Keith Weber

I am a researcher in mathematics education whose interests are in the mathematical cognition of doing advanced mathematics. I am particularly interested in mathematical proof, including how mathematicians and mathematics majors present, read, understand, and evaluate proofs.

I am part of the Proof Comprehension Research Group (PCRG) that investigates the issues described above. Our website, which contains copies of many of my papers, is:

pcrg.gse.rutgers.edu

• Expertise & Research Interest

  Mathematics

  Learning Sciences

  Learning, Cognition and Development

• Research Work With Students

  My research focuses on advanced mathematical thinking. I am particularly interested in how mathematics majors can understand and learn from proofs in their upper-level mathematics courses.

  My research group’s accomplishments can be found at:

  http://pcrg.gse.rutgers.edu/

• Recent & Selected Publications

  SELECTED JOURNAL ARTICLES:

  Weber, K. & Fukawa-Connelly, T. (in press). What mathematicians learn from attending other mathematicians’ lectures. To appear in Educational Studies in Mathematics. 

  Weber, K. (in press). The role of imagination and anticipation in accepting computability proofs: A challenge to the standard account of rigor. To appear in Philosophia Mathematica. 

  Weber, K. & Tanswell, F. (in press). Instructions and recipes in mathematical proofs. To appear in Educational Studies in Mathematics. 

  Weber, K., Mejia-Ramos, J.P., & Volpe, T. (2022) An empirical investigation into the relationship between proof, conviction, and certainty in mathematical practice. Journal for Research in Mathematics Education, 53, 65-84. 

  Weber, K. (2021). The role of syntactic representations in set theory. Synthese, 198, 6393-6412. 

  Leyva, L., Quea, R., Weber, K., Battey, D., & Lopez,, D. (2021). Detailing racialized and gendered mechanisms of undergraduate precalculus and calculus instruction. Cognition and Instruction, 39, 1-34.

  Olsen, J., Lew, K., & Weber, K. (2020). Metaphors for learning and doing mathematics in advanced mathematics lectures. Educational Studies in Mathematics, 105, 1-17.

  Czocher, J. & Weber, K. (2020). Proof as a cluster category. Journal for Research in Mathematics Education, 51, 50-74.

  Weber, K., Lew, K., & Mejia-Ramos, J.P. (2020). Using expectancy value theory to account for students’ mathematical justifications. Cognition and Instruction, 38, 27-56.

  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.

  Mejia-Ramos, J.P. & Weber, K. (2019). Mathematics majors diagram usage when writing proofs in calculus. Journal for Research in Mathematics Education, 50, 478-488.

  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, 379-406.

  Paoletti, T., Krupnik, V., Papodoupolas, D., Olsen, J., Fukawa-Connelly, T. & Weber, K. (2018). Teacher questioning and invitations to participate in advanced mathematics lectures. Educational Studies in Mathematics, 98, 1-17.

  Krupnik, V., Weber, K., & Fukawa-Connelly, T. (2018). Students’ epistemological frames and their interpretations of lectures in advanced mathematics. Journal of Mathematical Behavior, 49, 174-183.

  Weber, K. (2018). Book review: Dialogue, Argumentation and Education: History, Theory and Practice, by Baruch B. Schwarz & Michael J. Baker. Educational Studies in Mathematics, 97, 111-118.

  Fukawa-Connelly, T., Weber, K., & Mejia-Ramos, J.P. (2017). Informal content and student note-taking in advanced mathematics classes. Journal for Research in Mathematics Education, 48, 567-579.

  Dawkins, P. & Weber, K. (2017). Values and norms of proof for mathematicians and students. Educational Studies in Mathematics, 95, 123-142.

  Zazkis, D., Weber, K. & Mejia-Ramos, J.P. (2016). Bridging the gap between graphical arguments and verbal-syntactic proofs in a real analysis context. Educational Studies in Mathematics, 92, 155-173.

  Lew, K., Fukawa-Connelly, T., Mejia-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.

  Weber, K. (2016). Mathematical humor: Jokes that reveal how we think about mathematics and why we enjoy it. The Mathematics Intelligencer, 38, 56-61.

  Weber, K., Fukawa-Connelly, T., Mejia-Ramos, J.P., & Lew, K. (2016). How to help students understand lectures in advanced mathematics. Notices of the American Mathematical Society, 63, 1190-1193.

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

  Mejia-Ramos, J.P. & Weber, K. (2014). How and why mathematicians read proofs: Further evidence from a survey study. Educational Studies in Mathematics, 85, 161-173.

  Lai, Y. & Weber, K. (2014). Factors mathematicians profess to consider when presenting pedagogical proofs. Educational Studies in Mathematics, 85, 93-108.

  Weber, K. & Mejia-Ramos, J.P.  (2013). On mathematicians’ proof skimming. Journal for Research in Mathematics Education, 44, 464-471.

  Weber, K. & Mejia-Ramos, J.P.  (2013). On the influence of sources in the reading of mathematical text. Journal of Literacy Research, 45, 87-96.

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

  Lai, Y., Weber, K. & Mejia-Ramos, J.P. (2012). Mathematicians’ perspectives on features of a good pedagogical proof. Cognition and Instruction, 30, 146-169.

  Mejia-Ramos, J.P., Fuller, E., Weber, K., Samkoff, A. & Rhoads, K. (2012). A model for proof comprehension in undergraduate mathematics. Educational Studies in Mathematics, 79, 3-18.

  Radu, I. & Weber, K. (2011). Refinements on students reasoning on completed infinite iterative processes. Educational Studies in Mathematics, 78, 165-182.

  Weber, K. & Rhoads, K. (2011). Review of Leikin and Zazkis’ Leaning through teaching mathematics: Development of teachers’ knowledge and expertise in practice. Journal for Research in Mathematics Education, 42, 521-527.

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

  Weber, K. & Mejia-Ramos, J.P.  (2011). How and why mathematicians read proofs: An exploratory study. Educational Studies in Mathematics, 76, 329-344.

  Weber, K. (2010). Mathematics majors’ perceptions of conviction, validity, and proof. Mathematical Thinking and Learning, 12, 306-336.

  Weber, K. (2008). How mathematicians determine if an argument is a valid proof. Journal for Research in Mathematics Education, 39, 431-459.

  Weber, K., Maher, C., Powell, A. & Lee, H. (2008). Learning opportunities from group discussions: Warrants become the objects of debate. Educational Studies in Mathematics, 68, 247-261.

  Weber, K. (2006). Investigating and teaching the thought processes used to construct proofs. Research in Collegiate Mathematics Education, 6. 197-232.

  Weber, K. & Alcock, L. (2004) Semantic and syntactic proof productions. Educational Studies in Mathematics, 56(3), 209-234.

  Weber, K. (2004). Traditional instruction in advanced mathematics courses: A case study of one professor’s lectures and proofs in an introductory real analysis course. Journal of Mathematical Behavior, 23(2), 115-133.

  Weber, K. (2001). Student difficulties in constructing proofs: The need for strategic knowledge. Educational Studies in Mathematics, 48(1), 101-119.

  SELECTED BOOK CHAPTERS:

  Harel, G. & Weber, K. (in press). Deductive reasoning in mathematics education. In S. Lerman (Ed.) Encyclopedia of mathematics education.

  Stylianides, G., Stylianides, A. & Weber, K. (2017). Research on the teaching and learning of proof: Taking stock and moving forward. In J. Cai (ed.) Compendium for Research in Mathematics Education. National Council of Teachers of Mathematics: Reston, VA.

  Weber, K. (2018). The role of sourcing in mathematics. In J. Braasch, I Bråten, & M. McCrudden (Eds.) Handbook of Multiple Source Use. New York: Routledge.

  Weber, K. & Moore, K. (2018). The role of abstraction in multiple perspectives on mathematical thinking and reasoning. Invited chapter for V. Thompson & L. Ball (eds.) International Handbook on Thinking and Reasoning. Psychology Press.

  Weber, K.  & Leikin, R. (2016). Problem solving and problem posing. In A. Gutierez, G. Leder, & P. Boero (eds.) 2nd Handbook on the Psychology of Mathematics Education. Rotterdam: Sense Publishers. (pp. 353-382).

• Honors & Awards

  2020 Outstanding Reviewer, Journal for Research in Mathematics Education

  2019 Outstanding Reviewer. Journal of Mathematical Behavior.

  2017 Best Paper Award at the 20th Conference for Research in Undergraduate Mathematics Education

  2017 Honorable Mention (Runner-Up) for Best Paper at the 20th Conference for Research in Undergraduate Mathematics Education

  2015 Honorable Mention (Runner-Up) for Best Paper at the 18th Conference for Research in Undergraduate Mathematics Education

  2014 Best Paper Award at the 17th Conference for Research in Undergraduate Mathematics Education

  2012 Janet Duffin Award for the outstanding paper in the 2012 volume of Research in Mathematical Education

  2011 Rutgers Board of Trustees Award for Excellence in Research (highest research honor for a faculty member of Rutgers University)

  2010 Selden Prize by the Mathematical Association of America (MAA) for outstanding research in undergraduate mathematics education

  2010 Best Paper Award at the 13th Conference for Research in Undergraduate Mathematics Education

  2009 Best Paper Award at the 12th Conference for Research in Undergraduate Mathematics Education

  2009 Rutgers Board of Trustees Research Fellowship for Scholarly Excellence (given to the eight professors across Rutgers’ three campuses with the strongest tenure packages)

  2008 Honorable Mention (Runner-Up) for Best Paper at the 11th Conference for Research in Undergraduate Mathematics Education

  2008 Rutgers Graduate School of Education Alumni Association Faculty Award for Research

  2007 National Science Foundation Early Career Award

  2006 Early Career Publication Award—Awarded by the Special Interest Group for Research in Mathematics Education of the AERA for outstanding contribution to the field of mathematics education by a junior faculty member