Bibliography

Here is a more comprehensive list of papers on topics related to proof comprehension. If there is a paper that you think should be included in this list, please let us know!

We have further classified these papers according to the population (mathematics professors, school teachers, undergraduate students, and schoolchildren) and the activity of the studies they report. You can find and download this file here (to sort in the browser go to View and choose List).

Proof evaluation

• 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.
• 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.
• Mejia-Ramos, J. P., & Inglis, M. (2011). Semantic contamination and mathematical proof: Can a non-proof prove? Journal of Mathematical Behavior 30, 19-29.
• Pfeiffer, K. (2011). Features and purposes of mathematical proofs in the view of novice students: observations from proof validation and evaluation performances. Doctoral dissertation, National University of Ireland, Galway.
• Geist, C., Löwe, B. & Van Kerkhove, B. (2010). Peer review and knowledge by testimony in mathematics. In B. Löwe and T. Müller (Eds.), Philosophy of Mathematics: Sociological Aspects and Mathematical Practice (pp.155-178). London: College Publications.
• Heinze, A. (2010). Mathematicians’ individual criteria for accepting theorems as proofs: An empirical approach. In G. Hanna, H.N. Jahnke, & H. Pulte (Eds.), Explanation and Proof in Mathematics: Philosophical and Educational Perspectives (pp. 101-111). New York: Springer.
• Weber, K. (2010). Mathematics' majors perceptions of conviction, validity, and proof. Mathematical Thinking and Learning 12, 306-336.
• Inglis, M., & Mejia-Ramos, J. P. (2009). The effect of authority on the persuasiveness of mathematical arguments. Cognition and Instruction 27, 25-50.
• Inglis, M., & Mejia-Ramos, J. P. (2009). On the persuasiveness of visual arguments in mathematics. Foundations of Science 14, 97-110.
• Inglis, M., & Mejia-Ramos, J. P. (2008). How persuaded are you? A typology of responses. Research in Mathematics Education 10(2), 119-133.
• Weber, K. (2008). How mathematicians determine if an argument is a valid proof. Journal for Research in Mathematics Education 39, 431-459.
• Morris, A. (2007). Factors affecting pre-service teachers' evaluations of the validity of students' mathematical arguments in classroom contexts. Cognition and Instruction 25, 479-522.
• Alcock, L., & Weber, K. (2005). Proof validation in real analysis: Inferring and checking warrants. Journal of Mathematical Behavior 24, 125-134.
• Weber, K., & Alcock, L. (2005). Using warranted implications to understand and validate proofs. For the Learning of Mathematics 25(1), 34–38.
• Selden, A., & Selden, J. (2003). Validations of proofs considered as texts: Can undergraduates tell whether an argument proves a theorem? Journal for Research in Mathematics Education 34 (1), 4-36.
• Raman, M. (2003). Key ideas: What are they and how can they help us understand how people view proof? Educational Studies in Mathematics 52, 319–325.
• Morris, A. (2002). Mathematical reasoning: Adults' ability to make the inductive-deductive distinction. Cognition and Instruction 20, 79-118.
• Healy, L., & Hoyles, C. (2000). A study of proof conceptions in algebra. Journal for Research in Mathematics Education 31, 396–428.
• Segal, J. (1999). Learning about mathematical proof: Conviction and validity. Journal of Mathematical Behavior 18(2), 191-210.
• Martin, W. G., & Harel, G. (1989). Proof frames of preservice elementary teachers. Journal for Research in Mathematics Education 20 (1), 41-51.
• Fischbein, E. (1982). Intuition and proof. For the Learning of Mathematics 3(2), 9-24.

Proof comprehension

• 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.
• 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.
• 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.
• Yang, K.-L. (2012). Structures of cognitive and metacognitive reading strategy use for reading comprehension of geometry proof. Educational Studies in Mathematics 80(3), 307-326.
• 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.
• Weber, K., & Mejia-Ramos, J. P. (2011). Why and how mathematicians read proofs: An exploratory study. Educational Studies in Mathematics 76, 329-344.
• Wilkerson-Jerde, M. & Wilensky, U. (2011). How do mathematicians learn math?: Resources and acts for constructing and understanding mathematics. Educational Studies in Mathematics, 78(1), 21-43.
• Yang, K.-L., & Lin, F.-L. (2008). A model of reading comprehension of geometry proof. Educational Studies in Mathematics 67, 59–76.
• Lin, F.-L., & Yang, K.-L. (2007). The reading comprehension of geometric proofs: The contribution of knowledge and reasoning. International Journal of Science and Mathematics Education 5, 729-754.
• Adams, T. L. (2007). Reading mathematics: An introduction. Reading & Writing Quarterly 23(2), 117-119.
• Osterholm, M. (2005). Characterizing reading comprehension of mathematical texts. Educational Studies in Mathematics 63, 325-346.
• Conradie, J., & Frith, J. (2000). Comprehension tests in mathematics. Educational Studies in Mathematics 42, 225–235.
• Konior, J. (1993). Research into the construction of mathematical texts. Educational Studies in Mathematics 24, 251-256.

Proof presentation

• Lai, Y., Weber, K., & Mejia-Ramos, J. P. (2012). Mathematicians’ perspectives on features of a good pedagogical proof. Cognition and Instruction, 30, 146-169.
• Mathematicians' perspectives on their pedagogical practice with respect to proof. International Journal of Mathematics Education in Science and Technology, 43, 463-482.
• 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
• Malek, A., & Movshovitz-Hadar, N. (2011). The effect of using transparent pseudo proofs in linear algebra. Research in Mathematics Education 13(1), 33–58.
• Hemmi, K. (2010). Three styles characterising mathematicians' pedagogical perspectives on proof. Educational Studies in Mathematics 75, 271-291.
• Roy, S., Alcock, L., & Inglis, M. (2010). Undergraduates proof comprehension: A comparative study of three forms of proof presentation. In Proceedings of the 13th Conference for Research in Undergraduate Mathematics Education.
• Alcock, L. (2009). e-Proofs: Students experience of online resources to aid understanding of mathematical proofs. In Proceedings of the 12th Conference for Research in Undergraduate Mathematics Education.
• 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, 115-133.
• Rowland, T. (2001). Generic proofs in number theory. In S. Campbell & R. Zazkis (Eds.), Learning and teaching number theory: Research in cognition and instruction (pp. 157–184). Westport: Ablex.
• Leron, U. (1983). Structuring mathematical proofs. The American Mathematical Monthly, 90(3), 174–184.