Mathematics Education

My research is in the area of Undergraduate Mathematics Education, with a focus on mathematical content knowledge of preservice teachers and the ways in which this knowledge is acquired and modified. Teaching, learning and understanding elementary number theory was a specific topic of my recent studies. This research was funded by 5 standard SSHRC grants and several internal grants.

Updated information and downloadable files are available at http://www.sfu.ca/~zazkis/.

Email: rina_zazkis@sfu.ca

Selected Publications

Articles in Refereed Journals (selected, since 1998)

Zazkis, R. & Chernoff, E. (in press). What makes a counterexample exemplary? Educational Studies in Mathematics.

Zazkis, R. (in press). Number Theory in mathematics education: Queen and Servant. Mediterranean Journal of Mathematics Education.

Zazkis, R., Liljedahl, P. & Chernoff, E. (in press). The role of examples on forming and refuting generalizations. Zentralblatt für Didaktic en Mathematik.

Liljedahl, P., Chernoff. E., & Zazkis, R. (in press). Interweaving mathematics and pedagogy in task design: A tale of one task. Journal of Mathematics Teacher Education.

Zazkis, R. & Leikin, R. (2007).  Generating examples: From pedagogical tool to a research tool. For the Learning of Mathematics, 27(2), 15-21.

Zazkis, R & Sirotic, N. (in press). Representing and defining irrational numbers: Exposing the missing link. Research in Collegiate Mathematics Education.

Sirotic, N. & Zazkis, R. (2007). Irrational numbers: The gap between formal and intuitive knowledge. Educational Studies in Mathematics, 65(1), 49-76.

Sirotic, N. & Zazkis, R. (2007). Irrational numbers on a number line – Where are they? International Journal of Mathematical Education in Science and Technology, 38(4), 477-488.

Sinclair, N., Liljedahl, P. & Zazkis, R. (2006). A coloured window on preservice teacher’s conceptions of rational numbers. International Journal of Computers for Mathematical Learning, 11(2), 177-203.

Zazkis, R., Sinclair, N. & Liljedahl, P. (2006). Conjecturing in a computer microworld: Zooming out and zooming in. Focus on Learning Problems in Mathematics, 28(2), 1-19.

Liljedahl, P., Sinclair, N. & Zazkis, R. (2006). Number concepts with Number Worlds: Thickening understandings. International Journal of Mathematical Education in Science and Technology, 37(3), 253-275.

Zazkis, R. (2005). Representing numbers: Prime and irrational. International Journal of Mathematical Education in Science and Technology, 36(2-3), 207-218.

Hazzan, O., & Zazkis, R. (2005). Reducing abstraction: The case of school mathematics. Educational Studies in Mathematics, 58(1), 101-119.

Zazkis, R. & Liljedahl, P.  (2004). Understanding primes: The role of representation. Journal for Research in Mathematics Education, 35(3), 164-186.

Sinclair, N., Zazkis, R. & Liljedahl, P. (2004). Number Worlds: Visual and experimental access to number theory concepts. International Journal of Computers for Mathematical Learning, 8(3), 235-263.

Zazkis, R., Liljedahl, P. & Gadowsky, K. (2003). Students’ conceptions of function translation: Obstacles, intuitions and rerouting. Journal of Mathematical Behavior, 22, 437-450.34.

Hazzan. O. & Zazkis. R. (2003). Mimicry of proofs with computers: The case of Linear Algebra. Intenational Journal of Mathematics Education in Science and Technology 34(3), 385-402.

Zazkis, R. & Liljedahl, P. (2002). Generalization of patterns: The tension between algebraic thinking and algebraic notation. Educational Studies in Mathematics, 49. 379-402.

Zazkis, R. & Liljedahl, P. (2002). Arithmetic sequence as a bridge among conceptual fields. Canadian Journal of Science, Mathematics and Technology Education, 2(1). 91-118.

Zazkis, R. & Levy, B. (2001) Truth value of mathematical statements: Can fuzzy logic illustrate students’ decision making? Focus on Learning Problems in Mathematics, 23(4). 1-26.

Moor, J. & Zazkis, R. (2000). Learning mathematics in a virtual classroom: Reflection on experiment. Journal of Computers in Mathematics and Science Teaching, 19(2). 89-114.

Zazkis, R. (2000) Using Code-switching as a tool for learning mathematical language. For the Learning of Mathematics, 20(3). 38-43.

Zazkis, R. (2000). Factors, divisors and multiples: Exploring the web of students’ connections. Research in Collegiate Mathematics Education. Vol. 4. 210-238.

Zazkis, R. (1999). Intuitive rules in number theory: Example of “the more of A, the more of B” rule implementation. Educational Studies in Mathematics, 40(2), 197-209.

Zazkis, R. (1999). Divisibility: A problem solving approach through generalizing and specializing. Humanistic Mathematics Network Journal, Issue #21, 34-38.

Zazkis, R. (1999). Challenging basic assumptions: Mathematical experiences for preservice teachers. International Journal of Mathematics Education in Science and Technology, 30(5), 631-650.

Hazzan, O. & Zazkis, R. (1999). A perspective on “give an example” tasks as opportunities to construct links among mathematical concepts. Focus on Learning Problems in Mathematics, 21(4), 1-14.

Zazkis, R. & Hazzan, O. (1998). Interviewing in mathematics education research: Choosing the questions. Journal of Mathematical Behavior, 17(4), 429-239.

Zazkis, R. (1998). Divisors and quotients: Acknowledging polysemy. For the Learning of Mathematics, 18(3), 27-30.

Zazkis, R. (1998). Odds and ends of odds and evens: An inquiry into students’ understanding of even and odd numbers. Educational Studies in Mathematics, 36(1), 73-89.

Chapters in Edited Books (refereed)

Zazkis, R. (in press). Divisibility and transparency of number representations. In M. Carlson & C. Rasmussen (Eds.), Making the Connection: Research and practice in undergraduate mathematics. MAA notes.

Zazkis, R. & Liljedahl, P. (2006). On the path to number theory: Repeating patterns as a gateway. In R. Zazkis and S.R. Campbell (Eds.), Number Theory in mathematics education: Perspectives and prospects (pp. 99-114). Lawrence Erlbaum Press.

Zazkis, R. & Campbell, S.R. (2006). Number Theory in mathematics education research: Perspectives and prospects. In R. Zazkis and S.R. Campbell (Eds.), Number Theory in mathematics education: Perspectives and prospects (pp. 1-18). Lawrence Erlbaum Press.

Campbell, S. R., & Zazkis, R. (2002). Toward number theory as a conceptual field. In Campbell, S. R, & Zazkis, R. (Eds.) Learning and teaching number theory: Research in cognition and instruction (pp. 1-14). Westport, CT: Ablex Publishing.

Edwards, L & Zazkis, R. (2002). Pre-service teachers’ generalizations on a number theory task. Campbell. S. R., & Zazkis, R. (Eds.) Learning and teaching number theory: Research in cognition and instruction (pp.139-156). Westport, CT: Ablex Publishing.

Zazkis, R. (2002) Language of number theory: Metaphor and rigor.  Campbell. S. R., & Zazkis, R. (Eds.) Learning and teaching number theory: Research in cognition and instruction (pp. 83-96). Westport, CT: Ablex Publishing.

Zazkis, R. & Gadowsky, K. (2001). Attending to transparent features of opaque representations of natural numbers. In A. Cuoco (Ed.), NCTM 2001 Yearbook: The roles of representation in school mathematics (pp. 41-52). Reston, VA: NCTM.

Books and Monographs

Zazkis, R. & Campbell, S. R. (Eds). (2006). Number theory in mathematics education: Perspectives and prospects. Lawrence Erlbaum Press.

Zazkis, R & Holton, D. (Eds.). (2005). New trends and developments in tertiary mathematics education: ICME-10 perspectives. Special Issue of the International Journal of Mathematics Education in Science and Technology. Taylor & Francis.

Campbell, S. R., & Zazkis, R. (Eds.) (2002). Learning and teaching number theory: Research in cognition and instruction. Westport, CT: Ablex Publishing.

Articles in Refereed Conference Proceedings (Recent)

Leikin, R. & Zazkis, R. (2007). A view on the teachers’ opportunities to learn mathematics through teaching. Proceedings of 31st International Conference for Psychology of Mathematics Education. Vol. 1 (pp. 122-128). Seoul, Korea.

Zazkis, R. & Applebaum, M. (2007). Advancing mathematical thinking: Looking back on one problem. Proceedings of the Conference for European Research in Mathematics Education. Larnaca, Cyprus.

Berezovski, T. & Zazkis, R. (2006). Logarithms: Snapshots from Two Tasks. Proceedings of 30th International Conference for Psychology of Mathematics Education. Vol. 2. (pp. 145-152). Prague, Czech Republic.

Zazkis, R. & Chernoff, E. (2006). Cognitive conflict and its resolution via pivotal/bridging example. Proceedings of 30th International Conference for Psychology of Mathematics Education. Vol. 4. (pp. 465-472). Prague, Czech Republic.

Sirotic, N. & Zazkis, R. (2005). Locating irrational numbers on a number line. Proceedings of the Conference for Psychology of Mathematics Education – North American Chapter. Roanoke, VA.

Gholamazad, S., Liljedahl, P., & Zazkis, R. (2004). What counts as a proof? Investigation of Pre-service elementary teachers’ evaluation of presented ‘proofs’. Proceedings of the conference for Psychology of Mathematics Education – North American Chapter. Vol. 2 (pp. 639-646). Toronto, Canada.

Sirotic, N. & Zazkis, R. (2004). Irrational numbers: Dimensions of Knowledge. Proceedings of the conference for Psychology of Mathematics Education – North American Chapter. Vol. 1. (pp. 171-178). Toronto, Canada.

Zazkis, R. (2004). Representing numbers: Prime and Irrational. Electronic proceedings of the 10th International Congress for Mathematics Education. Copenhagen, Denemark. http://www.icme-10.dk/

Zazkis, R & Sirotic, N. (2004). Making sense of irrational numbers: Focusing on representation. Proceedings of 28th International Conference for Psychology of Mathematics Education. Vol. 4. (pp. 497-505). Bergen, Norway.

Sinclair, N., Watson, A. & Zazkis, R. (2004). Learner-generated examples. Working group report. (pp. 45-54). Laval, Quebec.

Zazkis, R., Liljedahl, P. & Gadowsky, K. (2003). Translation of a function: Coping with perceived inconsistency. Proceedings of the 27th International Conference for Psychology of Mathematics Education. Honolulu. HI.

Gholamazad, S., Liljedahl, P., & Zazkis, R. (2003). One line proof: What can go wrong? Proceedings of the 27th International Conference for Psychology of Mathematics Education. Honolulu. HI.

Zazkis, R. & Liljedahl, P. (2002). Repeating patterns as a gateway. Proceedings of the 26th International Conference for Psychology of Mathematics Education. Norwich, UK.

Zazkis, R. (2001). From arithmetic to algebra via “big” numbers. Proceedings of the International Congress of Mathematics Education Study on Algebra. Melbourne, Australia.

Zazkis, R. (2001). Elementary Number theory: Issues in research and pedagogy. Proceedings of the 25th meeting of the Canadian Mathematics Education Study Group.

Zazkis, R. & Liljedahl, P. (2001). Exploring multiplicative and additive structure of arithmetic sequence. Proceedings of the 25th  International Conference for Psychology of Mathematics Education. Utrecht, Netherlands.

Liljedahl, P. & Zazkis, R. (2001). Analogy in the exploration of repeating patterns. Proceedings of the 25th  International Conference for Psychology of Mathematics Education. Utrecht, Netherlands.

Research and Development Projects (funded, since 1998)

2007-2008	Principal Investigator Paradoxes of infinity. Research project supported by a small SSHRC grant – internal Simon Fraser University fund, $4,999 for 18 months.
2007-	Co-investigator Mathematical Visualization in Virtual Environments. Development grant (for CTEF) from the Research Opportunities Committee. $5000.
2007-	Co-director David Wheeler Institute for Research in Mathematics Education. Seed funding for centre development from the Dean of Education. $15,000
2005-2008	Principal Investigator The discursive perspective on reconstruction of knowledge by preservice elementary school teachers. Research project supported by a standard SSHRC grant, $165,000 for 3 years.
2004-2006	Principal Investigator Understanding Logarithms. Research project supported by a small SSHRC grant – internal Simon Fraser University fund, $4,500 for 18 months.
2002-2005	Principal Investigator Relearning mathematics: The reconstruction of knowledge by preservice elementary school teachers. Research project supported by a standard SSHRC grant, $175,000 for 3 years.
2001-2002	Principal Investigator Irrational Numbers: Investigation of understanding of students and teachers. Research project supported by a small SSHRC grant – internal Simon Fraser University fund, $4,500 for 18 months.
1999-2002	Principal Investigator Learning number theory: Exploring the web of students’ links. Research project supported by a standard SSHRC grant, $105,000 for 3 years.
1999-2000	Principal Investigator Fuzzy logic as a tool for analyzing students’ reasoning. Research project supported by a small SSHRC grant – internal Simon Fraser University fund, $4,976 for 18 months.
1998-1999	Principal Investigator Learning mathematics on the World Wide Web. Research project supported by a small SSHRC grant – internal Simon Fraser University fund, $4,999 for 18 months.

Service Highlights (since 2000)

National and International Activity

Reviewing and Editorial Activity (current)

University Activity (current)

Faculty Activity, Faculty of Education, SFU

Graduate Student Supervision

Theses Completed (since 2000)

Senior supervisor for 5 doctoral students in progress