Juan Pablo Mejía Ramos

Associate Professor

Contact Details

Department of Learning & Teaching:
Of. GSE-234 (College Avenue)
Tel. +1-732-932-7496 x.8153

Department of Mathematics:
Of. HILL-207 (Busch)
Tel. +1-732-445-2390 x.6034

WebLinks

Articles:
Exemplification
Mathematician/Educationalist
Students' difficulties with proof

Bibliographies:
G.H.'s bibliography on proof 1
G.H.'s bibliography on proof 2
Newsletter on proof
PCRG
RUME bibliographic database

Collaborators:
Lara Alcock
Evan Fuller
Paola Iannone
Matthew Inglis
Yvonne Lai
Adrian Simpson
David Tall
Keith Weber

Conferences:
PMENA-37 (Nov. 2015)
CRUME-18 (Feb. 2016)

Groups, Networks, & Societies:
AERA SIG/RME
BSRLM
ERME
MERGA
MMESN
PCRG
PME
RUMEonline!

Journals:
C&I
ESM
FLM
JMB
JRME
MTL
RELIME
RME
ZDM

Hello   Hola

I am an Associate Professor of Mathematics Education at Rutgers University, where I am jointly appointed in the Department of Learning and Teaching within the Graduate School of Education and the Department on Mathematics within the School of Arts and Sciences. In this page you find information about my education, teaching at Rutgers, and academic writing. Please contact me if you have any questions/comments or if you would like an electronic copy of one of the papers listed below.

Research

I am mainly interested in mathematical argumentation and proof, particularly the ways in which university students and research-active mathematicians construct, read and present arguments and proofs in mathematics. Some of my most recent research projects focus on:
  • the reasoning styles of mathematics undergraduate students as they construct 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 and this one provides information on a recent project to validate proof comprehension tests in undergraduate mathematics. For more information on the other projects (and to download related papers), please visit the website of our research group: Proof Comprehension Research Group.

Education

PhD (Mathematics Education), University of Warwick, 2008;
MS (Mathematics Education), University of Warwick, 2004;
BS (Mathematics), Universidad de Los Andes, 2003.

Teaching

Abstract Algebra;
Introduction to Mathematical Reasoning;
Linear Algebra;
Mathematical Problem Solving;
Seminar in Mathematical Ideas;
Supervised Undergraduate Tutoring in Mathematics;
Teaching Internship Seminar.

Writing

Refereed Journal Papers

  • Lew, K., Fukawa-Connelly, T., Mejia-Ramos, J.P., & Weber, K. (accepted). Lectures in advanced mathematics: Why students might not understand what the professor is trying to convey. To appear in Journal for Research in Mathematics Education. [preprint]

  • Zazkis, D., Weber, K., & Mejia-Ramos, J.P. (accepted). Bridging the gap between informal argument and mathematical proof. To appear in Educational Studies in Mathematics.

  • Zhen, B. Mejia-Ramos, J.P. & Weber, K. (in press). Mathematics majors’ perceptions on the permissibility of graphs in proofs. To appear in International Journal for Research in Undergraduate Mathematics Education. [preprint]

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

  • Zazkis, D., Weber, K., & Mejia-Ramos, J. P. (2015). Two proving strategies of highly successful mathematics majors. Journal of Mathematical Behavior, 39, 11-27.

  • Fuller, E., Weber, K., Mejia-Ramos, J. P., Samkoff, A., & Rhoads, K. (2014). Comprehending structured proofs. International Journal for Studies in Mathematics Education 7(1), 1-32.[journal]

  • Weber, K., Inglis, M., & Mejia-Ramos, J. P. (2014). How mathematicians obtain conviction: Implications for mathematics instruction and research on epistemic cognition. Educational Psychologist, 49(1), 36-58. [preprint] [journal]

  • Mejia-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. [preprint] [journal]

  • Weber, K., & Mejia-Ramos, J. P. (2014). Mathematics majors' beliefs about proof reading. International Journal of Mathematical Education in Science and Technology, 45(1), 89-103.[preprint] [journal]

  • Weber, K., & Mejia-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.

  • Weber, K., & Mejia-Ramos, J. P. (2013). On mathematicians' proof skimming: A reply to Inglis and Alcock. Journal for Research in Mathematics Education, 44(2), 464-471.

  • Inglis, M., Mejia-Ramos, J. P., Weber, K., & Alcock, L. (2013). On mathematicians’ different standards when evaluating elementary proofs. Topics in Cognitive Science, 5(2), 270-282. [preprint]

  • Lai, Y., Weber, K., & Mejia-Ramos, J. P. (2012). Mathematicians' perspectives on features of a good pedagogical proof. Cognition and Instruction, 30(2), 146-169. [preprint] [journal]

  • Mejia-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. [preprint] [journal]

  • Iannone, P., Inglis, M., Mejia-Ramos, J. P., Simpson, A. & Weber, K. (2011). Does generating examples aid proof production? Educational Studies in Mathematics, 77, 1-14.

  • Mejia-Ramos, J. P. & Inglis, M. (2011). Semantic contamination and mathematical proof: Can a non-proof prove? Journal of Mathematical Behavior, 30, 19-29. [preprint] [journal]

  • Weber, K. & Mejia-Ramos, J. P. (2011). Why and how mathematicians read proofs: An exploratory study. Educational Studies in Mathematics, 76, 329-344. [preprint] [journal]

  • Weber, K. & Mejia-Ramos, J. P. (2009). An alternative framework to evaluate proof productions. Journal of Mathematical Behavior, 28, 212-216.

  • Inglis, M., & Mejia-Ramos, J. P. (2009). The effect of authority on the persuasiveness of mathematical arguments. Cognition and Instruction, 27, 25-50. [preprint] [journal]

  • Inglis, M., & Mejia-Ramos, J. P. (2009). On the persuasiveness of visual arguments in mathematics. Foundations of Science, 14, 97-110. [preprint] [journal]

  • Mejia-Ramos, J. P., & Inglis, M. (2009). What are the argumentative activities associated with proof? Research in Mathematics Education, 11, 77-78.

  • Inglis, M., & Mejia-Ramos, J. P. (2008). How persuaded are you? A typology of responses. Research in Mathematics Education, 10(2), 119-133. [preprint] [journal]

  • Inglis, M., & Mejia-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., Mejia-Ramos, J. P., & Simpson, A. (2007). Modelling mathematical argumentation: The importance of qualification. Educational Studies in Mathematics, 66, 3-21. [preprint] [journal]

  • Inglis, M., & Mejia-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. [preprint]

Book Chapters

  • Inglis, M., & Mejia-Ramos, J. P. (in press). How persuaded are you? A typology of responses. To appear in A. Aberdein & I. Dove (Eds.) The Argument of Mathematics. This chapter is a reprint of the journal article published in Research in Mathematics Education 10(2), 119-133.

  • Tall, D. O., & Mejia-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). New York: Springer.

  • Mejia-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). Prague: Karlova Univerzita v Praze, Pedagogick Fakulta.

Refereed Conference Papers

  • Lai, Y., Mejia-Ramos, J.P., & Weber, K. (2011). Improving the Quality of Proofs for Pedagogical Purposes: A Quantitative Study. In S. Brown, S. Larsen, K. Marrongelle, and M. Oehrtman (Eds.), Proceedings of the 14th Conference on Research in Undergraduate Mathematics Education (Vol. 3, pp. 88-91). Portland, Oregon.

  • Fuller, E., Mejia-Ramos, J. P., Weber, K., Samkoff, A., Rhoads, K., Doongaji, D, & Lew, K. (2011). Comprehending Leron’s structured proofs. In S. Brown, S. Larsen, K. Marrongelle, and M. Oehrtman (Eds.), Proceedings of the 14th Conference on Research in Undergraduate Mathematics Education (Vol. 1, pp. 84-102). Portland, Oregon.

  • Mejia Ramos, J. P., Weber, K., Fuller, E., Samkoff, A., Search, R., & Rhoads, K. (2010). Modeling the comprehension of proof in undergraduate mathematics. In Proceedings of the 13th Conference on Research in Undergraduate Mathematics Education, Raleigh, NC, February, 2010.

  • Inglis, M., & Mejia-Ramos, J. P. (2010). Language, semantic contamination and mathematical proof. In Proceedings of the 13th Conference on Research in Undergraduate Mathematics Education, Raleigh, NC, February, 2010.

  • Iannone, P., Inglis, M., Mejia-Ramos, J. P., Siemons, J., & Weber, K. (2009). How do undergraduate students generate examples of mathematical concepts? In M. Tzekaki, M. Kaldrimidou, and H. Sakonidis (Eds.), Proceedings of the 33rd Conference of the International Group for the Psychology of Mathematics Education (pp. 217-224), Thessaloniki, Greece.

  • Mejia-Ramos, J. P., & Inglis, M. (2009). Argumentative and proving activities in mathematics education research. In F.-L. Lin, F.-J. Hsieh, G. Hanna, and M. de Villiers (Eds.), Proceedings of the ICMI Study 19 conference: Proof and Proving in Mathematics Education (Vol. 2, pp. 88-93), Taipei, Taiwan.

  • Mejia-Ramos, J. P., & Inglis, M. (2009). Different ways of assessing the persuasiveness of mathematical arguments. In Proceedings of the 12th Conference on Research in Undergraduate Mathematics Education, Raleigh, NC, 26 February - 1 March.

  • Inglis, M., & Mejia-Ramos, J. P. (2006). Applying informal logic to arguments in mathematics. In Proceedings of the 3rd International Congress on the Teaching of Mathematics, Istanbul, Turkey, 30 June - 5 July 2006.

  • Mejia-Ramos, J. P., & Tall, D. O. (2005). Personal and public aspects of formal proof: a theory and a single-case study. In D. Hewitt and A. Noyes (Eds.), Proceedings of the 6th British Congress of Mathematics Education (pp. 97-104), London: BSRLM.

Recent Presentations

Keynote or Plenary Addresses

  • Mejia-Ramos, J. P. (2012, November). Reading mathematics: Empirical research on expert mathematical practices. Plenary address at the conference Cultures of Mathematics and Logic, Guangzhou, China.

  • Mejia-Ramos, J. P. (2012, September). How are mathematical proofs read? Plenary address at the 6th International Meeting on the Teaching of Calculus, Mexico City, Mexico.

  • Mejia-Ramos, J. P. (2011, September). Argumentation and Proof in Calculus. Plenary address at the 5th International Meeting on the Teaching of Calculus, Toluca, Mexico.

Invited Addresses

  • Mejia-Ramos, J. P. (2012, November). Explaining and comprehending mathematical proofs. Invited presentation at the Mathematics Education Seminar Series, University of Auckland, NZ.

  • Mejia-Ramos, J. P. (2012, November). Reading comprehension tests in calculus. Invited workshop at the Auckland Mathematics Association Calculus Day, University of Auckland, NZ.

  • Mejia-Ramos, J. P. (2011, November). Educational research on argumentation in university mathematics. Invited presentation at the Mathematics Education Seminar Series, York College of the City University of New York, NY.

  • Fuller, E., Weber, K., & Mejia-Ramos, J. P. (2011, October). Assessing students’ understanding of mathematical proofs. Invited workshop at the Meeting of the New Jersey Section of The Mathematical Association of America, Montclair State University, Montclair.

  • Mejia-Ramos, J. P. (2011, August). An assessment model of proof comprehension in undergraduate mathematics. Invited presentation at the Loughborough Mathematical Reading Workshop, Loughborough University, Loughborough, U.K.

  • Mejia-Ramos, J. P. (2011, February). Research on argumentation in undergraduate mathematics education. Invited presentation at the Mathematics and Science Education Research Seminar Series, University of California San Diego, La Jolla.

  • Mejia-Ramos, J. P. (2010, July). Modeling the comprehension of proofs in undergraduate mathematics. Invited presentation at the Winter School of Research in Mathematics Education, Federal University of the State of Rio de Janeiro, Rio de Janeiro.

  • Weber, K., & Mejia-Ramos, J. P. (2010, February). Proof presentation: Existing research and open questions. Invited presentation for the Working Group on Proof Presentation at the 13th Conference for Research in Undergraduate Mathematics Education, Raleigh, NC.

  • Mejia-Ramos, J. P. (2010, January). Undergraduate students’ assessment of the persuasiveness of mathematical arguments: Beyond private and public senses of conviction. Invited presentation at the 2010 Joint Mathematics Meetings, San Francisco.

Other Conference Presentations

  • Fuller, E., Weber, K., Mejia-Ramos, J. P., Rhoads, K., & Samkoff, A. (2012, April). Comprehending Leron’s structured proofs. Poster to be presented at the 2012 Annual Meeting of the American Educational Research Association. Vancouver, Canada.

  • Samkoff, A., Weber, K., & Mejia-Ramos, J. P. (2012, February). What’s the big idea?: Mathematicians’ and undergraduates’ proof summaries. To be presented at the 15th Conference on Research in Undergraduate Mathematics Education. Portland, Oregon.

  • Weber, K., Fuller, E., Mejia-Ramos, J. P., Lew, K., Benjamin, P., & Samkoff, A. (2012, February). Do generic proofs improve proof comprehension? To be presented at the 15th Conference on Research in Undergraduate Mathematics Education. Portland, Oregon.

  • Mejia-Ramos, J. P., Weber, K., Fuller, E., Samkoff, A., & Calkins, K. (2012, February). Factors influencing students’ propensity for semantic and syntactic reasoning in proof writing: A case study. To be presented at the 15th Conference on Research in Undergraduate Mathematics Education. Portland, Oregon.

  • Weber, K., & Mejia-Ramos, J. P. (2012, February). How and why mathematicians read proofs: A qualitative exploratory study and a quantitative confirmatory study. To be presented at the 15th Conference on Research in Undergraduate Mathematics Education. Portland, Oregon.

  • Inglis, M., Mejia-Ramos, J. P., Weber, K., & Alcock, L. (2012, February). On mathematicians’ different standards when evaluating elementary proofs. To be presented at the 15th Conference on Research in Undergraduate Mathematics Education. Portland, Oregon.

  • Mejia-Ramos, J. P., & Weber, K. (2011, September). The effect of proof format on proof comprehension: Are structured proofs easier to understand?. Paper presented at the 14th Biennial EARLI Conference for Research on Learning and Instruction, Exeter, U.K.

  • Mejia-Ramos, J. P., Weber, K., Fuller, E., Samkoff, A., Rhoads, K., & Search, R. (2010, July). Proof comprehension at the Undergraduate level. Poster session at the Conference of the International Group for the Psychology of Mathematics Education, Belo Horizonte, Brazil.

  • Mejia-Ramos, J. P., Weber, K., Fuller, E., Samkoff, A., Rhoads, K., & Search, R. (2010, January). Understanding mathematical proofs: What does it mean and how can it be assessed? Presented at the 2010 Joint Mathematics Meetings, San Francisco.