Unpublished Dissertation (PhD Mathematics Education): Pre-Service Teachers' Constructions of Formulas through Covariational Reasoning with Dynamic Objects
Committee: Kevin C. Moore (Advisor), Leslie Steffe, Amy Ellis, Edward Azoff
Unpublished Masters Thesis (MA Mathematics): Topological Data Analysis and the MAA National Study of College Calculus
Committee: Noah Giansiracusa (Advisor), Jason Cantarella, Edward Azoff
Charlotte Research Scholars: Statistical Modeling of Gene Duplication
Mentor: Jessica Schlueter
D’Alessandro, W., & Stevens, I. E. (2024). Mature intuition and mathematical understanding. Journal of Mathematical Behavior, 76. https://doi.org/10.1016/j.jmathb.2024.101203
Paoletti, T., Stevens, I. E.; Acharya, S., Margolis, C.; Olshefke, A; Gantt, A. (2024). Exploring and promoting a student’s covariational reasoning and developing graphing meanings. Journal of Mathematical Behavior, 74. https://doi.org/10.1016/j.jmathb.2024.101156
Herbst, P., Brown, A., Chazan, D., Boileau, N., & Stevens, I. (2023). Framing, responsiveness, serviceability, and normativity: Categories of perception teachers use to relate to students mathematical contributions in problem-based lessons. School Science and Mathematics 2023, 1– 16. DOI: 10.1111/ssm.12600
Paoletti, T., Stevens, I. E., & Vishnubhotla, M. (2021). Comparative and restrictive inequalities. 63, 14. https://doi-org.proxy.lib.umich.edu/10.1016/j.jmathb.2021.100895
Moore, K. C., Stevens, I. E., Paoletti, T., Hobson, N. L. F., & Liang, B. (2019). Pre-service teachers’ figurative and operative graphing actions. The Journal of Mathematical Behavior, 56, 100692. https://doi.org/10.1016/j.jmathb.2019.01.008
Paoletti, T., Stevens, I. E., Hobson, N. L. F., Moore, K. C., & LaForest, K. R. (2017). Inverse function: Pre-service teachers' techniques and meanings. Educational Studies in Mathematics, 97, 93–109. doi:10.1007/s10649-017-9787-y
Paoletti, T. , Stevens, I. E. & Moore, K. C. (2017). Tricks May Inhibit Students' Reasoning. The Mathematics Teacher, 110(6), 446-453. doi:10.5951/mathteacher.110.6.0446
Moore, K. C., Liang, B., Stevens, I. E., Tasova, H. I., & Paoletti, T. (2022). Abstracted Quantitative Structures: Using Quantitative Reasoning to Define Concept Construction. In G. Karagöz Akar, İ. Ö. Zembat, S. Arslan, & P. W. Thompson (Eds.), Quantitative Reasoning in Mathematics and Science Education (pp. 35–69). Springer International Publishing. https://doi.org/10.1007/978-3-031-14553-7_3
Milewski, A., Stevens, I., Herbst, P., & Huhn, C. (2021). Confronting teachers with contingencies to support their learning about situation-specific pedagogical decisions in an online context. In K. F. Hollebrands & R. Anderson (Eds.), Online Learning in Mathematics Education. Springer.
Milewski, A., Herbst, P, & Stevens, I. (2020). Managing to collaborate with secondary mathematics teachers at a distance: Using storyboards as a virtual place for practice and consideration of realistic classroom contingencies. Teaching, Technology, and Teacher Education during the COVID-19 Pandemic: Stories from the Field. R. E. Ferdig, E. Baumgartner, R. Hartshorne, R. Kaplan-Rakowski and C. Mouza, Association for the Advancement of Computing in Education (AACE): 623–630.
Moore, K. C., Tasova, H. I., Stevens, I. E., & Liang, B. (2024). Competing meanings, perturbations, and engendering shifts in (prospective) teachers’ meanings. In Kosko, K. W., Caniglia, J., Courtney, S., Zolfaghari, M., & Morris, G. A., (Eds.). Proceedings of the forty-sixth annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 1145-1155). Kent State University.
Stevens, I. E., Hardison, H., & Brown, A. (2024). High school students’ figurative and operative thought when reasoning about distances. In Kosko, K. W., Caniglia, J., Courtney, S., Zolfaghari, M., & Morris, G. A., (Eds.). Proceedings of the forty-sixth annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 499-508). Kent State University.
Stevens, I. E. (2024). What A=2rh tells us: A framework for multiplicative objects with formulas. In T. Evans, O. Marmur, J. Hunter, G. Leach, & J. Jhagroo (Eds.). Proceedings of the 47th Conference of the International Group for the Psychology of Mathematics Education (Vol. 1, p. 221). PME.
Moore, K. C., Wood, E., Yasuda, S., Liang, B., Stevens, I. E., & Tasova, H. I. (2024). Operationalizing re-presentation to investigate and support students’ covariational reasoning. In T. Evans, O. Marmur, J. Hunter, G. Leach, & J. Jhagroo (Eds.). Proceedings of the 47th Conference of the International Group for the Psychology of Mathematics Education (Vol. 3, pp. 233-240). PME.
Moore, K. C., Stevens, I. E., Waswa, A., & Yasuda, S. (2024). The Precalculus Concept Assessment (PCA) and prospective secondary teachers. Cook, S., Katz, B. & Moore-Russo D. (Eds.). Proceedings of the 26th Annual Conference on Research in Undergraduate Mathematics Education. (pp. 1270–1272). Omaha, NE.
Stevens, I. E., Tolchinsky, J., & Robillard, M. (2024). What is the Correct Amount of Change? A Case Study on Kala’s Covariational Reasoning. In Cook, S., Katz, B. & Moore-Russo D. (Eds.). Proceedings of the 26th Annual Conference on Research in Undergraduate Mathematics Education. (pp. 45–53). Omaha, NE.
Stevens, I. E. (2023). Implications of faster/slower language on undergraduate precalculus students’ graphing. In Lamberg, T., & Moss, D. (2023). Proceedings of the forty-fifth annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (Vol. 2). University of Nevada, Reno. (pp. 894–903)
Stevens, I. E. (2023). Magnitude bars and covariational reasoning. Cook, S., Katz, B. & Moore-Russo D. (Eds.). (2023). Proceedings of the 25th Annual Conference on Research in Undergraduate Mathematics Education. Omaha, NE. (pp. 752–761)
Schwarts, G., Stevens, I. E., Herbst, P., & Brown, A. (2022). “It’s a different mindset here”: Facilitation challenges in a practice-based professional development. Proceedings of the forty-fourth annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. Nashville, TN. (pp. 1479–1487)
Stevens, I. E. (2022). “A=2πrh is the surface area for a cylinder”: Figurative and operative thought with formulas. In Karunakaran, S. S., & Higgins, A. (Eds.) Proceedings of the 24th Annual Conference on Research in Undergraduate Mathematics Education. Boston, MA. (pp. 613–621)
Stevens, I. E. & Herbst, P. (2021). “What got flipped?”: Teacher’s use of contrasting conceptions to support students’ development of inverse functions. In Olanoff, D., Johnson, K., & Spitzer, S. M. (Eds.) Proceedings of the forty-third annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. Philadelphia, PA. (pp. 1623–1624)
Stevens, I. E., & Boileau, N. (2021). Understanding student behaviour as evidence of student conceptions and instructional norms. In Olanoff, D., Johnson, K., & Spitzer, S. M. (Eds.) Proceedings of the forty-third annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. Philadelphia, PA. (pp. 1899–1900)
Spiteri, A., Stevens, I. E., & Herbst, P. (2021). Supporting the construction of variables in an inverse function context through targeted questions. In Olanoff, D., Johnson, K., & Spitzer, S. M. (Eds.) Proceedings of the forty-third annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. Philadelphia, PA. (pp. 1623–1624)
Stevens, I. E. (2020). “Solving versus Relating”: Pre-service teachers’ conflicting images of formulas and dynamic contexts. In A.I. Sacristán, J.C. Cortés-Zavala & P.M. Ruiz-Arias, (Eds.). Mathematics Education Across Cultures: Proceedings of the 42nd Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, Mexico (pp. 1223–1227). Cinvestav /AMIUTEM / PME-NA. 10.51272/pmena.42.2020-192
Stevens, I. E., Ko, I., Paoletti, T., Boileau, N., & Herbst, P. (2020). Introducing inverse function to high school students: Relating convention and reasoning. In A.I. Sacristán, J.C. Cortés-Zavala & P.M. Ruiz-Arias, (Eds.). Mathematics Education Across Cultures: Proceedings of the 42nd Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, Mexico (pp. 227–235). Cinvestav /AMIUTEM / PME-NA. 10.51272/pmena.42.2020-192
Stevens, I. E. (2020). Elementary school geometry to university level calculus: Building upon learning trajectories rooted in covariational reasoning with area contexts to support covariational reasoning related to implicit differentiation. Proceedings of the Twenty-Third Annual Conference on Research in Undergraduate Mathematics Education (p. 1287–1288). Boston, MA.
Moore, K. C., Liang, B., Stevens, I. E., Tasova, H., Paoletti, T., & Ying, Y. (2020). A quantitative reasoning framing of concept construction. Proceedings of the Twenty-Third Annual Conference on Research in Undergraduate Mathematics Education (pp. 752–761). Boston, MA.
Moore, K. C., Liang, B., Tasova, H. I., & Stevens, I. E. (2019). Abstracted quantitative structures. Proceedings of the 41st Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 1879–1883). St. Louis, MO.
Stevens, I. E. (2019). The role of multiplicative objects in a formula. In A. Weinberg, D. Moore-Russo, H. Soto, & M. Wawro (Eds.), Proceedings of the Twenty-Second Annual Conference on Research in Undergraduate Mathematics Education (pp. 273–281). Oklahoma City, OK.
Stevens, I. E. (2019). Using a dynamic geometric context to support students’ constructions of variables. In A. Weinberg, D. Moore-Russo, H. Soto, & M. Wawro (Eds.), Proceedings of the Twenty-Second Annual Conference on Research in Undergraduate Mathematics Education (pp. 576–585). Oklahoma City, OK.
Stevens, I. E. (2018). The parallelogram problem: Supporting covariational reasoning in the construction of formulas. In Hodges, T. E., Roy, G. J., & Tyminski, A. M. (Eds.), Proceedings of the 40th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 624–627). Greenville, SC: University of South Carolina & Clemson University.
Liang, B., Stevens, I. E., Tasova, H. I., & Moore, K. C. (2018). Magnitude reasoning: Characterizing a pre-calculus student’s quantitative comparison between covarying magnitudes. In Hodges, T. E., Roy, G. J., & Tyminski, A. M. (Eds.), Proceedings of the 40th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 608–611). Greenville, SC.
Stevens, I. E. (2018). Insights into students' images of a geometric object and its formula from a covariational reasoning perspective. In A. Weinberg, C. Rasmussen, J. Rabin, M. Wawro & S. Brown (Eds.), Proceedings of the Twenty-First Annual Conference on Research in Undergraduate Mathematics Education (pp. 997-1005). San Diego, CA.
Tasova, H., Stevens, I. E., & Moore, K. C. (2018). A framework for analyzing written curriculum from a shape-thinking and (co)variational reasoning perspective. In A. Weinberg, C. Rasmussen, J. Rabin, M. Wawro & S. Brown (Eds.), Proceedings of the Twenty-First Annual Conference on Research in Undergraduate Mathematics Education (pp. 1527-1533). San Diego, CA.
Hardison, H., Stevens, I. E., Lee, H. Y., & Moore, K. C. (2017). Lydia's circle concept: The intersection of figurative thought and covariational reasoning. In E. Galindo & J. Newton (Eds.), Proceedings of the 39th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education(pp. 391). Indianapolis, IN: Hoosier Association of Mathematics Teacher Educators.
Stevens, I. E. & Moore, K. C. (2017). The intersection between quantification and an all-encompassing meaning for a graph. In E. Galindo & J. Newton (Eds.), Proceedings of the 39th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education(pp. 709-716). Indianapolis, IN: Hoosier Association of Mathematics Teacher Educators.
Stevens, I. E. (2017). A critical examination of the critiques of radical constructivismas an epistemology for education. In Kaur, B., Ho, W. K., Toh T.L., & Choy, B.H. (Eds.). Proceedings of the 41stConference of the International Group for the Psychology of Mathematics Education,Vol 1, p. 270. Singapore: PME.
Stevens, I. E., Paoletti, T., Moore, K. C., Liang, B. & Hardison, H. (2017). Principles for designing tasks that promote covariational reasoning. In A. Weinberg, C. Rasmussen, J. Rabin, M. Wawro & S. Brown (Eds.), Proceedings of the 20th Annual Conference on Research in Undergraduate Mathematics Education (pp. 928-936). San Diego, CA.
Stevens, I. E., & Moore, K. C. (2016). The Ferris wheel and justifications of curvature. In M. B. Wood, E. E. Turner, M. Civil, & J. A. Eli (Eds.), Proceedings of the 38th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education(pp. 644-651). Tucson, AZ: The University of Arizona.
Moore, K. C., Stevens, I. E., Paoletti, T. & Hobson, N. L. F. (2016). Graphing habits: “I just don’t like that”. In (Eds.) T. Fukawa-Connelly, N. Infante, M. Wawro, and S. Brown, Proceedings of the 19th Annual Conference on Research in Undergraduate Mathematics Education, Pittsburgh, Pennsylvania.
Paoletti, T.,Mauldin, K. D., Moore, K. C., Stevens, I. E., Hobson, N. L. F., & LaForest,K. R. (2015). Changing cones: Students’ images of a dynamic situation. In T. G. Bartell, K. N. Bieda, R. T. Putnam, K. Bradfield, & H. Dominguez (Eds.), Proceedings of the 37th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (p. 427). East Lansing,MI: Michigan State University.
Stevens, I. E.,Hobson, N. L. F., Moore, K. C., Paoletti, T., LaForest, K. R., & Mauldin,K. D. (2015). Changing cones: Themes in students' representation of a dynamic situation. In T. G. Bartell, K. N. Bieda, R. T. Putnam, K. Bradfield, & H.Dominguez (Eds.), Proceedings of the 37th annual meeting of the NorthAmerican Chapter of the International Group for the Psychology of MathematicsEducation (pp. 363–370). East Lansing, MI: Michigan State University.
Stevens, I. E.,LaForest, K. R., Hobson, N. L. F., Paoletti, T., & Moore, K. C. (2015). Undergraduate students’ inverse strategies and meanings. In T. G. Bartell, K. N. Bieda, R. T.Putnam, K. Bradfield, & H. Dominguez (Eds.), Proceedings of the 37th annual meeting of the North American Chapter of the International Group for thePsychology of Mathematics Education (p. 262). East Lansing, MI: MichiganState University.
Paoletti, T., Stevens, I. E., Hobson, N. L. F., Moore, K. C., & LaForest, K. R. (2015). Pre-service teachers' inverse function meanings. In T. Fukawa-Connelly, N.Infante, K. Keene, & M. Zandieh (Eds.), Proceedings of the Eighteenth Annual Conference on Research in Undergraduate Mathematics Education (pp.853–867). Pittsburgh, PA: West Virginia University.
Stevens, I. E. (2023). Active learning of covariational reasoning in an undergraduate precalculus course. In Abstracts of Papers Presented to the American Mathematical Society.
Herbst, P., Stevens, I. E., Milewski, A., Ion, M., & Ko, I. (2020). State of the undergraduate Geometry courses for secondary Teachers: Curriculum, Instructional Practices, and Student achievement. In Abstracts of Papers Presented to the American Mathematical Society, 41(1), 435.
Stevens, I. E. (2020). The role of multiplicative objects in a formula. In Abstracts of Papers Presented to the American Mathematical Society, 41(1), pp. 367-368.
Tasova, H. I., Liang, B., Stevens, I. E., & Moore, K. C. (2019). Undergraduate students’ quantitative comparisons of covarying quantities’ magnitudes. In C. D. Savage, G. Benkart, B. D. Boe, M. L. Lapidus, & S. H. Weintraub. Abstracts of Papers Presented to the American Mathematical Society, 40(1), 421.
Moore, K. C., Stevens, I. E., Liang, B., & Tasova, H. I. (2019). Concept construction and abstracted quantitative structures. In C. D. Savage, G. Benkart, B. D. Boe, M. L. Lapidus, & S. H. Weintraub. Abstracts of Papers Presented to the American Mathematical Society, 40(1), 421.
Stevens, I. E. (2018). How a pre-calculus student was able to reason about rates of change using magnitudes. In C. D. Savage, G. Benkart, B. D. Boe, M. L. Lapidus, & S. H. Weintraub. Abstracts of Papers Presented to the American Mathematical Society, 39(1), 466-467.
Stevens, I. E. (2017). Topological Data Analysis of Students’ Responses to MAA Surveys on College Calculus. In C. D. Savage, G. Benkart, G., B. D. Boe, M. L. Lapidus, & S. H. Weintraub, Abstracts of Papers Presented to the American Mathematical Society: Vol. 38(187), p. 565.
Stevens, I. E. & Moore, K. C. (2017). A case study: When graphs contain everything. In C. D. Savage, G. Benkart, B. D. Boe, M. L. Lapidus, & S. H. Weintraub. Abstracts of Papers Presented to the American Mathematical Society, 38(1), 461-462.