Professor KONTOROVICH, Igor’

My main research themes are:

• mathematics learning and teaching in university and secondary school, including the secondary-tertiary transition and advanced mathematics studies; 
• coming to grips with fundamental concepts and processes in mathematics (e.g., problem solving & posing, proving, defining, exemplifying) and investigating how digital resources and AI can be of help;
• mathematicians' teaching practices, research, and the interrelations between them;
• mathematical communication online and in hybrid spaces; 
• theories of learning with a special interest in discursive and socio-cultural approaches.

I am currently seeking PhD applications with a strong mathematical background and keen interest in these or other themes. If you are interested in pursuing a PhD or a Research Assistant position, please fill out the Expression of Interest (EOI) Form on the left-hand side of this page.

Dean's Award for Teaching Excellence in Leadership in Teaching, the University of Auckland, 2024

Early Career Research Excellence Award, the University of Auckland, 2022

Vivian Konigsberg Award for Teaching Excellence, Technion, 2012

Miriam and Aaron Gutwirth Memorial Fellowship for Research Excellence, Technion, 2010

Friendship and Support Fellowship for Research Excellence, Technion, 2009

Academic Excellence Scholarship, Technion, 2008

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. 

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?

Collaborative learning - not as straightforward as it may sound

​In 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 on a fine-grained level.

Mathematics learning with automated feedback

Contemporary AI-based 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 these technological affordances can be mobilized for students' learning.

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 lives 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. 

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?

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.

46. Wallach, M. N., & Kontorovich, I. (2024). When learner-centered teaching and learning goes online: Zooming into Linear Algebra tutorials during the pandemic. International Journal of Research in Undergraduate Mathematics Education. https://doi.org/10.1007/s40753-024-00244-4 

45. Kontorovich, I., Liu, N. Q., & Kang, S.-w. (2024). Transitioning to proof via writing scripts on the rules of a new discourse. Educational Studies in Mathematics, 117, 143–162. https://doi.org/10.1007/s10649-024-10324-6

44. Kontorovich, I. (2024). The road to “good” problems goes through initial responses to stimulating socio-mathematical situations. The Journal of Mathematical Behavior, 101125. https://doi.org/10.1016/j.jmathb.2024.101135  

43. Locke, K., Kontorovich, I., & Darragh, L. (2023). Transforming mathematical identity: Changes in one international student’s positioning during first-year mathematics tutorials. International Journal of Mathematics Education in Science and Technology, 54(9), 1785–1803. https://doi.org/10.1080/0020739X.2023.2259917 

42. Andrà, C., Kontorovich, I., & Brunetto, D. (2023). Two technology-enthusiastic teachers, two instructional mathematical videos, and two very different lessons. For the Learning of Mathematics, 43(3), 32–37. 

41. 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, 10, 516–546. https://doi.org/10.1007/s40753-023-00217-z 

40. Knox, J., & Kontorovich, I. (2023). Leveraging interdiscursivity to support elementary students in bridging the empirical-deductive gap: The case of parity. The Journal of Mathematical Behavior, 70, 101052. https://doi.org/10.1016/j.jmathb.2023.101052  

39. 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

38. Kontorovich, I., & Ovadiya, T. (2023). How narratives about the secondary-tertiary transition shape undergraduate tutors’ sense-making of their teaching. Educational Studies in Mathematics, 113, 125– 146. https://doi.org/10.1007/s10649-023-10211-6

37. 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 

36. 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 

35. Kinnear, G., Jones, I., Sangwin, C., Alarfaj, M., Davies, B., Fearn, S., Foster, C., Heck, A., Henderson, K., Hunt, T., Iannone, P., Kontorovich, I., Larson, N., Lowe, T., Meyer, J. C., O’Shea, A., Rowlett, P., Sikurajapathi, I., & Wong, T. (2022). A collaboratively-derived research agenda for e-assessment in undergraduate mathematics. International Journal of Research in Undergraduate Mathematics Education. https://doi.org/10.1007/s40753-022-00189-6 

34. 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 

33. Knox, J., & Kontorovich, I. (2022). Growing research groves to visualize young students’ learning in small groups. Mathematics Education Research Journal. https://doi.org/10.1007/s13394-022-00422-0 

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

31. Kontorovich, I. (2021). Pre-academic students square-root from squared things: A commognitive account of apparent conflicts within mathematical discourses. The Journal of Mathematical Behavior, 64, 100910. https://doi.org/10.1016/j.jmathb.2021.100910 

30. Kontorovich, I. (2021). Book review. International Journal of Research in Undergraduate Mathematics Education, 7(3), 519–524. https://doi.org/10.1007/s40753-021-00147-8 

29. Kontorovich, I., & Bartlett, P. (2021). Implementation of research on scriptwriting in an undergraduate mathematics course: A study of teacher-researcher collaboration. ZDM - Mathematics Education, 53, 1109–1120. https://doi.org/10.1007/s11858-021-01281-y

28. 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. https://doi.org/10.1007/s10649-021-10035-2 

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

26. Kontorovich, I. (2020). Problem-posing triggers or where do mathematics competition problems come from? Educational Studies in Mathematics, 105, 389–406. https://doi.org/10.1007/s10649-020-09964-1 

25. Kontorovich, I. (2020). Theorems or procedures? Exploring undergraduates’ methods to solve problems in linear algebra. Mathematics Education Research Journal, 32, 589–605. https://doi.org/10.1007/s13394-019-00272-3 

24. Kontorovich, I. (2019). Why do students not 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. https://doi.org/10.1080/0020739X.2019.1650304  

23. Rouleau, A., Kontorovich, I., & Zazkis, R. (2019). Mathematics teachers’ first engagement with research articles in mathematics education: Sketches of new praxeologies. Mathematics Teacher Education and Development, 21(2), 42–63.

22. 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. https://doi.org/10.1016/j.jmathb.2019.04.003 

21. Kontorovich, I. (2019). Non-examples of problem answers in mathematics with particular reference to linear algebra. The Journal of Mathematical Behavior, 54, 100685. https://doi.org/10.1016/j.jmathb.2019.01.001

20. Kontorovich, I. (2018). Tacit models that govern undergraduates’ reasoning about subspaces. International Journal of Research in Undergraduate Mathematics Education, 4(3), 393–414. https://doi.org/10.1007/s40753-018-0078-5 

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

18. Kontorovich, I. (2018). Undergraduates’ images of the root concept in R and in C. The Journal of Mathematical Behavior, 49, 184–193. https://doi.org/10.1016/j.jmathb.2017.12.002 

17. 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. https://doi.org/10.1007/s10649-017-9778-z 

16. Kontorovich, I., & Rouleau, A. (2018). To teach or not to teach? Teacher-researchers cope with misconceptions in interview settings. Canadian Journal of Science, Mathematics and Technology Education, 18(1), 9–20. https://doi.org/10.1007/s42330-018-0004-5 

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

14. Kontorovich, I. (2016). √9=? The answer depends on your lecturer. Research in Mathematics Education, 18(3), 284–299.http://dx.doi.org/10.1080/14794802.2016.1234405 

13. Kontorovich, I. (2016). Students’ confusions with reciprocal and inverse functions. International Journal of Mathematical Education in Science and Technology, 48(2), 278–284. https://doi.org/10.1080/0020739X.2016.1223361  

12. Zazkis, R. & Kontorovich, I. (2016). A curious case of superscript (-1): Prospective secondary mathematics teachers explain. The Journal of Mathematical Behavior, 43, 98–110. https://doi.org/10.1016/j.jmathb.2016.07.001 

11. Kontorovich, I., & Zazkis, R. (2016). Turn vs. shape: Teachers cope with incompatible perspectives on angle. Educational Studies in Mathematics, 93(2), 223–243. https://doi.org/10.1007/s10649-016-9699-2 

10. 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. https://doi.org/10.1080/14926156.2016.1189623 

9. Kontorovich, I. (2016). Considerations of aptness in mathematical problem posing: students, teachers and expert working on Billiard task. Far East Journal of Mathematical Education, 16(3), 243–260. https://doi.org/10.17654/ME016030243

8. Kontorovich, I. (2016). Theoretical framework of researcher knowledge development in mathematics education. International Journal of Education in Mathematics, Science and Technology, 4(2), 101–111. https://doi.org/10.18404/ijemst.90629

7. Kontorovich, I., & Koichu, B. (2016). A case study of an expert problem poser for mathematics competitions. International Journal of Science and Mathematics Education, 14(1), 81–99. https://doi.org/10.1007/s10763-013-9467-z 

6. Kontorovich, I. (2015). Learning from the experts in mathematics education research. Far East Journal of Mathematics Education, 15(1), 35–56. http://dx.doi.org/10.17654/FJMEAug2015_035_056

5. Kontorovich, I., & Zazkis, R. (2015). Development of researcher knowledge in mathematics education: Towards a confluence framework. International Journal of Social, Behavioral, Educational, Economic and Management Engineering, 9(5), 1433–1438. doi.org/10.5281/zenodo.1100675

4. Kontorovich, I. (2014). A book review of N. Fried and T. Dreyfus (2014) Mathematics and mathematics education: Searching for common ground. Canadian Journal of Science, Mathematics and Technology Education, 14(3), 299–305. https://doi.org/10.1080/14926156.2014.935529 

3. Koichu, B., & Kontorovich, I. (2013). Dissecting success stories on mathematical problem posing: a case of the Billiard Task. Educational Studies in Mathematics, 83(1), 71–86. https://doi.org/10.1007/s10649-012-9431-9

2. Kontorovich, I., & Koichu, B. (2012). Feeling of innovation in expert problem posing.Nordic Studies in Mathematics Education, 17(3–4), 199–212. 

1. Kontorovich, I., Koichu, B., Leikin, R., & Berman, A. (2012). An exploratory framework for handling the complexity of mathematical problem posing in small groups. The Journal of Mathematical Behavior, 31(1), 149–161. https://doi.org/10.1016/j.jmathb.2011.11.002

International Research Journals

Associate Editor of JMB (the Journal of Mathematical Behavior)

Senior Editor of IJSME (International Journal of Science and Mathematics Education)

Book Review Editor of IJRUME (International Journal of Research in Undergraduate Mathematics Education)

Editorial boards of ESM, RME, MERJ, IJSME

International Research Communities

Scientific committee of INDRUM (International Network for Didactic Research in University Mathematics)

Executive committee of RUME (Research in Undergraduate Mathematics Education)