Dr. Juan Pablo Mejía Ramos

Some of my most recent research projects focus on the reasoning of mathematics undergraduate students as they construct mathematical proofs, the reading of published proofs by research-active mathematicians, the assessment of proof comprehension at the university level, and the different ways in which mathematicians present proofs in their advanced mathematics courses.

This NSF website contains more information on my project on proving styles in undergraduate mathematics, this one and this one provide information on two projects to design and validate proof comprehension tests in undergraduate mathematics, and this one describes a project in which we designed, implemented, and assessed an innovative real analysis course for pre-service and in-service mathematics teachers. For more information on this last project, please visit the website for the ULTRA project. For information on other projects (and to download related papers), please visit the website of our research group: Proof Comprehension Research Group.

Many of my publications can be downloaded at the Proof Comprehension Research Group website: pcrg.gse.rutgers.edu

Book Chapters

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. (pp. 123-144). Bloomsbury. https://doi.org/10.5040/9781350039049.0009

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

Inglis, M., & Mejía Ramos, J. P. (2013). How persuaded are you? A typology of responses. In A. Aberdein & I. Dove (Eds.) The Argument of Mathematics (pp. 101-118). Springer. This chapter is a reprint of the journal article published in Research in Mathematics Education 10(2), 119-133. https://doi.org/10.1007/978-94-007-6534-4_7

Tall, D. O., & Mejía Ramos, J. P. (2010). The long-term cognitive development of reasoning and proof, in G. Hanna, H.N. Jahnke, and H. Pulte (Eds.), Explanation and Proof in Mathematics: Philosophical and Educational Perspectives (pp. 137-149). Springer. https://doi.org/10.1007/978-1-4419-0576-5_10

Mejía Ramos, J. P. (2006). An analysis of three modes of proof, in A. Simpson (Ed.), Retirement as Process and Concept: A Festschrift for Eddie Gray and David Tall, Prague, Czec Republic, 15-16 July 2006 (pp. 173-180). Karlova Univerzita v Praze, Pedagogick Fakulta.

Refereed Journal Papers

Weber, K., Mejía Ramos, J. P., & Volpe, T. (accepted). An empirical investigation into the relationship between proof and certainty in mathematical practice. Accepted for publication in Journal for Research in Mathematics Education.

Mejía Ramos, J. P., Evans, T., Rittberg, C., & Inglis, M. (in press). Mathematicians’ assessments of the explanatory value of proofs. To appear in Axiomathes.

Lew, K., Weber, K., & Mejía Ramos, J. P. (2020). Do generic proofs improve proof comprehension? Journal of Educational Research in Mathematics, Special Issue, 229–248. https://doi.org/10.29275/jerm.2020.08.sp.1.229

Weber, K., Dawkins, P., & Mejía Ramos, J. P. (2020). The relationship between mathematical practice and mathematics pedagogy in mathematics education research. ZDM Mathematics Education, 52(6), 1063–1074. https://doi.org/10.1007/s11858-020-01173-7

Mejía Ramos, J. P., & Weber, K. (2020). Using task-based interviews to generate hypotheses about mathematical practice: Mathematics education research on mathematicians’ use of examples. ZDM Mathematics Education, 52(6), 1099–1112. https://doi.org/10.1007/s11858-020-01170-w

Fukawa–Connelly, T., Mejía Ramos, J. P., Wasserman, N., & Weber, K. (2020). An evaluation of ULTRA: An experimental real analysis course built on a transformative theoretical model. International Journal of Research in Undergraduate Mathematics Education, 6(2), 159–185. https://doi.org/10.1007/s40753-019-00102-8

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

Wasserman, N., Weber, K., Fukawa-Connelly, T., & Mejía Ramos, J. P. (2020). Area-preserving transformations: Cavalieri in 2D. Mathematics Teacher: Learning and Teaching PK-12, 113(1), 53-60. https://doi.org/10.5951/MTLT.2019.0079

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

Inglis, M. & Mejía Ramos, J. P. (2019). Functional explanation in mathematics. Synthese. Advance online publication. https://doi.org/10.1007/s11229-019-02234-5

McGuffey, W., Quea, R., Weber, K., Wasserman, N., Fukawa-Connelly, T., & Mejía Ramos, J.P . (2019). Pre- and in-service teachers’ perceived value of an experimental real analysis course for teachers. International Journal of Mathematical Education in Science and Technology, 50(8), 1166-1190. https://doi.org/10.1080/0020739X.2019.1587021

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

Wasserman, N., Weber, K., Villanueva, M., & Mejía Ramos, J. P. (2018). Mathematics teachers’ views about the limited utility of real analysis: A transport model hypothesis. Journal of Mathematical Behavior, 50, 74-89. https://doi.org/10.1016/j.jmathb.2018.01.004

Fukawa-Connelly, T., Weber, K., & Mejía Ramos, J. P. (2017). Informal content and student note-taking in advanced mathematics classes. Journal for Research in Mathematics Education, 48(5), 567-579. https://doi.org/10.5951/jresematheduc.48.5.0567

Wasserman, N., Fukawa-Connelly, T., Villanueva, M., Mejía Ramos, J.P., & Weber, K. (2017). Making real analysis relevant to secondary teachers: Building up from and stepping down to practice. PRIMUS, 27(6), 559-578. https://doi.org/10.1080/10511970.2016.1225874

Mejía Ramos, J. P., Lew, K., de la Torre, J., & Weber, K. (2017). Developing and validating proof comprehension tests in undergraduate mathematics. Research in Mathematics Education, 19(2), 130-146. https://doi.org/10.1080/14794802.2017.1325776

Weber, K., Fukawa-Connelly, T., Mejía Ramos, J. P., & Lew, K. (2016). How to help students understand lectures in advanced mathematics. Notices of the AMS, 63(10), 1190-1193. https://doi.org/10.1090/noti1435

Lew, K., Fukawa-Connelly, T., Mejía Ramos, J.P., & Weber, K. (2016). Lectures in advanced mathematics: Why students might not understand what the professor is trying to convey. Journal for Research in Mathematics Education, 47, 162-198. https://doi.org/10.5951/jresematheduc.47.2.0162

Zazkis, D., Weber, K., & Mejía Ramos, J.P. (2016). Bridging the gap between informal argument and mathematical proof. Educational Studies in Mathematics, 93(2), 155-173. https://doi.org/10.1007/s10649-016-9698-3

Zhen, B. Mejía Ramos, J.P. & Weber, K. (2016). Mathematics majors’ perceptions on the permissibility of graphs in proofs. International Journal for Research in Undergraduate Mathematics Education, 2, 1-29. https://doi.org/10.1007/s40753-015-0010-1

Mejía Ramos, J. P., Weber, K., & Fuller, E. (2015). Factors influencing students’ propensity for semantic and syntactic reasoning in proof writing: A single-case study. International Journal of Research in Undergraduate Mathematics Education, 1(2), 187-208. https://doi.org/10.1007/s40753-015-0014-x

Weber, K. & Mejía Ramos, J. P. (2015). The contextual nature of conviction in mathematics. For the Learning of Mathematics, 35(2), 9-14.

Zazkis, D., Weber, K., & Mejía Ramos, J. P. (2015). Two proving strategies of highly successful mathematics majors. Journal of Mathematical Behavior, 39, 11-27. https://doi.org/10.1016/j.jmathb.2015.04.003

Fuller, E., Weber, K., Mejía Ramos, J. P., Samkoff, A., & Rhoads, K. (2014). Comprehending structured proofs. International Journal for Studies in Mathematics Education 7(1), 1-32. https://doi.org/10.17921/2176-5634

Weber, K., Inglis, M., & Mejía Ramos, J. P. (2014). How mathematicians obtain conviction: Implications for mathematics instruction and research on epistemic cognition. Educational Psychologist, 49(1), 36-58. https://doi.org/10.1080/00461520.2013.865527

Mejía Ramos, J. P., & Weber, K. (2014). Why and how mathematicians read proofs: further evidence from a survey study. Educational Studies in Mathematics, 85(2), 161-173. https://doi.org/10.1007/s10649-013-9514-2

Weber, K., & Mejía Ramos, J. P. (2014). Mathematics majors’ beliefs about proof reading. International Journal of Mathematical Education in Science and Technology, 45(1), 89-103. https://doi.org/10.1080/0020739X.2013.790514

Weber, K., & Mejía Ramos, J. P. (2013). The influence of sources in the reading of mathematical text: A reply to Shanahan, Shanahan, and Misischia. Journal of Literacy Research, 45, 87-96. https://doi.org/10.1177/1086296X12469968

Weber, K., & Mejía Ramos, J. P. (2013). On mathematicians’ proof skimming: A reply to Inglis and Alcock. Journal for Research in Mathematics Education, 44(2), 464-471. https://doi.org/10.5951/jresematheduc.44.2.0464

Inglis, M., Mejía Ramos, J. P., Weber, K., & Alcock, L. (2013). On mathematicians’ different standards when evaluating elementary proofs. Topics in Cognitive Science, 5(2), 270-282. https://doi.org/10.1111/tops.12019

Lai, Y., Weber, K., & Mejía Ramos, J. P. (2012). Mathematicians’ perspectives on features of a good pedagogical proof. Cognition and Instruction, 30(2), 146-169. https://doi.org/10.1080/07370008.2012.661814

Mejía Ramos, J. P., Fuller, E., Weber, K., Rhoads, K., & Samkoff, A. (2012). An assessment model for proof comprehension in undergraduate mathematics. Educational Studies in Mathematics, 79(1), 3-18. https://doi.org/10.1007/s10649-011-9349-7

Iannone, P., Inglis, M., Mejía Ramos, J. P., Simpson, A. & Weber, K. (2011). Does generating examples aid proof production? Educational Studies in Mathematics, 77, 1-14. https://doi.org/10.1007/s10649-011-9299-0

Mejía Ramos, J. P. & Inglis, M. (2011). Semantic contamination and mathematical proof: Can a non-proof prove? Journal of Mathematical Behavior, 30, 19-29. https://doi.org/10.1016/j.jmathb.2010.11.005

Weber, K. & Mejía Ramos, J. P. (2011). Why and how mathematicians read proofs: An exploratory study. Educational Studies in Mathematics, 76, 329-344. https://doi.org/10.1007/s10649-010-9292-z

Weber, K. & Mejía Ramos, J. P. (2009). An alternative framework to evaluate proof productions. Journal of Mathematical Behavior, 28, 212-216. https://doi.org/10.1016/j.jmathb.2009.10.005

Inglis, M., & Mejía Ramos, J. P. (2009). The effect of authority on the persuasiveness of mathematical arguments. Cognition and Instruction, 27, 25-50. https://doi.org/10.1080/07370000802584513

Inglis, M., & Mejía Ramos, J. P. (2009). On the persuasiveness of visual arguments in mathematics. Foundations of Science, 14,97-110. https://doi.org/10.1007/s10699-008-9149-4

Mejía Ramos, J. P., & Inglis, M. (2009). What are the argumentative activities associated with proof? Research in Mathematics Education, 11, 77-78. https://doi.org/10.1080/14794800902732258

Inglis, M., & Mejía Ramos, J. P. (2008). How persuaded are you? A typology of responses. Research in Mathematics Education, 10(2), 119-133. https://doi.org/10.1080/14794800802233647

Inglis, M., & Mejía Ramos, J. P. (2008). Theoretical and methodological implications of a broader perspective on mathematical argumentation. Mediterranean Journal for Research in Mathematics Education, 7(2), 107-119.

Inglis, M., Mejía Ramos, J. P., & Simpson, A. (2007). Modelling mathematical argumentation: The importance of qualification. Educational Studies in Mathematics, 66, 3-21. https://doi.org/10.1007/s10649-006-9059-8

Inglis, M., & Mejía Ramos, J. P. (2005). La fuerza de la aserción y el poder persuasivo en la argumentación en matemáticas. Revista EMA: Investigación e Innovación en Educación Matemática, 10,327-352.