The PCRG is organizing research webinars on select Fridays this term (2pm-4pm EDT/EST). Members of the community are welcome to join us to discuss important topics in the field, and to attend related talks by invited speakers. You will need to register to receive information on how to join the meetings.
The workshop Understanding Mathematical Explanation: Uniting Philosophical and Educational Perspectives, originally scheduled on April 6-7 2020, was postponed due to COVID-19. New date to be announced.
Recently published papers
Weber, K., Mejía Ramos, J. P., & Volpe, T. (in press). An empirical investigation into the relationship between proof and certainty in mathematical practice. To appear in Journal for Research in Mathematics Education. [preprint]
Mejía Ramos, J. P., Evans, T., Rittberg, C., & Inglis, M. (2021). Mathematicians’ assessments of the explanatory value of proofs. Axiomathes. Advance online publication. https://doi.org/10.1007/s10516-021-09545-8
Harel, G. & Weber, K. (2020). Deductive reasoning in mathematics education. In S. Lerman (Ed.) Encyclopedia of Mathematics Education (pp. 183-190). Springer.
Woods, C., & Weber, K. (2020). The relationship between mathematicians’ pedagogical goals, orientations, and common teaching practices in advanced mathematics. Journal of Mathematical Behavior, 59, Article 100792. https://doi.org/10.1016/j.jmathb.2020.100792
Lew, K., Weber, K., & Mejía Ramos, J.P. (2020). Do generic proofs improve comprehension? Journal of Educational Research in Mathematics, Special Issue, 229–248. https://doi.org/10.29275/jerm.2020.08.sp.1.229
Olsen, J., Lew, K., & Weber, K. (2020). Metaphors for learning and doing mathematics in advanced mathematics lectures. Educational Studies in Mathematics, 105, 1-17. https://doi.org/10.1007/s10649-020-09968-x
Fukawa-Connelly, T., Mejía Ramos, J.P., Wasserman, K., & Weber, K. (2020) An evaluation of ULTRA, an experimental real analysis course for prospective teachers built on a transformative model. International Journal of Research in Undergraduate Mathematics Education, 6(2), 159–185. https://doi.org/10.1007/s40753-019-00102-8
Lockwood, E., Caughman, J., & Weber, K. (2020). An essay on proof, conviction, and explanation: Multiple representation systems in combinatorics. Educational Studies in Mathematics, 103, 173-189. https://doi.org/10.1007/s10649-020-09933-8
Weber, K., Mejía Ramos, J.P., Fukawa-Connelly, T., & Wasserman, N. (2020). Connecting the learning of advanced mathematics with the teaching of secondary mathematics: Inverse functions, domain restrictions, and the arcsine function. Journal of Mathematical Behavior, 57, Article 100752. https://doi.org/10.1016/j.jmathb.2019.100752
Lew, K., & Mejía Ramos, J. P. (2020). The linguistic conventions of mathematical proof writing across pedagogical contexts. Educational Studies in Mathematics, 103(1), 43-62. https://doi.org/10.1007/s10649-019-09915-5
Weber, K., Lew, K., & Mejía Ramos, J. P. (2020). Using expectancy value theory to account for students' mathematical justifications.Cognition and Instruction, 38(1), 27-56. https://doi.org/10.1080/07370008.2019.1636796
Czocher, J. & Weber, K. (2020). Proof as a cluster concept. Journal for Research in Mathematics Education, 51(1), 50-74. https://doi.org/10.5951/jresematheduc.2019.0007
Inglis, M., & Mejía Ramos, J. P. (2019). Functional explanation in mathematics. Synthese. Advance online publication. https://doi.org/10.1007/s11229-019-02234-5
Weber, K. (2019). The role of syntactic representations in set theory. Synthese. Advance online publication. https://doi.org/10.1007/s11229-019-02157-1
Weber, K. & Czocher, J. (2019). On mathematicians’ disagreement on what constitutes a proof. Research in Mathematics Education, 21(3), 251-270. https://doi.org/10.1080/14794802.2019.1585936
Mejía Ramos, J. P. & Weber, K. (2019). Mathematics majors’ diagram usage when writing proofs in calculus. Journal for Research in Mathematics Education, 50(5), 478-488. https://doi.org/10.5951/jresematheduc.50.5.0478
Wasserman, N., Weber, K., Fukawa-Connelly, T., & McGuffey, W. (2019). Designing advanced mathematics courses to influence secondary teaching: Fostering mathematics teachers’ ‘attention to scope’. Journal of Mathematics Teacher Education, 22(4), 379-406. https://doi.org/10.1007/s10857-019-09431-6. Correction: https://doi.org/10.1007/s10857-019-09442-3
Weber, K. & Mejía Ramos, J.P. (2019). An empirical study on the admissibility of graphical inferences in mathematical proofs. In A. Aberdein & M. Inglis (Eds.) Advances in Experimental Philosophy of Logic and Mathematics. Bloomsbury. https://doi.org/10.5040/9781350039049.0009
Lew, K., & Mejía Ramos, J. P. (2019). Linguistic conventions of mathematical proof writing at the undergraduate level: Mathematicians’ and students’ perspectives. Journal for Research in Mathematics Education, 50(2), 121-155. https://doi.org/10.5951/jresematheduc.50.2.0121
Mejía Ramos, J. P., Alcock, L., Lew, K., Rago, P., Sangwin, C., & Inglis, M. (2019). Using corpus linguistics to investigate mathematical explanation. In F. Eugen & C. Mark (Eds.) Methodological Advances in Experimental Philosophy (pp. 239-263). Bloomsbury. https://doi.org/10.5040/9781350069022.ch-009
ULTRA. Upgrading Learning for Teachers in Real Analysis is an NSF-funded collaborative project to design, implement, and assess an innovative real analysis course for pre-service and in-service mathematics teachers. [site]