Faculty Profiles

Melhuish, K. M., Patterson, C. L., & Dawkins, P. C. (n.d.). Broadening Views of Inquiry in Advanced Mathematics Through the Lens of Transformation. For the Learning of Mathematics.

Czocher, J. A., Dawkins, P. C., & Weber, K. (2024). Using Values and Norms to Explain the Rationality of Rejecting Probabilistic Proofs. Logique et Analyse, 261, 19–40. Retrieved from https://poj.peeters-leuven.be/content.php?url=article&id=3293133&journal_code=LEA

Dawkins, P. C., Oehrtman, M., & Reed, Z. (2024). Advanced students’ actions for operationalizing multiply quantified relationships. International Journal for Research in Undergraduate Mathematics Education. https://doi.org/https://doi.org/10.1007/s40753-024-00236-4

Dawkins, P. C., & Roh, K. H. (2024). Unitizing predicates and reasoning about the logic of proofs. Journal for Research in Mathematics Education, 55, 76–95. https://doi.org/10.5951/jresematheduc-2020-0155

Dawkins, P. C., Hackenberg, A. J., & Norton, A. (Eds.). (2024). Piaget’s Genetic Epistemology for Mathematics Education Research. Switzerland: Springer Nature. https://doi.org/10.1007/978-3-031-47386-9

Patterson, C. L., Dawkins, P. C., Zolt, H. M., Tucci, A. A., Lew, K. M., & Melhuish, K. M. (2024). Adapting the proof of Lagrange’s Theorem into a sequence of group-work tasks. PRIMUS, 1–15.

Melhuish, K. M., Guajardo, L. R., Lew, K. M., Dawkins, P. C., & Roh, K. H. (n.d.). An Elaboration of Master Narratives in Mathematics and How Undergraduates Relate to Counternarratives. In In Proceedings of the Forty-Fifth Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (PME-NA).

Roh, K. H., Contreras, N., Melhuish, K. M., Dawkins, P. C., Lew, K. M., & Guajardo, L. R. (n.d.). Symbolic Variations Across Mathematical Subareas: Exploring Challenges in Undergraduate Students’ Interpretation of Mathematical Symbols. In In Proceedings of the Forty-Fifth Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (PME-NA).

Melhuish, K. M., Patterson, C. L., Dawkins, P. C., & Lew, K. M. (2024). Moving Beyond Show and Tell in Proof-Based Courses. Notices of the American Mathematical Society, 72(1), 51–59.

Contreras, N., Dawkins, P. C., Guajardo, L. R., Harris, P., Lew, K. M., Melhuish, K. M., … Winger, A. (n.d.). Humanizing proof-based mathematics instruction through experiences reading rich proofs and mathematician stories. Canadian Journal of Science, Mathematics, and Technology Education.

Dawkins, P. C., & Buchbinder, O. (n.d.). Why and how to engage teachers in evaluating geometric proofs and arguments: Commentary on SLO2. In The GeT course: Resources and Objectives for the Geometry Courses for Teachers. USA: Mathematics Association of America.

Wasserman, N., & Dawkins, P. C. (n.d.). University Geometry Courses as part of Secondary Teacher Education: Empirically grounding the GeT SLOs. In The GeT course: Resources and Objectives for the Geometry Courses for Teachers. USA: Mathematics Association of America.

Dawkins, P. C., & Vroom, K. (n.d.). Researching proof viewed as a genre of text. In New directions for research on proving: Honoring the legacy of John and Annie Selden. Switzerland: Springer.

Küchle, V., & Dawkins, P. C. (2024). Genre Theories’ Potential for Researching Proof. In Proceedings of the 15th International Congress on Mathematical Education, TSG 3.13 Language and communication in the mathematics classroom.

Dawkins, P. C. (2024). Logic in Genetic Epistemology. In Piaget’s Genetic Epistemology for Mathematics Education Research (pp. 339–369). Switzerland: Springer Nature. https://doi.org/10.1007/978-3-031-47386-9_10

Dawkins, P. C. (2024). Skepticism and Constructivism. In Piaget’s Genetic Epistemology for Mathematics Education Research (pp. 541–562). Switzerland: Springer Nature. https://doi.org/10.1007/978-3-031-47386-9_16

Dawkins, P. C., Hackenberg, A. J., & Norton, A. (2024). Introduction to Piaget’s Genetic Epistemology. In Piaget’s Genetic Epistemology for Mathematics Education Research (pp. 3–10). Switzerland: Springer Nature. https://doi.org/10.1007/978-3-031-47386-9_1

Dawkins, P. C., Roh, K. H., Eckman, D., & Cho, Y. K. (2023). Theo’s reinvention of the logic of conditional statements’ proofs rooted in set-based reasoning. The Journal of Mathematical Behavior, 70, 101043. https://doi.org/10.1016/j.jmathb.2023.101043

Dawkins, P. C., & Weber, K. (2023). Identifying minimally invasive active classroom activities to be developed in partnership with mathematicians. In Mathematicians’ Reflections on Teaching: A Symbiosis with Mathematics Education Theories (Ed.) S. Stewart (pp. 103–121). Switzerland: Springer Nature. https://doi.org/10.1007/978-3-031-34295-0_6

Dawkins, P. C. (2023). Reinventing the Logic of Mathematical Disjunctions. In Sharing and Storing Knowledge about Teaching Undergraduate Mathematics An Introduction to a Written Genre for Sharing Lesson-specific Instructional Knowledge (pp. 21–32). Washington, D.C., United States of America: Mathematics Association of America. Retrieved from https://maa.org/sites/default/files/pdf/pubs/books/members/NTE95_web.pdf

Melhuish, K. M., Lew, K. M., Hicks, M. D., Guajardo, L. R., Dawkins, P. C., & Morey, S. (2023). Proving, Analyzing, and Deepening Understanding of a Structural Property in Abstract Algebra. In Sharing and Storing Knowledge about Teaching Undergraduate Mathematics An Introduction to a Written Genre for Sharing Lesson-specific Instructional Knowledge (pp. 129–140). Washington, D.C., United States of America: Mathematics Association of America. Retrieved from https://maa.org/sites/default/files/pdf/pubs/books/members/NTE95_web.pdf

Melhuish, K. M., Guajardo, L. R., Dawkins, P. C., Zolt, H. M., & Lew, K. M. (2023). The Role of Quotient Group Meanings in a Theorem and Proof Comprehension Task. Educational Studies in Mathematics.

Weber, K., Dawkins, P. C., & Lockwood, E. (2023). Proving as cooperative communication: Using Grice’s maxims and implicature to understand proof comprehension in undergraduate mathematics education. In RUME Conference Proceedings. Retrieved from http://sigmaa.maa.org/rume/RUME25v2.pdf

Melhuish, K. M., Lew, K. M., Dawkins, P. C., Strickland, S. K., & Patterson, C. L. (2023). Engineering Instructional Practices to Better Support Access and Participatory Equity in Authentic Proof Activity. In In Cook, S., Katz, B., & Moore-Russo D. (Eds.) Proceedings of the 26th Annual Conference on Research in Undergraduate Mathematics Education. Retrieved from http://sigmaa.maa.org/rume/RUME25v2.pdf

Ruiz, S., Roh, K. H., Dawkins, P. C., Eckman, D., & Tucci, A. A. (2023). Differences in Students’ Beliefs and Knowledge Regarding Mathematical Proof: Comparing Novice and Experienced Provers. In RUME Conference Proceedings. Retrieved from http://sigmaa.maa.org/rume/RUME25v2.pdf

Tucci, A. A., Dawkins, P. C., Roh, K. H., Eckman, D., & Ruiz, S. (2023). Student Explanations and Justifications Regarding Converse Independence. In RUME Conference Proceedings. Retrieved from http://sigmaa.maa.org/rume/RUME25v2.pdf

Eckman, D., Roh, K. H., Dawkins, P. C., Ruiz, S., & Tucci, A. A. (2023). Two Vignettes on Students’ Symbolizing Activity for Set Relationships. In RUME Conference Proceedings. Retrieved from http://sigmaa.maa.org/rume/RUME25v2.pdf

Roh, K. H., Dawkins, P. C., Eckman, D., Ruiz, S., & Tucci, A. A. (2023). Instructional interventions and teacher moves to support student learning of logical principles in mathematical contexts. In RUME Conference Proceedings. Retrieved from http://sigmaa.maa.org/rume/RUME25v2.pdf

Melhuish, K. M., Guajardo, L. R., Contreras, N., Dawkins, P. C., Diaz-Lopez, A., Garcia, R., … Winger, A. (n.d.). Opposing Dimensions in Mathematicians’ Counter Narratives Written for Undergraduate Students. In In Cook, S., Katz, B., & Moore-Russo D. (Eds.) Proceedings of the 26th Annual Conference on Research in Undergraduate Mathematics Education.

Dawkins, P. C., & Buchbinder, O. (n.d.). Why and how to engage GeT students in evaluating geometric proofs and arguments: Commentary on SLO2. In The GeT course: Resources and Objectives for the Geometry Course for Teachers. Washington, D.C., USA: Mathematical Association of America.

Wasserman, N., & Dawkins, P. C. (n.d.). University Geometry Courses as part of Secondary Teacher Education: Empirically grounding the GeT SLOs. In The GeT course: Resources and Objectives for the Geometry Course for Teachers. Washington, D.C., USA: Mathematical Association of America.

Küchle, V., & Dawkins, P. C. (n.d.). Genre Theories and Their Potential for Studying Proof. In Proceedings of the 26th Annual Conference on Research in Undergraduate Mathematics Education.

Dawkins, P. C., & Norton, A. (2022). Identifying Mental Actions Necessary for Abstracting the Logic of Conditionals. The Journal of Mathematical Behavior, 66, 100954.

Mirin, A., & Dawkins, P. C. (2022). Do mathematicians interpret equations symmetrically? The Journal of Mathematical Behavior, 66, 100959.

Dawkins, P. C. (2022). Mathematics Educators as Polymaths, Brokers, and Learners: Commentary on the Tertiary Chapters on Argumentation, Justification, and Proof. In Conceptions and Consequences of Argumentation, Justification, and Proof (pp. 265–273). Springer Cham. Retrieved from https://link.springer.com/book/10.1007/978-3-030-80008-6

Dawkins, P. C., & Roh, K. H. (2022). Aspects of Predication and their influence on reasoning about logic in discrete mathematics. ZDM Mathematics Education, 54, 881–893.

Dawkins, P. C., & Roh, K. H. (2022). The role of unitizing predicates in the construction of logic. In 12th Congress of the European Society for Research in Mathematics Education.

Fukawa-Connelly, T., Melhuish, K. M., Weber, K., Dawkins, P. C., & Orr-Woods, C. (2022). The Teaching of Proof-Based Mathematics Courses. In In Karunakaran, S. S., & Higgins, A. (Eds.) Proceedings of the 24th Annual Conference on Research in Undergraduate Mathematics Education.

Dawkins, P. C., Oehrtman, M., & Reed, Z. (2022). Advanced Students’ Actions for Operationalizing Quantification in Analysis. In 24th Annual Conference on Research in Undergraduate Mathematics Education,.

Melhuish, K. M., Fukawa-Connelly, T., Dawkins, P. C., Woods, C., & Weber, K. (2022). Collegiate Mathematics Teaching in Proof-Based Courses: Updated Evidence About an Important Practice. The Journal of Mathematical Behavior, 67.

Melhuish, K. M., Dawkins, P. C., Lew, K. M., & Strickland, S. K. (2022). Lessons learned about incorporating high-leverage teaching practices in the undergraduate proof classroom to promote authentic and equitable participation. International Journal of Research in Undergraduate Mathematics Education.

Dawkins, P. C., Zazkis, D., & Cook, J. P. (2022). How do transition to proof textbooks relate logic, proof techniques, and sets? PRIMUS, 32(1), 14–30. https://doi.org/https://doi.org/10.1080/10511970.2020.1827322

Dawkins, P. C., & Zazkis, D. (2021). Using Moment-by-Moment Reading Protocols to Understand Students’ Processes of Reading Mathematical Proof. Journal for Research in Mathematics Education, 52(5), 510–538.

Dawkins, P. C., Roh, K. H., Eckman, D., & Cho, Y. K. (2021). Theo’s reinvention of the logic of conditional statements’ proofs rooted in set-based reasoning. In 43rd Annual Meeting of the North American Chapter of the International Group for Psychology in Mathematics Education.

Cook, J. P., Dawkins, P. C., & Reed, Z. (2021). Explicating interpretations of equivalence in measurement contexts. For the Learning of Mathematics, 41(3), 36–41.

Dawkins, P. C., & Zazkis, D. (2020). Students’ moment-by-moment reading of mathematical proof: findings from adapting an assessment methodology to mathematics text. Journal for Research in Mathematics Education, 52, 510–538.

Dawkins, P. C., & Roh, K. H. (2020). Assessing the roles of syntax, semantics, and pragmatics in student interpretation of multiply quantified statements in mathematics. International Journal of Research in Undergraduate Mathematics Education., 6(1), 1–22.

Durand-Guerrier, V., & Dawkins, P. C. (2020). Logic in university mathematics education. In Encyclopedia of Mathematics Education (Ed.) S. Lerman. Dordrecht, Netherlands: Springer Science+Business Media. Retrieved from https://link.springer.com/referenceworkentry/10.1007/978-3-030-15789-0_100024

Weber, K., Dawkins, P. C., & Mejia-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/https://doi.org/10.1007/s11858-020-01173-7

Dawkins, P. C. (2020). Identifying aspects of mathematical epistemology that might influence productively student reasoning beyond mathematics. ZDM Mathematics Education, 52(6), 1177–1186. https://doi.org/https://doi.org/10.1007/s11858-020-01167-5

Weber, K., & Dawkins, P. C. (2020). The role of mathematicians’ practice in mathematics education research. ZDM Mathematics (6th ed., Vol. 52). Retrieved from https://link.springer.com/journal/11858/volumes-and-issues/52-6

Lew, K. M., Melhuish, K. M., & Dawkins, P. C. (2020). Proving Activities of Abstract Algebra Students in a Group Task-based Interview. In In Karunakaran, S. S., Reed, Z., & Higgins, A. (Eds.). Proceedings of the 23rd Annual Conference on Research in Undergraduate Mathematics Education.

Dawkins, P. C., & Roh, K. H. (2020). Coordinating Two Meanings of Variables in Proofs that Apply Definitions Repeatedly. In 23rd Annual Conference on RUME. Retrieved from http://sigmaa.maa.org/rume/RUME23.pdf

Dawkins, P. C., Oehrtman, M., & Mahavier, W. T. (2019). Professor goals and student experiences in an IBL Real Analysis course: A case study. International Journal for Research in Undergraduate Mathematics Education, 5(3), 315–336.

Dawkins, P. C. (2019). Students’ pronominal sense of reference in mathematics. For the Learning of Mathematics, 39(1), 13–18.

Dawkins, P. C., Inglis, M., & Wasserman, N. (2019). The Use(s) of is in mathematics. Educational Studies in Mathematics, 100(2), 117–137.

Dawkins, P. C., & Roh, K. H. (2019). How Do Students Interpret Multiply Quantified Statements in Mathematics? In 22nd Annual Conference on RUME.

Cook, J. P., Dawkins, P. C., & Zazkis, D. (2019). How do Transition to Proof Textbooks Relate Logic, Proof Techniques, and Sets? In 22nd Annual Conference on RUME.

Dawkins, P. C., & Zazkis, D. (2019). Observing Students’ Moment-by-Moment Reading of Mathematical Proof Activity. In 22nd Annual Conference on RUME.

Dawkins, P. C. (2019, December 14). Review of “International Reflections on the Netherlands Didactics of Mathematics.” Mathematics Association of America. Retrieved from https://www.maa.org/press/maa-reviews/international-reflections-on-the-netherlands-didactics-of-mathematics-visions-on-and-experiences

Dawkins, P. C. (2019, July 28). Review of “Mathematics, Education, and Other Endangered Species.” Mathematics Association of America. Retrieved from https://www.maa.org/press/maa-reviews/mathematics-education-and-other-endangered-species

Dawkins, P. C. (2018). Student interpretations of axioms in planar geometry. Investigations in Mathematics Learning, 10(4), 227–239.

Hub, A., & Dawkins, P. C. (2018). On the construction of set-based meaning for the truth of mathematical conditionals. The Journal of Mathematical Behavior, 50, 90–102.

Weber, K., & Dawkins, P. C. (2018). Toward an Evolving Theory of Mathematical Practice Informing Pedagogy: What standards for this research paradigm should we adopt? In Advances in Mathematics Education Research on Proof and Proving: An International Perspective (Eds.) A. Stylianides & G. Harel (pp. 69–82). Springer International Publishing.

Dawkins, P. C., & Zazkis, D. (2018). Computational and inferential orientations: Lessons from observing undergraduates read mathematical proofs. In Proceedings of the Research on Undergraduate Mathematics Education Conference.

Dawkins, P. C., Inglis, M., & Wasserman, N. (2018). The use(s) of “is” in mathematics. In Proceedings of the Research on Undergraduate Mathematics Education Conference.

Dawkins, P. C., Oehrtman, M., & Mahavier, W. T. (2018). Professor Goals and Student Experiences in an IBL Real Analysis Course: A Case Study. In Proceedings of the Research on Undergraduate Mathematics Education Conference.

Czocher, J. A., Dawkins, P. C., & Weber, K. (2018). Alternative perspectives on cultural dimensions on proof in the mathematical curriculum: a reply to Shinno et al. For the Learning of Mathematics, 38(2), 25–27. Retrieved from https://flm-journal.org/index.php?do=show&lang=en&vol=38&num=2

Dawkins, P. C. (2017). On the Importance of Set-based Meanings for Categories and Connectives in Mathematical Logic. International Journal for Research in Undergraduate Mathematics Education, 3(3), 496–522.

Dawkins, P. C., & Cook, J. P. (2017). Guiding reinvention of conventional tools of mathematical logic: Students’ reasoning about mathematical disjunctions. Educational Studies in Mathematics, 94(3), 241–256. https://doi.org/10.1007/s10649-016-9722-7

Dawkins, P. C., & Weber, K. (2017). Values and norms of proof for mathematicians and students. Educational Studies in Mathematics, 95(2), 123–142.

Dawkins, P. C. (2017). Helping students develop conscious understanding of axiomatizing. In B. Gold, C.E. Behrens, & R.A. Simons (Eds.). In Using the Philosophy of Mathematics in Teaching Undergraduate Mathematics (pp. 133–145). Washington, D.C., US: Mathematical Association of America.

Dawkins, P. C., & Hub, A. (2017). Explicating the concept of contrapositive equivalence.

Hub, A., & Dawkins, P. C. (2017). A Case Study in Constructing Set-based Meanings for Conditional Truth.

Dawkins, P. C., & Karunakaran, S. (2016). Why research on proof-oriented mathematical behavior should attend to the role of particular mathematical content. The Journal of Mathematical Behavior, 44, 65–75.

Dawkins, P. C., & Karunakaran, S. (2016). Why research on proof-oriented mathematical behavior should attend to the role of particular mathematical content.

Dawkins, P. C., & Roh, K. H. (2016). Promoting Metalinguistic and Metamathematical Reasoning in Proof-Oriented Mathematics Courses: a Method and a Framework. International Journal of Research in Undergraduate Mathematics Education, 2(2), 197–222. https://doi.org/10.1007/s40753-016-0027-0

Dawkins, P. C. (2015). Explication as a lens for the formalization of mathematical theory through guided reinvention. The Journal of Mathematical Behavior, 37, 63–82.

Dawkins, P. C. (2015). In Pursuit of Coherent and Formalizable Understanding: Reflections on David Tall’s Three Worlds Framework. International Journal of Research in Undergraduate Mathematics Education.

Dawkins, P. C. (2015). Students’ strategies for assessing mathematical disjunctions.

Dawkins, P. C., & Cook, J. P. (2015). Semantic and logical negation: Students’ non-normative interpretations of negative mathematical properties.

Dawkins, P. C., & Cook, J. P. (2015). Guiding reinvention of conventional tools of mathematical logic: Students’ reasoning about mathematical disjunctions.

Dawkins, P. C., & Cook, J. P. (2015). Semantic and logical negation: Students’ interpretations of negative predicates.

Dawkins, P. C. (2014). When proofs reflect more on assumptions than conclusions. For the Learning of Mathematics, 34(2), 17–23.

Dawkins, P. C., & Epperson, J. A. M. (2014). The development and nature of problem-solving among first-semester calculus students. International Journal of Mathematical Education in Science and Technology, 45(6), 839–862.

Dawkins, P. C. (2014). How students interpret and enact inquiry-oriented defining practices in undergraduate real analysis. The Journal of Mathematical Behavior, 33, 88–105.

Dawkins, P. C. (2014). Student Interpretations of Axiomatizing.

Dawkins, P. C. (2014). Disambiguating research on logic as it pertains to advanced mathematical practice.

Dawkins, P. C. (2013). Individual adherence to inquiry-oriented norms of defining in advanced mathematics.

Dawkins, P. C. (2013). Developing an explication analytical lens for proof-oriented mathematical activity.

Dawkins, P. C., & Roh, K. H. (2013). Using metaphors to support students’ ability to reason about logic.

Dawkins, P. C. (2012). Extensions of the semantic/syntactic reasoning framework. For the Learning of Mathematics, 32(3), 39–45.

Dawkins, P. C. (2012). Metaphor as a possible pathway to more formal understanding of the definition of sequence convergence. The Journal of Mathematical Behavior, 31(3), 331–343. https://doi.org/10.1016/j.jmathb.2012.02.002

Dawkins, P. C., & Roh, K. H. (2011). Mechanisms for scientific debate in real analysis classrooms.

Dawkins, P. C. (2011). Using concrete metaphor to encapsulate aspects of the definition of sequence convergence.

Dawkins, P. C. (2010). Communal communication in undergraduate real analysis: The Case of Cyan.