Igor' Kontorovich|Research projects for graduate students

Ongoing Projects

Collaborative learning - not as straightforward as it may sound

In undergraduate mathematics education, students’ collaborations have gained a reputation as a ‘good’ learning practice. A more complex image emerges once collaborations are construed as an arena where cognitive, social, and affective matters intertwine in ways that can fuel and impede learning. This project delves into this complexity aiming to understand the mechanisms of collaborative learning in fine-grain.

Kontorovich, I. (2023). When learning stumbles upon identity and affect: A loaded collaboration in Linear Algebra. International Journal of Mathematics Education in Science and Technology, 54, 1526-1540 https://doi.org/10.1080/0020739X.2023.2173102

Mathematics learning with automated feedback

Contemporary digital technology is capable of not only assessing the correctness of students' answers but also providing meaningful feedback regarding changes that need to be implemented. This project explores how small groups of students can mobilize this feedback for mathematics learning.

Kontorovich, I., & Locke, K. (2022). The area enclosed by a function is not always the definite integral: Re-learning through transitioning within learning-support systems. Digital

Experiences in Mathematics Education, 9, 255-282. https://doi.org/10.1007/s40751-022-00116-z

Undergraduates' grasp of fundamental concepts and processes in mathematics

First-year university mathematics courses have gained a reputation of being intense, lecturer-centered, and difficult for many students. This project attempts to understand specific mathematical challenges that students experience, consider them from different theoretical angles, and offer new approaches to overcome them.

Kontorovich, I. (2023). “Find the area enclosed by …” Parceling an especially robust model of reasoning among many first-year students. International Journal of Research in

Undergraduate Mathematics Education, 9, 149–172. https://doi.org/10.1007/s40753-023-00213-3

Kontorovich, I., & Li, T. (2022). Not as straightforward as it may appear: Undergraduates use areas to find definite integrals. International Journal of Science and Mathematics

Education, 21, 2027-2044. https://doi.org/10.1007/s10763-022-10339-6

Kontorovich, I. (2019). Why don’t students check their solutions to mathematical

problems? A field-based hypothesis on epistemological status. International Journal of

Mathematics Education in Science and Technology, 50(7), 1050–1062.

Kontorovich, I. (2020). Theorems or procedures? Exploring undergraduates’ methods to

solve problems in linear algebra. Mathematics Education Research Journal, 32, 589-605.

Griffith Moala, J., Yoon, C., & Kontorovich, I. (2019). Localized considerations and patching: Accounting for persistent attributes of an algorithm on a contextualized graph theory

task. The Journal of Mathematical Behavior, 55.

Kontorovich, I. (2019). Non-examples of problem answers in mathematics with particular reference to linear algebra. The Journal of Mathematical Behavior, 54.

Kontorovich, I. (2018). Tacit models that govern undergraduates’ reasoning about subspaces. International Journal of Research in Undergraduate Mathematics Education, 4(3), 393–414.

Kontorovich, I. (2016). Students’ confusions with reciprocal and inverse functions. International Journal of Mathematical Education in Science and Technology, 48(2), 278–284.

A topology course as a context for proof, proving, and learning

Kontorovich, I., & Greenwood, S. (2023). From collaborative construction, through whole- class presentation, to a posteriori reflection: Proof progression in a topology classroom. International Journal of Research in Undergraduate Mathematics Education.

https://doi.org/10.1007/s40753-023-00217-z

Kontorovich, I., L’Italien-Bruneau, R., & Greenwood, S. (2022). From “presenting inquiry results” to “mathematizing at the board as part of inquiry”: A commognitive look at the familiar practice. In R. Biehler, G. Gueudet, M. Liebendörfer, C. Rasmussen, & C. Winsløw

(Eds.), Practice-oriented research in tertiary mathematics education: New directions. Springer.

Kontorovich, I. (2021). Minding mathematicians’ discourses in investigations of their

feedback on students’ proofs: A case study. Educational Studies in Mathematics, 107(2), 213–

234.

Making sense of mathematical conventions

Conventions are fascinating creatures: some of them are reasonable and widely accepted, while others differ from one mathematical community to another. They are also rarely discussed in a classroom, which complicates the life of many newcomers to mathematics. This project engages students and teachers with conventions and explores what "big" lessons about mathematics can be learned from them.

Kontorovich, I., & Zazkis, R. (2017). Mathematical conventions: Revisiting arbitrary and necessary. For the Learning of Mathematics, 37(1), 29–34.

Kontorovich, I. (2016). √9=? The answer depends on your lecturer. Research in Mathematics Education, 18(3), 284–299.

Mathematics as an activity that develops throughout the curriculum

Some concepts appear multiple times in the students’ landscape of mathematics education when each time they are reconsidered in a new domain. For instance, angles in plane geometry and trigonometry, reciprocals of numbers and inverse functions, roots of real and complex numbers. A domanial shift is often accompanied by a redefinition, revision of familiar properties and an introduction of new ones. How do learners cope with new situations? How do they explain that something that was correct in one domain turns to be wrong in the new one? Are they even aware of the change? How does it feel when prior knowledge cannot be trusted?

Kontorovich, I. (2022). On the intricacies of the plus-minus symbol. For the Learning of Mathematics, 42(2), 18–21.

Kontorovich, I. (2021). Pre-academic students square-root from squared things: a commognitive account of apparent conflicts within mathematical discourses. Journal of Mathematical Behavior, 100910. https://doi.org/10.1016/j.jmathb.2021.100910

Zazkis, R., Mason, J., & Kontorovich, I. (2021). The learning and teaching of number: paths less traveled through well trodded terrain. Routledge Taylor and Francis Group.

Kontorovich, I., Zazkis, R., & Mason, J. (2021). From one kind of numbers to another: the metaphors of expansions and transition. For the Learning of Mathematics, 41(1), 47–49.

Kontorovich, I. (2018). Unacceptable discrepancy: The case of the root concept. For the Learning of Mathematics, 38(1), 17–19.

Kontorovich, I. (2018). Undergraduates images of the root concept in R and in C. The Journal of Mathematical Behavior, 49, 184–193.

Kontorovich, I. (2018). Why Johnny struggles when familiar concepts are taken to a new mathematical domain: Towards a polysemous approach. Educational Studies in Mathematics, 97(1), 5–20.

Zazkis, R. & Kontorovich, I. (2016). A curious case of superscript (-1): Prospective secondary mathematics teachers explain. The Journal of Mathematical Behavior, 43, 98–110.

Kontorovich, I., & Zazkis, R. (2016). Turn vs. shape: Teachers cope with incompatible perspectives on angle. Educational Studies in Mathematics, 93(2), 223–243.

Mathematicians-researcher collaborations

For too long, mathematics education research has treated mathematicians only as research subjects. This project reconsiders the relations between the community of mathematics education researchers and mathematicians, aiming to understand how the knowledge, skills, and resources that each community "brings to the table" can be leveraged to improve university mathematics education.

Publications from the project:

Kontorovich, I., & Bartlett, P. (2021). Implementation of research on scriptwriting in an

undergraduate mathematics course: a case study of teacher-researcher collaboration. ZDM -

Mathematics Education, 53, 1109-1120.

Mathematical communication in online forums

On the one hand, there is multiple evidence of a decline in students' interest in mathematics. On the other hand, there are infinitely many online forums with rich mathematical discussions. What is discussed there and how? How are these discussions different from the ones that we try to cultivate in our classrooms? How do students use these forums for coping with their classroom mathematics?

Kontorovich, I. (2018). Learning mathematics through online forums: A case of linear algebra. In E. Bergqvist, M. Österholm, C. Granberg and L. Sumpter (Eds.), Proceedings of the 42nd Conference of the International Group for the Psychology of Mathematics Education (vol. 3, pp. 235–243). Umeå, Sweden: PME.

Kontorovich, I. (2016). We all know that a0=1, but can you explain why? Canadian Journal of Science, Mathematics and Technology Education, 16(3), 237–246.