134/24864948.v1

Alcock, L. & and Davies, B. (2024). Believability in Mathematical Conditionals: A comparative judgement study. INDRUM, 2024.

Davies, B., Biza, I., Iannone, P., Kinnear, G., & Nieminen, J. (2024). Developing a research agenda for GenerativeAI in undergraduate Mathematics Education. British Society for Research into Learning Mathematics, February 2024.

Davies, B. (2023). Bringing SMP into the 21st century using STACK. British Society for Research into Learning Mathematics, November, 2023, University of Bristol.

Kinnear, G., Iannone, P., & Davies, B. (2023). Insights about functions from example-generation tasks: combining e-assessment and written responses. In CERME13 Proceeedings. Available here.

Davies, B. (2022). What do mathematicians mean by proof? Topics in Philosophy of Mathematical Practice. Online. Recording available here.

Infante, N., Schraeder, N. & Davies, B. (2022). Oral assessment in university mathematics: The role and variation of follow-up questions. To be presented at The 24th Annual Conference on Research on Undergraduate Mathematics Education, February, 2022. Boston, MA, USA. [Available here]

Davies, B., Smart, T., Geraniou, E. & Crisan, C. (2022). STACKification: automating assessments in tertiary mathematics. Presented at the Twelfth Congress of the European Society for Research in Mathematics Education, February 2022. Bolzano, Italy.

Davies, B., Iannone, P. & Kinnear, G. (2022). Student approaches to generating mathematical examples: comparing STACK and paper-based tasks. International Meeting of the STACK Community, 2022. Leoben, Austria. Montan Universität Leoben.

Davies, B. and Reynolds, R. (2021). Understanding students’ experiences with automated assessment in STACK. International Meeting of the STACK Community 2021. Recording available here. Tallinn, Estonia: TTK University of Applied Sciences.

Reynolds, R. and Davies, B. (2021). In parallel: Workshop on STACKification: from existing worksheets to coded question banks. International Meeting of the STACK Community 2021. Tallinn, Estonia: TTK University of Applied Sciences.

Infante, N., Schraeder, N., & Davies, B. (2020). Oral Assessment in University Mathematics: The Role and Variations of Follow-up Questions. In Proceedings of the 24th Annual Conference on Research in Undergraduate Mathematics Education. Boston, MA, USA. http://sigmaa.maa.org/rume/RUME24.pdf

Davies, B. Jones, I and Alcock, L. (2019). Comparative judgment and proof comprehension. Presentation at the Conference of the British Society for Research into Learning Mathematics. Abstract available at http://www.bsrlm.org.uk/wp-content/uploads/2018/11/BSRLM-Conference-Nov-2018-Abstracts-v3.pdf

Davies, B., Jones, I., and Alcock, L. (2018). What do mathematicians mean by proof? Poster presented at 21st SIGMAA on Research in Undergraduate Mathematics Education. San Diego, USA. Manuscript available at https://doi.org/10.13140/RG.2.2.14943.36006

Davies, B. (2017). A case for a new approach to establishing the validity of comparative judgement as an assessment tool for mathematics. In Proceedings of the 10th Congress of European Research in Mathematics Education. Manuscript available at https://hal.archives-ouvertes.fr/hal-01949283/

Other outputs

Davies, B. (coming soon). SMP 3.0 – An interactive textbook archieve for A-level mathematics.

Bokhove, C., Hyde, R., Davies, B. & Hill, C. (2026). Response to the Department for Education consultation on 16-19 Level 1 English and Maths Qualifications. Available here

Davies, B. (2020). Automated Theorem Provers and the future instruction of proof-based mathematics. Symposium on Imagining the Future of Undergraduate STEM Education. Essay submission commended by the National Academy of Sciences, Engineering, and Medicine. Available here.

Barton, B., Davies, B., Moala, J., and Yoon, C. (2017). How to: Generate conceptual readiness. Report by Ako Aotearoa. https://ako.ac.nz/knowledge-centre/undergraduate-mathematics

Invited Talks

Agentic AI, STACK, and the changing dynamics of question authoring. (2026, July 6th). California Institute of Technology (Caltech).

Novel assessments for Tertiary mathematics. (2023, July 21st) Keynote presentation at British Early Career Mathematicians’ Colloquium. Abstract available here.

On the role of summarising in tertiary mathematics education (2022, May 4th). University of Strathclyde.

Assessing proof reading comprehension using summaries (2021, July 15th). The University of Edinburgh. Recording available here.

Automated assessment of tertiary mathematics at UCL. (2021, May 20th). Institute of Education, University College London. Abstract available here.

Comparative Judgement, proof summaries and proof comprehension. (2021, Feb 11th). University of Auckland. Recording available here.

Assessing proof comprehension in University Mathematics. (2020, Feb 19th). West Virginia University colloquium. Abstract available here.

Comparative Judgement and proof. (2019). Loughborough University.

Theses

Davies, B. (2019). Comparative Judgment and Proof. Loughborough University Doctoral Thesis (unpublished). DOI: 10.13140/RG.2.2.33043.63527

Davies, B. (2015). New principles for designing quasi-induction tasks. University of Auckland Honours thesis (unpublished). https://www.researchgate.net/publication/323540471

Grants and Research Funding

Davies, B. (2026). SMP 3.0: Using Agentic AI to generate e-workbooks for A-level mathematics. Awarded by the Southampton SMP Fund. £4,500.

Davies, B. and Ogden, H. (2025). Statistics for Adaptive Learning. Awarded by the SMP Maths Education Fund. ~£20,000

Davies, B. & Whitburn, B. (2024). Strengthening Staff Capacity for Inclusive Communication Using Accessible Images. £3,000

Zheng, Y. and Davies, B. (2023). Exploring AI applications in essay-based assignments: comparability of human marking and potentials in assessing critical thinking. Awarded by The University of Southampton Centre for Higher Education Practice (CHEP). £5000.

Davies, B. (2023). SMP Online: Developing interactive e-workbooks for A-level mathematics. Awarded by the Higher Education Innovation Fund. £25,278.

Davies. B. and Thoma, A. (2023). STACK for stats: supporting education students learning quantitative research methods. School of Education Teaching support fund, University of Southampton. £3500.

Davies, B. (2021). Understanding undergraduate students’ experiences with computer-aided assessment. Awarded by the Department of Mathematics, University College London. £3000.

McEldowney, T., Deshler, J., Miller, D., Gallagher, K., and Davies, B. (2020). WVU Emerging Scholars Program Summer Bridge 2020. The Tensor Foundation and the Mathematical Association of America, USD$6000.

Davies, B. (2018) Loughborough University International Exchange fun. £5000. 

Davies, B. (2016) Loughborough University Doctoral Studentship. £45000.

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