Research Publications

Contreras, N., Dawkins, P. C., Guajardo, L. R., Harris, P., Lew, K. M., Melhuish, K. M., Roh, K. H., Williams II, D. A., Winger, A. (2025). Humanizing proof-based mathematics instruction through experiences reading rich proofs and mathematician stories. Canadian Journal of Science, Mathematics, and Technology Education, 25, 130–145.

Czocher, J. A. (2016). Introducing modeling transition diagrams as a tool to connect mathematical modeling to mathematical thinking. Mathematical Thinking and Learning, 18(2), 77-106.

Czocher, J. A. (2017). How can emphasizing mathematical modeling principles benefit students in a traditionally taught differential equations course?. The Journal of Mathematical Behavior, 45, 78-94.

Czocher, J. A. (2018). How does validating activity contribute to the modeling process?. Educational studies in mathematics, 99(2), 137-159.

Czocher, J. A., & Weber, K. (2020). Proof as a cluster category. Journal for Research in Mathematics Education, 51(1), 50-74.

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.

Czocher, J. A., Hardison, H. L., & Kularajan, S. S. (2022). A bridging study analyzing mathematical model construction through a quantities-oriented lens. Educational Studies in Mathematics, 111(2), 299-321.

Czocher, J. A., Kularajan, S. S. (2025). Manifestations of quantitative reasoning during mathematical modeling. Mathematical Thinking and Learning.

Czocher, J. A., Melhuish, K. M. (2024). Attending to Coherence Among Research Questions, Methods, and Claims in Coding Studies. Journal for Research in Mathematics Education, 55(3), 148-155.

Czocher, J. A., Melhuish, K., & Kandasamy, S. S. (2020). Building mathematics self-efficacy of STEM undergraduates through mathematical modelling. International Journal of Mathematical Education in Science and Technology, 51(6), 807-834.

Czocher, J. A., Roan, E. A., Kularajan, S. S. K. (2024). Scaffolding Moves for Constructing Cognitively Meaningful Models of a Predator-Prey Scenario. PRIMUS, 26(6), 638-652.

Czocher, J. A., Roan, E. A., Quansah, A. L., Baas, A. (2024). Calculus is the study of change…but differential equations students need help quantifying it. International Journal of Mathematics Education in Science and Technology.

Czocher, J. A., Tague, J., & Baker, G. (2013). Where does the calculus go? An investigation of how calculus ideas are used in later coursework. International Journal of Mathematical Education in Science and Technology, 44(5), 673-684.

Czocher, J. A., White, A., Kularajan, S. S. K., Roan, E. A., Baas, A. B. (2025). Quantizing and Visualizing the Influence of Scaffolding Moves on Mathematical Modeling Competencies. Methods in Psychology.

Czocher, J., Melhuish, K., Kandasamy, S. S., & Roan, E. (2021). Dual Measures of Mathematical Modeling for Engineering and Other STEM Undergraduates. International Journal of Research in Undergraduate Mathematics Education, 7(2), 328-350.

Dawkins, P. C. (2017). On the importance of set-based meanings for categories and connectives in mathematical logic. International Journal of 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.

Dawkins, P. C., & Karunakaran, S. 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., & 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.

Dawkins, P. C., & Roh, K. H. (2020). Assessing the influence 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.

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., Inglis, M., & Wasserman, N. (2019). The use (s) of is in mathematics. Educational Studies in Mathematics, 100(2), 117-137.

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

Dawkins, P. C., Oehrtman, M., Reed, Z. (2024). Advanced students’ actions for operationalizing multiply quantified relationships. International Journal for Research in Undergraduate Mathematics Education.

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. (2024). Unitizing predicates and reasoning about the logic of proofs. Journal for Research in Mathematics Education, 55, 76-95.

Dawkins, P. C., Roh, K. H. (2025). Building set relationships by exploring sets defined by their properties. PRIMUS, 1-16.

Dawkins, P. C., Roh, K. H. (2025). Talking with Introduction to Proof Students About the Scope of Variables. PRIMUS.

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.

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.

Ellis, B. M., Alzaga Elizondo, T. (2026). Emergent storylines that influence positions and mathematical status in collaborative small-group proof activity. Educational Studies in Mathematics.

Ellis, B., Larsen, S., Voigt, M., & Vroom, K. (2021). Where calculus and engineering converge: An analysis of curricular change in calculus for engineers. International Journal of Research in Undergraduate Mathematics Education, 7(2), 379-399.

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

Johnson, E., Andrews-Larson, C., Keene, K., Melhuish, K., Keller, R., & Fortune, N. (2020). Inquiry and gender inequity in the undergraduate mathematics classroom. Journal for Research in Mathematics Education, 51(4), 504-516.

Kularajan, S. S., & Czocher, J. A. (2025). Differential equation students’ quantification of attributes while modeling dynamic scenarios. Mathematical Thinking and Learning.

Kularajan, S. S., Czocher, J. A. (2025). The role of reasoning with quantities in undergraduates’ modeling activities. International Journal of Research in Undergraduate Mathematics Education.

Kularajan, S., Czocher, J. A. (2024). Quantitative Operators as an Analytical Tool for Explaining Differential Equation Students’ Construction of New Quantities During Modeling. Journal of Mathematical Behavior, 76.

Lawrence-Wallquist, A. C., Ford, L. L., Kirmizi, M., Patterson, C. L. (2023). Developing Our Teaching Praxis Using a Japanese Lesson Study Model Applied to Corequisite Mathematics. Journal of College Academic Support Programs, 6(1), 55-61.

Lew, K. M., Guajardo, L. R., Gonzalez, M. A., Melhuish, K. M. (2024). Using Extant Proofs in the Classroom: A Comprehension Activity Structure. PRIMUS.

Lew, K., & Mejía Ramos, J. P. (2020). Linguistic conventions of mathematical proof writing across pedagogical contexts. Educational Studies in Mathematics, 103(1), 43-62.

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.

Lew, K., & Zazkis, D. (2019). Undergraduate mathematics students’ at-home exploration of a prove-or-disprove task. The Journal of Mathematical Behavior, 54, 100674.

Lew, K., Fukawa-Connelly, T. P., Mejía-Ramos, J. P., & Weber, K. (2016). Lectures in advanced mathematics: Why students might not understand what the mathematics professor is trying to convey. Journal for Research in Mathematics Education, 47(2), 162-198.

Mejía-Ramos, J. P., Alcock, L., Lew, K., Rago, P., Sangwin, C., & Inglis, M. (2019). Using corpus linguistics to investigate mathematical explanation. Methodological advances in experimental philosophy, 239-264.

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.

Melhuish, K. (2018). Three conceptual replication studies in group theory. Journal for Research in Mathematics Education, 49(1), 9-38.

Melhuish, K. (2019). The Group Theory Concept Assessment: A tool for measuring conceptual understanding in introductory group theory. International Journal of Research in Undergraduate Mathematics Education, 5(3), 359-393.

Melhuish, K. M., Guajardo, L. R., Lew, K. M., Dawkins, P. C., Diaz-Lopez, A., Garcia, R., Harris, P. E., Jones, E., Patel, P., Roh, K. H., Walker, S., Williams II, D. A., Winger, A. (2026). Diverse Storylines of Entering the Mathematics Professoriate. Educational Studies in Mathematics.

Melhuish, K. M., Patterson, C. L., Dawkins, P. C. (2025). Can Consuming Mathematics Be Compatible With Inquiry? For the Learning of Mathematics, 45(3), 9-13.

Melhuish, K. M., Patterson, C. L., Dawkins, P. C., Lew, K. M. (2025). Moving Beyond Show and Tell in Proof-Based Courses. Notices of the American Mathematical Society, 72(1), 51-59.

Melhuish, K., & Czocher, J. A. (2020). Division Is Pretty Much Just Multiplication. For the Learning of Mathematics, 40(1), 38-43.

Melhuish, K., & Hicks, M. D. (2019). A validity argument for an undergraduate mathematics concept inventory. In Quantitative Measures of Mathematical Knowledge (pp. 121-151). Routledge.

Melhuish, K., Dawkins, P. C., Lew, K., & 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, 1-34.

Melhuish, K., Ellis, B., & Hicks, M. D. (2020). Group theory students’ perceptions of binary operation. Educational Studies in Mathematics, 103(1), 63-81.

Melhuish, K., Fukawa-Connelly, T., Dawkins, P. C., Woods, C., & Weber, K. (2022). Collegiate mathematics teaching in proof-based courses: What we now know and what we have yet to learn. The Journal of Mathematical Behavior, 67, 100986.

Melhuish, K., Guajardo, L., Dawkins, P. C., Zolt, H., & Lew, K. (2023). The role of the partitioning and coset algorithm quotient group partial meanings in comprehending the First Isomorphism Theorem and its proof: Melhuish et al. Educational Studies in Mathematics, 113(3), 499-517.

Melhuish, K., Larsen, S., & Cook, S. (2019). When students prove a theorem without explicitly using a necessary condition: Digging into a subtle problem from practice. International Journal of Research in Undergraduate Mathematics Education, 5(2), 205-227.

Melhuish, K., Lew, K., & Hicks, M. (2022). Comparing Student Proofs to Explore a Structural Property in Abstract Algebra. PRIMUS, 32(1), 57-73.

Melhuish, K., Lew, K., Hicks, M. D., & Kandasamy, S. S. (2020). Abstract algebra students’ evoked concept images for functions and homomorphisms. The Journal of Mathematical Behavior, 60, 100806.

Melhuish, K., Vroom, K., Lew, K., & Ellis, B. (2022). Operationalizing authentic mathematical proof activity using disciplinary tools. The Journal of Mathematical Behavior, 68, 101009.

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

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

Park, J., Czocher, J. A., White, R. (2025). Exploring STEM students’ modeling sub-competency: model validations based on types of tasks in data-rich situations. International Journal of Science and Mathematics Education.

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.

Patterson, C. L., Koehne, C., Warshauer, H. K., Cui, X., Bhattacharyya, S., & Warshauer, M. (2026). Examining professional development grounded in collaborative teaching: resources that inservice and preservice teachers contribute to analysis of practice. Journal of Mathematics Teacher Education, 1-27.

Roan, E. A., Czocher, J. A. (2024). Instructors’ beliefs and practices regarding mathematical modelling at the periphery of STEM. International Journal of Mathematics Education in Science and Technology, 1-29.

Roan, E., Kularajan, S. S., Czocher, J. A. (2025). Reconsidering Task Classification Systems for Situations That Can Be Modelled with Multiplication. ZDM.

Ruiz, S., Gonzalez, M. A., Dawkins, P. C., Roh, K. H. (2025). Experienced provers’ operative logical principles for evaluating proofs of conditional claims. The Journal of Mathematical Behavior, 80, 101282.

Stillman, G., Brown, J., & Czocher, J. (2020). Yes, mathematicians do X so students should do X, but it’s not the X you think!. ZDM, 52(6), 1211-1222.

Tucci, A. A., Dawkins, P. C., Roh, K. H. (2025). Student justifications regarding converse independence. The Journal of Mathematical Behavior, 80, 101269.

Vroom, K., Ellis, B. M. (2024). Sociomathematical scaffolding as students engage in revising draft definitions, conjectures, and proofs. Educational Studies in Mathematics, 116, 27-47.

Vroom, K., Gehrtz, J., Apkarian, N., Alzaga Elizondo, T., Ellis, B., & Hagman, J. (2022). Characteristics of interactive classrooms that first year students find helpful. International Journal of STEM Education, 9(1), 1-17.

Weber, K., & Czocher, J. (2019). On mathematicians’ disagreements on what constitutes a proof. Research in Mathematics Education, 21(3), 251-270.

Weber, K., & Melhuish, K. (2022). Can we engage students in authentic mathematical activity while embracing critical pedagogy? A commentary on the tensions between disciplinary activity and critical education. Canadian Journal of Science, Mathematics and Technology Education, 22(2), 305-314.

Weber, K., Dawkins, P., & Mejía-Ramos, J. P. (2020). The relationship between mathematical practice and mathematics pedagogy in mathematics education research. ZDM, 52(6), 1063-1074.

Weber, K., Fukawa-Connelly, T. P., Mejía-Ramos, J. P., & Lew, K. (2016). How to help students understand lectures in advanced mathematics. Notices of the AMS, 63(10).

Weber, K., Lew, K., & Mejía-Ramos, J. P. (2020). Using expectancy value theory to account for individuals’ mathematical justifications. Cognition and Instruction, 38(1), 27-56.

Zolt, H. M., Wrightsman, E., Ford, L. L., Patterson, C. L. (2022). Believing in infinity: Exploring students' conceptions of improper integrals. PRIMUS: Problems, Resources, and Issues in Mathematics Undergraduate Studies, 33(5), 502-516