My Other MicroBlog

Egan J Chernoff (@MatthewMaddux), PhD

 

Assistant Professor, Mathematics Education

 

•Research Interests
•Teaching Interests
•Mathematical Interests
•Personal Interests
•Academic Appointments
•Related Positions
•Articles in Refereed Journals
•Articles in Refereed Conference Proceedings
•Chapters in Edited Books
•Books and Monographs
•Dissertation
•Edited Volumes
•Editorials
•Book Reviews
•ePublications
•Articles in Non-Refereed Journals
•Articles in Non-Refereed Conference Proceedings
•Other Publications
•Invited Colloquia
•Invited Academic Conference Presentations and Workshops
•Academic Conference Presentations
•Invited Public/Professional Conference Presentations
•Public/Professional Conference Presentations
•Invited Professional Development Workshops
•University of Saskatchewan
•Simon Fraser University
•University of British Columbia
•Killarney Secondary School
•Lord Byng Secondary School
•Academic Community Service
•University Service
•Faculty Service
•Public and Community Service
•Digital Service
•Academic Prizes
•Fellowships
•Stipends
•Scholarships
•Grants
•Merit Awards
•Nominations

FORTHCOMING

Chernoff, E. J. & Sterenberg, G. (Eds.) (in development). Selected writings from the Journal of the Mathematics Council of the Alberta Teachers’ Association: Celebrating 50 years (1962-2012) of delta-K.  Charlotte, NC: Information Age Publishing.

  • Chernoff, E. J. (in development). Preface. In E. J. Chernoff & G. Sterenberg (Eds.), Selected writings from the Journal of the Mathematics Council of the Alberta Teachers’ Association: Celebrating 50 years (1962-2012) of delta-K. Charlotte, NC: Information Age Publishing.

  • Sterenberg, G., & Chernoff, E. J. (in development). Introduction. In E. J. Chernoff & G. Sterenberg (Eds.), Selected writings from the Journal of the Mathematics Council of the Alberta Teachers’ Association: Celebrating 50 years (1962-2012) of delta-K. Charlotte, NC: Information Age Publishing.

  • Chernoff, E. J., & Sterenberg, G. (in development). Commentary. In E. J. Chernoff & G. Sterenberg (Eds.), Selected writings from the Journal of the Mathematics Council of the Alberta Teachers’ Association: Celebrating 50 years (1962-2012) of delta-K. Charlotte, NC: Information Age Publishing.

Chernoff, E. J. (2013, August). Solving equations: a make-work project for math teachers. Presentation at the 2013 Prince Albert and Area Teachers' Convention. Prince Albert, Saskatchewan.

Chernoff, E. J., Liljedahl, P., & Chorney, S. (Eds.) (in development). Selected writings from the Journal of the British Columbia Association of Mathematics Teachers: Celebrating 50 years of Vector. Charlotte, NC: Information Age Publishing.

  • Chernoff, E. J. (in development). Preface. In E. J. Chernoff, P. Liljedahl, & S. Chorney (Eds.), Selected writings from the Journal of the British Columbia Association of Mathematics Teachers: Celebrating 50 years of Vector. Charlotte, NC: Information Age Publishing.

  • Liljedahl, P., Chorney, S., & Chernoff, E. J. (in development). Introduction. In E. J. Chernoff, P. Liljedahl, & S. Chorney (Eds.), Selected writings from the Journal of the British Columbia Association of Mathematics Teachers: Celebrating 50 years of Vector. Charlotte, NC: Information Age Publishing.

  • Chernoff, E. J., Liljedahl, P., & Chorney, S. (in development). Commentary. In E. J. Chernoff, P. Liljedahl, & S. Chorney (Eds.), Selected writings from the Journal of the British Columbia Association of Mathematics Teachers: Celebrating 50 years of Vector. Charlotte, NC: Information Age Publishing.

Chernoff, E. J., & Russell, G. L. (2013, November). Comparing The Relative Likelihood Of Events: The Fallacy Of Composition. Research Report Presentation at 35th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. Chicago, IL: University of Illinois at Chicago.

Chernoff, E. J., & Russell, G. L. (accepted). Comparing The Relative Likelihood Of Events: The Fallacy Of Composition. Proceedings of the 35th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. Chicago, IL: University of Illinois at Chicago.

Russell, G. L., & Chernoff, E. J. (2013, November). Unifying challenges in the teaching and learning of mathematics: Two can become one. Research Report Presentation at the 35th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. Chicago, IL: University of Illinois at Chicago.

Russell, G. L., & Chernoff, E. J. (accepted). Unifying challenges in the teaching and learning of mathematics: Two can become one. Proceedings of the 35th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. Chicago, IL: University of Illinois at Chicago.

Chernoff, E. J., Russell, G. L., & Sriraman, B. (Eds.) (in development). Selected writings from the Journal of the Saskatchewan Mathematics Teachers’ Society: Celebrating 50 years (1961-2011) of vinculum. Charlotte, NC: Information Age Publishing.

  • Chernoff, E. J. (in development). Preface. In E. J. Chernoff, G. L. Russell, & B. Sriraman (Eds.), Selected writings from the Journal of the Saskatchewan Mathematics Teachers’ Society: Celebrating 50 years (1961-2011) of vinculum. Charlotte, NC: Information Age Publishing.

  • Chernoff, E. J., Russell, G. L., & Sriraman, B. (in development). Introduction. In E. J. Chernoff, G. L. Russell, & B. Sriraman (Eds.), Selected writings from the Journal of the Saskatchewan Mathematics Teachers’ Society: Celebrating 50 years (1961-2011) of vinculum. Charlotte, NC: Information Age Publishing.

  • Chernoff, E. J. (in development). Preface: The Sixties. In E. J. Chernoff, G. L. Russell, & B. Sriraman (Eds.), Selected writings from the Journal of the Saskatchewan Mathematics Teachers’ Society: Celebrating 50 years (1961-2011) of vinculum. Charlotte, NC: Information Age Publishing.

  • Chernoff, E. J. (in development). Preface: The Seventies. In E. J. Chernoff, G. L. Russell, & B. Sriraman (Eds.), Selected writings from the Journal of the Saskatchewan Mathematics Teachers’ Society: Celebrating 50 years (1961-2011) of vinculum. Charlotte, NC: Information Age Publishing.

  • Chernoff, E. J. (in development). Commentary: The Seventies. In E. J. Chernoff, G. L. Russell, & B. Sriraman (Eds.), Selected writings from the Journal of the Saskatchewan Mathematics Teachers’ Society: Celebrating 50 years (1961-2011) of vinculum. Charlotte, NC: Information Age Publishing.

  • Chernoff, E. J. (in development). Preface: The Eighties. In E. J. Chernoff, G. L. Russell, & B. Sriraman (Eds.), Selected writings from the Journal of the Saskatchewan Mathematics Teachers’ Society: Celebrating 50 years (1961-2011) of vinculum. Charlotte, NC: Information Age Publishing.

  • Chernoff, E. J. (in development). Preface: The Nineties. In E. J. Chernoff, G. L. Russell, & B. Sriraman (Eds.), Selected writings from the Journal of the Saskatchewan Mathematics Teachers’ Society: Celebrating 50 years (1961-2011) of vinculum. Charlotte, NC: Information Age Publishing.

  • Chernoff, E. J. (in development). Preface: The Aughts. In E. J. Chernoff, G. L. Russell, & B. Sriraman (Eds.), Selected writings from the Journal of the Saskatchewan Mathematics Teachers’ Society: Celebrating 50 years (1961-2011) of vinculum. Charlotte, NC: Information Age Publishing.

  • Chernoff, E. J., Russell, G. L., & Sriraman, B. (in development). Commentary. In E. J. Chernoff, G. L. Russell, & B. Sriraman (Eds.), Selected writings from the Journal of the Saskatchewan Mathematics Teachers’ Society: Celebrating 50 years (1961-2011) of vinculum. Charlotte, NC: Information Age Publishing.

Topic Convenor (2014). Topic 6: Innovation and reform in teaching probability within statistics. 9th International Conference on Teaching Statistics (ICOTS9). Flagstaff, Arizona, USA.

Chernoff, E. J. (Guest Editor) (2015). Special Issue: Risk-Mathematical or Otherwise. The Mathematics Enthusiast, 12(1&2).

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INTERESTS

Research Interests

By investigating the probabilistic content knowledge of prospective mathematics teachers, my research, in general, contributes to the (documented) limited research on teachers’ probabilistic knowledge. More specifically, my work has led to the development of a variety of theories, models and frameworks, which account for relative likelihood comparisons made by prospective teachers. Currently, I am incorporating more recent developments from the field of cognitive psychology (e.g., attribute substitution), which (I argue) have largely been ignored by those investigating probabilistic thinking and the teaching and learning of probability in the field of mathematics education; and, in addition, I am establishing that informal logical fallacies (e.g., the fallacy of composition, the appeal to ignorance and others) are an effective means to account for normatively incorrect, inconsistent, sometimes inexplicable responses to a variety of probabilistic tasks.

Other research interests include: (classical, frequentist, and subjective) interpretations of probability, coin flips, sample space, abduction, equiprobability, perceived randomness, heuristic and biases, relativism, and coin flip sequence multivalence.

Teaching Interests

The new math, the new new math, the math wars and, especially, exposing and exploring the false dichotomy (i.e., traditional versus reform) associated with teaching and learning mathematics by (1) modelling the reform approach to teaching and learning mathematics and (2) illustrating – as a character (cf. Colbert) – certain absurdities associated with the traditional approach to teaching and learning mathematics.

Mathematical Interests

probability, combinatorics and alternative base (especially base golden ratio) arithmetic.

Personal Interests

stand up comedy (e.g., Richard Jeni, Greg Giraldo, Jeremy Hotz, Louis C. K., John Pinette, Jeffrey Ross, Danny Bhoy, Tommy Tiernan, Mitch Hedberg, Kathleen Madigan), sports (e.g., squash, tennis, golf, ball hockey, Moksha Yoga, U of S Faculty/Staff Hockey League), Apple Inc. (e.g., iPhone, iPad, iMac, MacBook Air), walking (my dog), my dog Scout's behaviour, playing the lottery (e.g., Lotto 6/49), poker, television, podcasts (e.g., The Age of Persuasion), non-fiction (e.g., earlier Chuck Klosterman), social media (for mathematics education).

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EDUCATION

Ph.D. (2009). Simon Fraser University, Faculty of Education, David Wheeler Institute for Research in Mathematics Education, Mathematics Education, Vancouver, British Columbia, Canada. [view PhD defense presentation slides]

M.Sc. Course Work (2004-2005). Simon Fraser University, Faculty of Education & Department of Mathematics, Secondary Mathematics Education Program, Vancouver, British Columbia, Canada.

B.Ed. (2001). University of British Columbia, Faculty of Education, Department of Curriculum and Pedagogy, Secondary Mathematics Integrated Project (SMIP), Vancouver, British Columbia, Canada.

B.Sc. (1999). Thompson Rivers University, Mathematics and Statistics Department, Mathematics, Kamloops, British Columbia, Canada.

Dogwood Diploma: British Columbia Certificate of Graduation (1995). Kamloops Senior Secondary School, Kamloops, British Columbia, Canada.

Grade 10 (1993). Valley View Junior Secondary School, Kamloops, British Columbia, Canada.

Grade 7 (1990). Robert Logan (RL) Clemitson Elementary School, Kamloops, British Columbia, Canada.

Preschool (1982). Barnhartvale Hall  Preschool, Kamloops, British Columbia, Canada.

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APPOINTMENTS

Academic Appointments

Associate Member (2009-present). University of Saskatchewan, College of Graduate Studies and Research, Saskatoon, Saskatchewan, Canada.

Assistant Professor (2008-present). University of Saskatchewan, College of Education, Department of Curriculum Studies, Secondary Mathematics, Saskatoon, Saskatchewan, Canada.

Sessional Instructor (2006-2008). Simon Fraser University, Faculty of Education, Vancouver, British Columbia, Canada.

Sessional Instructor (2008). University of British Columbia, Faculty of Education, Department of Curriculum and Pedagogy, Vancouver, British Columbia, Canada.

Research Assistant (2005-2008). Simon Fraser University, Faculty of Education, Vancouver, British Columbia, Canada.

Site Assistant (2007-2008). Simon Fraser University, Faculty of Education, Community Graduate Programs: Kelowna, Master of Education Degree Program in Curriculum & Instruction with a focus on Numeracy, Vancouver, British Columbia, Canada.

Site Assistant (2005-2007). Simon Fraser University, Faculty of Education, Community Graduate Program: Yukon, Master of Education Degree Program in Curriculum & Instruction with a focus on Numeracy, Vancouver, British Columbia, Canada.

Related Positions

Sponsor Teacher (2006). Simon Fraser University, Faculty of Education, Professional Development Program, Mind and Heart Module, Vancouver, British Columbia, Canada.

Mathematics Teacher (2001-2006). Vancouver School District, Lord Byng Secondary & Killarney Secondary, Vancouver, British Columbia, Canada.

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RESEARCH PROJECTS

Chernoff, E. J. (2011). Investigating relative likelihood comparisons between contextualized sequences.  University of Saskatchewan President’s SSHRC Research Grant ($7000).

Chernoff, E. J., Russell, G. L., Hossain, M., Campbell, K., Reeves, T., & Stobart Community School (2011). Teaching and learning mathematics within a First Nations and Métis worldview: Impacts on the affective domain and academic achievement. Dr. Stirling McDowell Foundation for Research into Teaching Grant ($21250).

Chernoff, E. J. (2010). Investigating prospective mathematics teachers’ perceptions of randomness: Transitioning to contextualized sequences. SSHRC Standard Research Grant (1A Successful from supplementary list 4A). Social Sciences and Humanities Research Council of Canada ($51573).

Chernoff, E. J. (2010). Investigating prospective mathematics teachers’ relative likelihood judgements. John Ranton McIntosh Research Grant. College of Education, University of Saskatchewan. Saskatoon, SK, Canada ($10000).

Chernoff, E. J. (2007). Different perceptions of chance: Impacts on stochastics education. SSHRC Doctoral Fellowship. Social Sciences and Humanities Research Council of Canada ($20,000).

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PUBLICATIONS

Articles in Refereed Journals

Chernoff, E. J. (2013). Probabilistic relativism: a multivalentological investigation of normatively incorrect relative likelihood comparisons [Special issue: Postmodern Mathematics/Mathematics Education]. Philosophy of Mathematics Education Journal, 27, 1-30. Retrieved from http://people.exeter.ac.uk/PErnest/pome27/index.html

Russell, G. L. & Chernoff, E. J. (2013). The marginalization of Indigenous students within school mathematics and the math wars: seeking resolutions within ethical spaces [Special issue: Mathematics Education with/for Indigenous Peoples]. Mathematics Education Research Journal, 25(1), 109-127. doi: 10.1007/s13394-012-0064-1

Chernoff, E. J. (2012). Logically fallacious relative likelihood comparisons: the fallacy of composition [Special issue: National Year of Mathematics]. Experiments in Education, 40(4), 77-84.

Chernoff, E. J. (2012). Recognizing revisitation of the representativeness heuristic: an analysis of answer key attributes [Themed issue: Probability in Reasoning About Data and Risk]. ZDM - The International Journal on Mathematics Education, 44(7), 941-952. doi: 10.1007/s11858-012-0435-9

Chernoff, E. J., & Russell, G. L. (2012). The fallacy of composition: Prospective mathematics teachers’ use of logical fallacies. Canadian Journal of Science, Mathematics and Technology Education, 12(3), 259-271. doi: 10.1080/14926156.2012.704128

Chernoff, E. J. & Russell, G. L. (2011). The sample space: One of many ways to partition the set of all possible outcomes. The Australian Mathematics Teacher, 67(2), 24-29.

Chernoff, E. J. & Zazkis, R. (2011). From personal to conventional probabilities: from sample set to sample space. Educational Studies in Mathematics, 77(1), 15-33. doi: 10.1007/s10649-010-9288-8

Russell, G., & Chernoff, E. J. (2011). Seeking more than nothing: Two elementary teachers’ conceptions of zero. The Montana Mathematics Enthusiast 8(1&2), 77-112.

Chernoff, E. J. (2009). Sample space partitions: An investigative lens. Journal of Mathematical Behavior, 28(1), 19-29. doi: 10.1016/j.jmathb.2009.03.002

Chernoff, E. J. (2008). The state of probability measurement in mathematics education: A first approximation. Philosophy of Mathematics Education Journal, 23, 1-23. Retrieved from http://people.exeter.ac.uk/PErnest/pome23/index.htm

Zazkis, R., & Chernoff, E. (2008). What makes a counterexample exemplary? Educational Studies in Mathematics, 68(3), 195-208. doi: 10.1007/s10649-007-9110-4

Zazkis, R., Liljedahl, P. & Chernoff, E. (2008). The role of examples on forming and refuting generalizations [Themed issue: From Patterns to Generalization: Development of Algebraic Thinking]. ZDM - The International Journal on Mathematics Education, 40(1), 131-141. doi: 10.1007/s11858-007-0065-9

Liljedahl, P., Chernoff. E., & Zazkis, R. (2007). Interweaving mathematics and pedagogy in task design: A tale of one task [Special issue: The Nature and Role of Tasks in Mathematics Teachers’ Education]. Journal of Mathematics Teacher Education, 10(4-6), 239-249. doi: 10.1007/s10857-007-9047-7

Articles in Refereed Conference Proceedings

Chernoff, E. J., & Russell, G. L. (2012). Why order does not matter: an appeal to ignorance. In Van Zoest, L. R., Lo, J.-J., & Kratky, J. L. (Eds.), Proceedings of the 34th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 1045-1052). Kalamazoo, MI: Western Michigan University.

Russell, G. L., & Chernoff, E. J. (2012). Unifying challenges in the teaching and learning of mathematics: Two can become one. In Van Zoest, L. R., Lo, J.-J., & Kratky, J. L. (Eds.), Proceedings of the 34th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 367-370). Kalamazoo, MI: Western Michigan University.

Chernoff, E. J. (2012). Unintended relative likelihood comparisons. Proceedings of Topic Study Group 11: Teaching and learning of probability. 12th International Congress on Mathematics Education (ICME-12). Seoul, Korea.

Russell, G. L. & Chernoff, E. J. (2012). Unknown Occurrences of Polysemy in English Mathematics Classrooms. Proceedings of Topic Study Group 28: Language and communication in mathematics education. 12th International Congress on Mathematics Education (ICME-12). Seoul, Korea.

Chernoff, E. J. (2012). Providing answers to a question that was not asked. In S. Brown, S. Larsen, K. Marrongelle & M. Oehrtman (Eds.), Proceedings of the 15th Annual Conference on Research in Undergraduate Mathematics Education (pp. 32-38). Portland, Oregon.

Chernoff, E. J., & Russell, G. L. (2011). An informal fallacy in teachers’ reasoning about probability. In L. R. Wiest & T. Lamberg (Eds.), Proceedings of the 33rd Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 241-249). Reno, NV: University of Nevada, Reno.

Russell, G. L., & Chernoff, E. J. (2011). Transforming mathematics education: applying new ideas or commodifying cultural knowledge. In L. R. Wiest & T. Lamberg (Eds.), Proceedings of the 33rd Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 970-977). Reno, NV: University of Nevada, Reno.

Chernoff, E. J., & Russell, G. L. (2011). An investigation of relative likelihood comparisons: the composition fallacy. In B. Ubuz (Ed.), Proceedings of the Thirty fifth annual meeting of the International Group for the Psychology of Mathematics Education (Vol. II, pp. 225-232). Ankara, Turkey: Middle East Technical University.

Russell, G. L., & Chernoff, E. J. (2011). Logical fallacies in reasoning about a correct solution. In B. Ubuz (Ed.), Proceedings of the Thirty fifth annual meeting of the International Group for the Psychology of Mathematics Education (Vol. I, p. 379). Ankara, Turkey: Middle East Technical University.

Chernoff, E. J. (2011). Investigating relative likelihood comparisons of multinomial, contextual sequences. In M. Pytlak, T. Rowland, & E. Swoboda (Eds.), Proceedings of the Seventh Congress of the European Society for Research in Mathematics Education (pp. 755-765). University of Rzeszów, Poland.

Chernoff, E. J., & Zazkis, R. (2010). A problem with the problem of points. In P. Brosnan, D. Erchick, & L. Flevares (Eds.), Proceedings of the Thirty-Second Annual Meeting of the North-American Chapter of the International Group for the Psychology of Mathematics Education (Vol. VI, pp. 969-977). Columbus, OH: Ohio State University.

Russell, G., & Chernoff, E. J. (2010). Beyond nothing: Teachers’ conceptions of zero. In P. Brosnan, D. Erchick, & L. Flevares (Eds.), Proceedings of the Thirty-Second Annual Meeting of the North-American Chapter of the International Group for the Psychology of Mathematics Education (Vol. VI, pp. 1039-1046). Columbus, OH: Ohio State University.

Chernoff, E. J. (2009). The subjective-sample-space. In S. L. Swars, D. W. Stinson & S. Lemons-Smith (Eds.), Proceedings of the Thirty-First Annual Meeting of the North-American Chapter of the International Group for the Psychology of Mathematics Education (Vol. 5, pp. 628-635). Atlanta, GA: Georgia State University.

Chernoff, E. J. (2009). Explicating the multivalence of a probability task. In S. L. Swars, D. W. Stinson & S. Lemons-Smith (Eds.), Proceedings of the Thirty-First Annual Meeting of the North-American Chapter of the International Group for the Psychology of Mathematics Education (Vol. 5, pp. 653-661). Atlanta, GA: Georgia State University.

Chernoff, E. J. (2008). Sample space: An investigative lens. In J. Cortina (Ed.), Proceedings of the Joint Meeting of the International Group and the North American Chapter for the Psychology of Mathematics Education (Vol. 2, pp. 313-320). Morelia, Michoacn, Mexico.

Chernoff, E. (2007). Sample space rearrangement (SSR): The example of switches and runs. In T. Lamberg & L. Wiest (Eds.), Proceedings of the Twenty Ninth Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. (Vol. 1, pp. 433-436). Stateline (Lake Tahoe), NV: University of Nevada, Reno.

Chernoff, E. (2007). Probing Representativeness: Switches and runs, In J. Woo, H. Lew, and D. Seo (Eds.), Proceedings of the Thirty first annual meeting of the International Group for the Psychology of Mathematics Education. (Vol. 1, pp. 207). Seoul, South Korea: Seoul National University.

Chernoff, E. (2007). The Monistic Probabilistic Perspective. In J. Woo, H. Lew, and D. Seo (Eds.), Proceedings of the Thirty first annual meeting of the International Group for the Psychology of Mathematics Education.. (Vol. 1, pp. 308). Seoul, South Korea: Seoul National University.

Chernoff, E., & Zazkis, R. (2006). Intuitive probability in action: A case in elementary number theory. In S. Alatorre, J. L. Cortina, M. Sáiz, & A. Méndez (Eds.), Proceedings of the Twenty Eighth annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. (Vol. 2, pp. 756-758). Mérida, Mexico: Universidad Pedagógica Nacional.

Zazkis, R., & Chernoff, E. (2006). Examples that change minds. In S. Alatorre, J. L. Cortina, M. Sáiz, & A. Méndez (Eds.), Proceedings of the Twenty Eighth annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. (Vol. 2, pp. 756-758). Mérida, Mexico: Universidad Pedagógica Nacional.

Chernoff, E., & Zazkis, R. (2006). Decision making at uncertainty: Moving on a prime ladder. In J. Novotná, H. Moraová, M. Krátká, & N. Stehlíková (Eds.), Proceedings of the Thirtieth annual meeting of the International Group for the Psychology of Mathematics Education. (Vol. 1, pp. 234). Prague, Czech Republic: Charles University.

Zazkis, R., & Chernoff, E. (2006). Cognitive conflict and its resolution via pivotal/bridging example. In J. Novotná, H. Moraová, M. Krátká, & N. Stehlíková (Eds.), Proceedings of the Thirtieth annual meeting of the International Group for the Psychology of Mathematics Education. (Vol. 5, pp. 465-472). Prague, Czech Republic: Charles University.

Chapters in Edited Books

Chernoff, E. J., & Sriraman, B. (in press). Introduction to Probabilistic Thinking: Presenting Plural Perspectives. In E. J. Chernoff & B. Sriraman (Eds.), Probabilistic Thinking: Presenting Plural Perspectives (pp. ). Berlin/Heidelberg: Springer Science.

Chernoff, E. J., & Russell, G. L. (in press). Preface to Perspective I: Mathematics and Philosophy. In E. J. Chernoff & B. Sriraman (Eds.), Probabilistic Thinking: Presenting Plural Perspectives (pp. ). Berlin/Heidelberg: Springer Science.

Chernoff, E. J., & Russell, G. L. (in press). Preface to Perspective III: Stochastics. In E. J. Chernoff & B. Sriraman (Eds.), Probabilistic Thinking: Presenting Plural Perspectives (pp. ). Berlin/Heidelberg: Springer Science.

Chernoff, E. J., & Russell, G. L. (in press). Preface to Perspective IV: Mathematics Education. In E. J. Chernoff & B. Sriraman (Eds.), Probabilistic Thinking: Presenting Plural Perspectives (pp. ). Berlin/Heidelberg: Springer Science.

Chernoff, E. J., & Sriraman, B. (in press). Commentary on Probabilistic Thinking: Presenting Plural Perspectives. In E. J. Chernoff & B. Sriraman (Eds.), Probabilistic Thinking: Presenting Plural Perspectives (pp. ). Berlin/Heidelberg: Springer Science.

Books and Monographs

Chernoff, E. J., & Sriraman, B. (Eds.) (in press). Probabilistic thinking: Presenting plural perspectives (Volume 7 of Advances in Mathematics Education Series). Berlin/Heidelberg: Springer Science.

Chernoff, E. J. (2009). The subjective-sample-space: Subjective probabilities derived from the perceived randomness of sequences of outcomes*. Saarbrücken, Germany: VDM Verlag.
*note: this monograph is a verbatim reprint of my doctoral dissertation

Dissertation

Chernoff, E. J. (2009). Subjective probabilities derived from the perceived randomness of sequences of outcomes. Unpublished doctoral dissertation. Simon Fraser University, Vancouver, British Columbia, Canada.

Edited Volumes

Chernoff, E. (Ed.) (in press). Celebrating 50 years (1961-2011) of the SMTS: The Aughts. vinculum: Journal of the Saskatchewan Mathematics Teachers’ Society, 3(2.2000).

Chernoff, E. (Ed.) (in press). Celebrating 50 years (1961-2011) of the SMTS: The Nineties. vinculum: Journal of the Saskatchewan Mathematics Teachers’ Society, 3(2.1990).

Chernoff, E. (Ed.) (2012). Celebrating 50 years (1961-2011) of the SMTS: The Eighties. vinculum: Journal of the Saskatchewan Mathematics Teachers’ Society, 3(2.1980). 56 pages.

Chernoff, E. (Ed.) (2012). Celebrating 50 years (1961-2011) of the SMTS: The Seventies. vinculum: Journal of the Saskatchewan Mathematics Teachers’ Society, 3(2.1970). 64 pages.

Chernoff, E. (Ed.) (2012). Celebrating 50 years (1961-2011) of the SMTS: The Sixties. vinculum: Journal of the Saskatchewan Mathematics Teachers’ Society, 3(2.1960). 49 pages.

Chernoff, E. (Ed.) (2011). Theme: Problems and reflections. vinculum: Journal of the Saskatchewan Mathematics Teachers’ Society, 3(1). 56 pages.

Chernoff, E. J. (Ed.) (2010). Theme: First Nations and Métis content, perspectives, and ways of knowing. vinculum: Journal of the Saskatchewan Mathematics Teachers’ Society, 2(2). 68 pages.

Chernoff, E. (Ed.) (2010). Theme: Curricular edition. vinculum: Journal of the Saskatchewan Mathematics Teachers’ Society, 2(1). 60 pages.

Chernoff, E. (Ed.) (2009). Theme: Student-centered edition. vinculum: Journal of the Saskatchewan Mathematics Teachers’ Society, 1(2). 52 pages.

Chernoff, E. (Ed.) (2009). vinculum: Journal of the Saskatchewan Mathematics Teachers’ Society, 1(1). 44 pages.

Editorials

Chernoff, E. (in press). Editorial: the aughts. vinculum: Journal of the Saskatchewan Mathematics Teachers’ Society, 3(2.2000).

Chernoff, E. (in press). Editorial: the nineties. vinculum: Journal of the Saskatchewan Mathematics Teachers’ Society, 3(2.1990).

Chernoff, E. (2012). Editorial: the eighties. vinculum: Journal of the Saskatchewan Mathematics Teachers’ Society, 3(2.1980), 1.

Chernoff, E. (2012). Editorial: the seventies. vinculum: Journal of the Saskatchewan Mathematics Teachers’ Society, 3(2.1970), 1.

Russell, G. & Chernoff, E. (2012). Editorial: The sixties: "The times they are a-changin". vinculum: Journal of the Saskatchewan Mathematics Teachers’ Society, 3(2.1960), 4.

Chernoff, E. (2012). Preface: celebrating 50 years (1961-2011) of the SMTS. vinculum: Journal of the Saskatchewan Mathematics Teachers’ Society, 3(2.1960), 2-3.

Chernoff, E. (2011). Editorial: No, not that kind of problem. vinculum: Journal of the Saskatchewan Mathematics Teachers’ Society, 3(1), 3-4.

Chernoff, E. (2010). Editorial: Two years and four issues later. vinculum: Journal of the Saskatchewan Mathematics Teachers’ Society, 2(2), 2-6.

Chernoff, E. (2010). Editorial: Curricular edition. vinculum: Journal of the Saskatchewan Mathematics Teachers’ Society, 2(1), 2-3.

Chernoff, E. (2009). Editorial: Student-centered edition. vinculum: Journal of the Saskatchewan Mathematics Teachers’ Society, 1(2), 3-4.

Chernoff, E. (2009). Editorial: Change(s). vinculum: Journal of the Saskatchewan Mathematics Teachers’ Society, 1(1), 2.

Book Reviews

Chernoff, E. (2009). Innumeracy: Mathematical illiteracy and its consequences: A review. vinculum: Journal of the Saskatchewan Mathematics Teachers’ Society, 1(1), 36-41.

ePublications

Chernoff, E. J. (2012). Mathematics Education Images by MatthewMaddux. Available on iTunes (36 pages).

Chernoff, E. J. (2012). @MatthewMaddux 2011: Chronicled Tweet by Tweet. Available on iTunes (182 pages).

Chernoff, E. J. (2012). MatthewMaddux Education 2011. Retrieved from http://www.eganchernoff.com/downloads/open-access-publications/ (220 pages).

Articles in Non-Refereed Journals

Chernoff, E. J. (2011). Where have all the submissions gone? Vector: Journal of the British Columbia Association of Mathematics Teachers, 52(3), 10-14.

Chernoff, E. J. (2010). Coming to terms with probability terminology. Vector: Journal of the British Columbia Association of Mathematics Teachers, 51(2), 13-16.

Chernoff, E. J. (2008). Now that’s what I call alternative base representation. Vector: Journal of the British Columbia Association of Mathematics Teachers, 49(2), 49-55.

Articles in Non-Refereed Conference Proceedings

Chernoff, E. J. (2011). Mathematics education networking experiences: The necessary, the unnecessary, and the digital. Proceedings of the Third Annual Mathematics Education Graduate Students’ Association (MEGA) Conference and Meeting. Vancouver, Canada: University of British Columbia. [Online: http://m1.cust.educ.ubc.ca/mega2011/proceedings.html]

Chernoff, E. J. (2011). Subjective probabilities derived from the perceived randomness of sequences of outcomes. New PhD report for the proceedings the 34th annual meeting of the Canadian Mathematics Education Study Group/Groupe Canadien d'Étude en Didactique des Mathématiques. (pp. 165-170). Vancouver, Canada: Simon Fraser University.

Chernoff, E. J., Knoll, E., & Mamolo, A. (2011). Noticing and engaging the mathematicians in our classrooms. Working group F report for the Proceedings of the 34th annual meeting of the Canadian Mathematics Education Study Group/Groupe Canadien d'Étude en Didactique des Mathématiques. (pp. 107-120). Vancouver, Canada: Simon Fraser University.

Chernoff, E. J., Chorney, S., & Liljedahl, P. (2011). Editing mathematics teachers’ journals in Canada: Bridging the gap between researchers and teachers. Ad-hoc presentation report for the proceedings of the 34th annual meeting of the Canadian Mathematics Education Study Group/Groupe Canadien d'Étude en Didactique des Mathématiques. (pp. 217-218). Vancouver, Canada: Simon Fraser University.

Chernoff, E. J. (2009). Panel I Report: What did I need then? What do I need now? Proceedings of the 2009 Canadian Mathematics Education Forum. Vancouver, Canada.

Chernoff, E. J. (2009). The Kamloops Golf and University Country Club. In R. C. Brewster, & J. G. McLoughlin (Eds.), Proceedings of the first annual Sharing Mathematics: A Tribute to Jim Totten conference. (pp. 86-87). Kamloops, British Columbia, Canada.

Chernoff, E., & Savard, A. (2008). Probability. Proceedings of the 2007 Annual Meeting of the Canadian Mathematics Education Study Group/Groupe Canadien d'Étude en Didactique des Mathématiques.

Other Publications

Chernoff, E. J. (2010). In memoriam: Craig Newell.

Chernoff, E. J. (2007). Chances are…you’ll learn something new about probability: Conference notes. Conference notes for Workshop #1 presented at the 9th annual Changing the Culture conference presented by the Pacific Institute for the Mathematical Sciences. Vancouver, Canada.

Chernoff, E. J. (2007). A CMESG/GCEDM first-timer reflects on Calgary 2006. CMESG Newsletter, 23(2).

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PRESENTATIONS AND WORKSHOPS

Invited Colloquia

Chernoff, E. J. (2013, February). Relative Likelihood Comparisons: A Comparative Overview of the Research. Colloquium of the School of Mathematical and Statistical Sciences, Arizona State University. Phoenix, Arizona, USA.

Chernoff, E. J. (2013, February). Relative Likelihood Comparisons: Heuristics, Biases and Fallacies. Colloquium of the Department of Mathematical Sciences, The University of Montana. Missoula, Montana, USA.

Invited Academic Conference Presentations and Workshops

Chernoff, E. J. (2013, May). Social media and mathematics education: whenever the twain shall meet? Topic Session presented at the 37th Annual Meeting of the Canadian Mathematics Education Study Group/Groupe Canadien d'Étude en Didactique des Mathématiques (CMESG/GCEDM 2013). St. Catharines, ON, Canada.

Session Chair (2012, July). Session 1: Curriculum Development and Policies. Topic Study Group 11: Teaching and learning of probability. 12th International Congress on Mathematics Education (ICME-12). Seoul, Korea.

Chernoff, E. J. (2012, June). Solving equations: A make-work project for math teachers. Connections in Mathematics Education Session at the 2012 Canadian Mathematical Society (CMS) Summer Meeting. Regina, Saskatchewan, Canada.

Session Chair (2012, April). Effective Mathematics Teaching: Is There a Best Approach? Roundtable session of the Special Interest Group: Research in Mathematics Education (SIG/RME) at the 2012 Annual Meeting of the American Educational Research Association. Vancouver, BC.

Chernoff, E. J. (2012, February). Egan Chernoff and MatthewMaddux: How we're related. Inaugural lecture: Second Life Lecture Series on Wheeler Island. David Wheeler Institute for Research in Mathematics Education (Simon Fraser University, Vancouver, BC, Canada). Second Life, Wheeler Island (139, 28, 30).

Chernoff, E. J., Knoll, E., & Mamolo, A. (2010, May). Noticing and engaging the mathematicians in our classrooms. Working group F of the 34th annual meeting of the Canadian Mathematics Education Study Group/Groupe Canadien d'Étude en Didactique des Mathématiques. Vancouver, BC, Canada.

Chernoff, E. J. (2010, May). Subjective probabilities derived from the perceived randomness of sequences of outcomes. New PhD Session presented at the 34th annual meeting of the Canadian Mathematics Education Study Group/Groupe Canadien d'Étude en Didactique des Mathématiques.Vancouver, BC, Canada.

Chernoff, E. (2009, April). Panel I: What did I need then? What do I need now? Panel Chair for the 2009 Canadian Mathematics Education Forum (CMEF). Vancouver, Canada.

Chernoff, E. (2007, April). Chances are…you’ll learn something new about probability. Workshop presented at the 9th annual Changing the Culture conference presented by the Pacific Institute for the Mathematical Sciences. Vancouver, Canada.

Chernoff, E. (2007, December). Teaching Mathematics with Manipulatives. Five day workshop conducted at IAIN Ar-Raniry (through McGill University’s IAIN Indonesia Social Equity Project). Banda Aceh, Indonesia.

Academic Conference Presentations

Russell, G. L., & Chernoff, E. J. (2012, November). Working Title. Presentation at the 2012 Learning from Practice Conference. Dr. Stirling McDowell Foundation for Research into Teaching. Saskatoon, SK, Canada.

Chernoff, E. J., & Russell, G. L. (2012, November). Why order does not matter: an appeal to ignorance. Presentation at the 34th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education Kalamazoo, MI, USA.

Russell, G. L., & Chernoff, E. J. (2012, November). Unifying challenges in the teaching and learning of mathematics: Two can become one. Presentation at the 34th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education Kalamazoo, MI, USA.

Chernoff, E. J. (2012, July). Unintended relative likelihood comparisons. Long presentation for Topic Study Group 11: Teaching and learning of probability. 12th International Congress on Mathematics Education (ICME-12). Seoul, Korea.

Russell, G. L. & Chernoff, E. J. (2012, July). Unknown Occurrences of Polysemy in English Mathematics Classrooms. Short presentation for Topic Study Group 28: Language and communication in mathematics education. 12th International Congress on Mathematics Education (ICME-12). Seoul, Korea.

Chernoff, E. J. (2012, February). Providing answers to a question that was not asked. Contributed research report presentation at the fifteenth annual conference of the Special Interest Group of the Mathematical Association of American on Research in Undergraduate Mathematics Education (SIGMAA on RUME). Portland, Oregon.

Chernoff, E. J., & Russell, G. L. (2011, October). An informal fallacy in teachers’ reasoning about probability. Research report presentation at the Thirty third annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. Reno, Nevada.

Russell, G. L., & Chernoff, E. J. (2011, October). Transforming mathematics education: applying new ideas or commodifying cultural knowledge. Brief research report presentation at the Thirty third annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. Reno, Nevada.

Chernoff, E. J., & Russell, G. L. (2011, July). An investigation of relative likelihood comparisons: The composition fallacy. Research report presentation at the Thirty fifth annual meeting of the International Group for the Psychology of Mathematics Education. Ankara, Turkey.

Russell, G. L., & Chernoff, E. J. (2011, July). Logical fallacies in reasoning about a correct solution. Short oral presentation at the Thirty fifth annual meeting of the International Group for the Psychology of Mathematics Education. Ankara, Turkey.

Chernoff, E. J. (2011, February). Mathematics education networking experiences: The necessary, the unnecessary, and the digital. Presentation at the Third Annual Mathematics Education Graduate Students’ Association (MEGA) Conference and Meeting. Vancouver, Canada.

Chernoff, E. J. (2011, February). Investigating relative likelihood comparisons of multinomial, contextual sequences. Presentation for Working Group 5: Stochastic Thinking at the Seventh Congress of the European Society for Research in Mathematics Education (CERME7). Rzeszów, Poland.

Chernoff, E. J., & Zazkis, R. (2010, October). A problem with the problem of points. Presentation at the Thirty-Second Annual Meeting of the North-American Chapter of the International Group for the Psychology of Mathematics Education. Columbus, OH: Ohio State University.

Russell, G., & Chernoff, E. J. (2010, October). Beyond nothing: Teachers’ conceptions of zero. Presentation at the Thirty-Second Annual Meeting of the North-American Chapter of the International Group for the Psychology of Mathematics Education. Columbus, OH: Ohio State University.

Chernoff, E. J., Chorney, S., & Liljedahl, P. (2010, May). Editing mathematics teachers’ journals in Canada: Bridging the gap between researchers and teachers. Ad-hoc presentation at the 34th annual meeting of the Canadian Mathematics Education Study Group. Vancouver, BC, Canada.

Chernoff, E. J. (2009, September). The subjective-sample-space. The Thirty-first Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. Atlanta, Georgia.

Chernoff, E. J. (2009, September). Explicating the multivalence of a probability task. The Thirty-first Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. Atlanta, Georgia.

Chernoff, E. (2008, July). Sample Space: An Investigative Lens. Paper presented at the joint meeting of the International Group and the North American Chapter of Psychology of Mathematics Education (PME 32 & PME-NA XXX), Morelia, Mexico.

Chernoff, E. (2008, January). Sample Space Rearrangement. Paper presented at the Second Annual Simon Fraser University Mathematics Education Doctoral Students’ Conference. Vancouver, Canada.

Chernoff, E. (2007, October) Sample space rearrangement (SSR): The example of switches and runs. Paper presented at the 29th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. Reno, USA.

Chernoff, E. (2007, July). Probing Representativeness: Switches and runs. Paper presented at the 31st annual meeting of the International Group for the Psychology of Mathematics Education. Seoul, South Korea.

Chernoff, E. (2007, July). The Monistic Probabilistic Perspective. Paper presented at the 31st annual meeting of the International Group for the Psychology of Mathematics Education. Seoul, South Korea.

Chernoff, E., & Savard, A. (2007, June). Probability. Ad-hoc presentation at the 31st annual meeting of the Canadian Mathematics Education Study Group. Fredericton, Canada.

Chernoff, E. (2007, February). Extending the Descriptive Powers of Heuristics and Biases. Paper presented at the 10th annual Conference on Research in Undergraduate Mathematics Education. San Diego, USA.

Chernoff, E. (2007, January). Heuristics, Biases, and Elementary Number Theory. Paper presented at the First Annual Simon Fraser University Mathematics Education Doctoral Students’ Conference. Vancouver, Canada.

Chernoff, E., & Zazkis, R. (2006, November). Intuitive probability in action: A case in elementary number theory. Paper presented at the 28th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. Mérida, Mexico.

Zazkis, R., & Chernoff, E. (2006, November). Examples that change minds. Paper presented at the 28th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. Mérida, Mexico.

Chernoff, E., & Zazkis, R. (2006, July). Decision making at uncertainty: moving on a prime ladder. Paper presented at the 30th annual meeting of the International Group for the Psychology of Mathematics Education. Prague, Czech Republic.

Zazkis, R., & Chernoff, E. (2006, July). Cognitive conflict and its resolution via pivotal/bridging example. Paper presented at the 30th annual meeting of the International Group for the Psychology of Mathematics Education. Prague, Czech Republic.

Invited Public/Professional Conference Presentations

Chernoff, E. (2013, May). Mathematics Education Images by MatthewMaddux: An Exhibition at SUM Art Gallery. Presentation at Saskatchewan Understands Math (SUM) 2013 hosted by the Saskatchewan Mathematics Teachers’ Society. Saskatoon, SK, Canada.

Panel Member (2013, May). Teaching and Learning Mathematics. Panel discussion at the Saskatchewan Mathematics Teachers’ Society’s (SMTS) 5th annual Saskatchewan Understands Mathematics (SUM) conference. Saskatoon, Canada.

Chernoff, E. J. (2012, May). Celebrating 50 years of the Saskatchewan Mathematics Teachers' Society (SMTS). Presentation at the Saskatchewan Mathematics Teachers’ Society’s (SMTS) 4th annual Saskatchewan Understands Mathematics (SUM) conference. Saskatoon, Canada.

Panel Member (2012, May). Panel. Panel discussion at the Saskatchewan Mathematics Teachers’ Society’s (SMTS) 4th annual Saskatchewan Understands Mathematics (SUM) conference. Saskatoon, Canada.

Sterenberg, G., & Chernoff, E. J. (2011, October). Celebrating 50 years of delta-K. Presentation at the 2011 Annual Conference of the Mathematics Council of the Alberta Teachers’ Association (MCATA). Enoch, Alberta.

Chernoff, E. J. (2011, May). Engaged in mathematics: voices from our community. Presentation at the Saskatoon Public Schools Collegiate Renewal Secondary Mathematics Conference. Saskatoon, SK, Canada.

Chernoff, E. J. (2011, May). You say SOHCAHTOA, I say SYRCXRTYX....for a reason. Presentation at the Saskatchewan Mathematics Teachers’ Society’s (SMTS) 3rd annual Saskatchewan Understands Mathematics (SUM) conference. Saskatoon, Canada.

Chernoff, E. (2010, November). So you have to implement a reform mathematics curriculum: Now what? Presentation at the 2010 Horizon School Division Convention. Saskatoon, SK, Canada.

Chernoff, E. (2010, November). This new approach to teaching and learning mathematics sounds great and all, but I teach high school mathematics. Presentation at Sciematics 2010 hosted by the Saskatchewan Science Teachers’ Society and the Saskatchewan Mathematics Teachers’ Society. Regina, SK, Canada.

Chernoff, E. (2010, November). We’re talking the talk, but are we walking the walk? Presentation at Sciematics 2010 hosted by the Saskatchewan Science Teachers’ Society and the Saskatchewan Mathematics Teachers’ Society. Regina, SK, Canada.

Chernoff, E. J. (2010, May). Teaching and learning combinatorics in the senior high school mathematics classroom with no calculator and no formulas: No way! Presentation at the Saskatchewan Mathematics Teachers’ Society’s (SMTS) 2nd annual Saskatchewan Understands Mathematics (SUM) conference. Saskatoon, Canada.

Chernoff, E. J. (2010, May). Non-combinatorial probability problems in the senior high school mathematics classroom. Presentation at the Saskatchewan Mathematics Teachers’ Society’s (SMTS) 2nd annual Saskatchewan Understands Mathematics (SUM) conference. Saskatoon, Canada.

Chernoff, E. J. (2010, March). Traditional and reform approaches to teaching and learning mathematics. Presentation at the Saskatchewan Community Schools Association (SCSA) Conference 2010. Saskatchewan Community Schools Association. Saskatoon, Canada.

Chernoff, E. (2009, May). (WNC)Probability. Presentation at the Saskatchewan Mathematics Teachers’ Society’s (SMTS) 1st annual Saskatchewan Understands Mathematics (SUM) conference. Saskatoon, Canada.

Chernoff, E. (2008, November). A Multivalentological Approach to Probability Research. Presentation at The Eleventh Annual Department of Curriculum Studies Mini-Conference. Saskatoon, Canada.

Chernoff, E. (2008, October). The probability you have read this title: 1. Presentation at Sciematics 2008 hosted by the Saskatchewan Science Teachers’ Society and the Saskatchewan Mathematics Teachers’ Society. Saskatoon, Canada.

Chernoff, E. (2008, October). Back to ‘Basecs’. Presentation at Sciematics 2008 hosted by the Saskatchewan Science Teachers’ Society and the Saskatchewan Mathematics Teachers’ Society. Saskatoon, Canada.

Chernoff, E. (2006, February). Golden ratio number system. Presentation at the Vancouver Secondary Teachers’ Association Mathematics Conference. Vancouver, Canada.

Chernoff, E. & Cacchioni, D. (2005, February). Humour in Teaching Mathematics (gr. 8-12). Presentation at the Vancouver Secondary Teachers’ Association Mathematics Conference. Vancouver, Canada.

Public/Professional Conference Presentations

Chernoff, E. (2013, May). Solving equations. Presentation at Sciematics 2013 hosted by the Saskatchewan Science Teachers’ Society. Saskatoon, SK, Canada.

Chernoff, E. J., Liljedahl, P., & Chorney, S. (2012, Ocotber). Celebrating 50 years of the British Columbia Association of Mathematics Teachers (BCAMT). Presentation at the 51st Northwest Mathematics Conference (NWMC). Victoria, BC, Canada.

Russell, G. L. & Chernoff, E. J. (2012, Ocotber). Talking about nothing. Presentation at the 51st Northwest Mathematics Conference (NWMC). Victoria, BC, Canada.

Invited Professional Development Workshops

Chernoff, E. J. (2013, May). Experiencing a new approach to the teaching and learning of mathematics: the instructors become the students. Workshop for the Senior Basic Education Mathematics Instructors from the Kelsey, Palliser, Wascana and Woodland Campuses of the Saskatchewan Institute of Applied Science and Technology (SIAST). SIAST Kelsey Campus, Saskatoon, Canada.

Chernoff, E. J. (2012, August). What do you mean there is more than one type of probability?. CTA Convention 2012, Chinook School Division, Swift Current, Saskatchewan, Canada.

Chernoff, E. J. (2012, August). To convert from decimal to percent you multiply by 100 and other "errors" found in the mathematics classroom. CTA Convention 2012, Chinook School Division, Swift Current, Saskatchewan, Canada.

Chernoff, E. J. (2012, August). The SPSD Summer MatthewMaddux Institute: Day 1. Ignite 2012, Saskatoon Public School Division (SPSD), Saskatoon, Saskatchewan, Canada.

Chernoff, E. J. (2012, August). The SPSD Summer MatthewMaddux Institute: Day 2. Ignite 2012, Saskatoon Public School Division (SPSD), Saskatoon, Saskatchewan, Canada.

Chernoff, E. (2011, January). Getting a handle on manipulatives. Workshop conducted for the Prince Albert Grand Council Education Board. Prince Albert Grand Council. Prince Albert, Canada.

Chernoff, E. (2011, January). Technology does not necessarily equal calculator: Coping with the exponential growth of technology in our classrooms. Workshop conducted for the mathematics teachers of Fairhaven, John Lake, and Mayfair elementary schools. Saskatoon Public Schools. Saskatoon, Canada.

Chernoff, E. (2011, January). Making multi-level mathematics classrooms more manageable. Workshop conducted for the Prince Albert Grand Council Education Board. Prince Albert Grand Council. Prince Albert, Canada.

Chernoff, E. (2010, October). Experiencing the reform approach to teaching and learning grade 6-12 mathematics: Algebra tiles, Cuisenaire rods, and pattern blocks. Workshop conducted for the grade 6-12 mathematics teachers of the Lac La Ronge Indian Band. Lac La Ronge Indian Band Education. Lac La Ronge, Saskatchewan, Canada.

Chernoff, E. (2010, October). Experiencing the reform approach to teaching and learning grade K-5 mathematics: Pattern blocks, and base ten blocks. Workshop conducted for the grade K-5 mathematics teachers of the Lac La Ronge Indian Band. Lac La Ronge Indian Band Education. Lac La Ronge, Saskatchewan, Canada.

Chernoff, E. (2010, September). FNMI content, perspectives, and ways of knowing in the elementary mathematics classroom. Workshop conducted for the mathematics teachers of Fairhaven, John Lake, and Mayfair elementary schools. Saskatoon Public Schools. Saskatoon, Canada.

Chernoff, E. (2010, August). Basically, let’s revisit elementary arithmetic for an afternoon. Workshop conducted for the mathematics teachers of Fairhaven, John Lake, and Mayfair elementary schools. Saskatoon Public Schools. Saskatoon, Canada.

Chernoff, E. (2010, May). Using little pink pigs to “make sense” of the reform approach to teaching and learning mathematics. Workshop conducted for Pearson’s Numeracy Network. Pearson Education Canada. Saskatoon, Canada.

Chernoff, E. (2010, February). Experiencing the reform approach to teaching and learning mathematics. Professional development workshop conducted for mathematics teachers of Greater Saskatoon Catholic Schools. Greater Saskatoon Catholic School Division. Saskatoon, Canada.

Chernoff, E. (2010, January). Using the dishwasher problem to model a Reform mathematics classroom. Professional development workshop conducted for Mayfair Community School. Saskatoon Public Schools. Saskatoon, Canada.

Chernoff, E. (2009, November). Traditional or reform: Using inclusive “or” to avoid a “war”. Workshop conducted for the Prince Albert Grand Council Education coordinators/Directors meeting. Prince Albert Grand Council. Prince Albert, Canada.

Chernoff, E. (2009, May). Relativism and highschool probability. Workshop conducted at Walter Murray Collegiate Institute. Saskatoon Public Schools. Saskatoon, Canada.

Chernoff, E. (2009, February). Exploring the union of probability and the Prairie Spirit School Division. Workshop conducted for Prairie Spirit School Division’s High school Mathematics Teachers. Saskatoon, Canada.

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TEACHING RECORD

University of Saskatchewan (2012-2013)

ECUR 318.3 (02) Methods in Seconday Mathematics (Winter)
ECUR 316.3 (30) Teaching K-9 Mathematics: Part II (Winter).
ECUR 312.3 (02) Methods in Elementary Mathematics (Winter)
ECUR 312.3 (01) Methods in Elementary Mathematics (Fall)
ECUR 312.3 (03) Methods in Elementary Mathematics (Fall)

 

University of Saskatchewan (2011-2012)

ECUR 312.3 (02) Methods in Elementary Mathematics (Winter)
ECUR 312.3 (04) Methods in Elementary Mathematics (Winter)
ECUR 318.3 (02) Methods in Secondary Mathematics (Winter)
ECUR 805.3 (07) Curriculum, Theory and Teaching Mathematics (Fall)
ECUR 312.3 (01) Methods in Elementary Mathematics (Fall)

 

University of Saskatchewan (2010-2011)

ECUR 898.3 (18) Ethnomathematics (Winter)
ECUR 899.3 (01) Teaching and Learning Mathematics (Winter)
ECUR 312.3 (02) Methods in Elementary Mathematics (Winter)
ECUR 312.3 (04) Methods in Elementary Mathematics (Winter)
ECUR 318.3 (02) Methods in Secondary Mathematics (Winter)
ECUR 899.6 Teaching and Learning Mathematics (Fall).

 

University of Saskatchewan (2009-2010)

ECUR 819.3 (02) Topics in Mathematics Education (Winter)
ECUR 318.3 (02) Mathematics Secondary 1 (Winter)
ECUR 316.3 (30) Teaching K-9 Mathematics: Part II (Winter)
ECUR 316.3 (G78) Teaching K-9 Mathematics: Part II (Winter)
ECUR 311.3 (29) Teaching K-9 Mathematics: Part I (Fall)
ECUR 311.3 (G77) Teaching K-9 Mathematics: Part I (Fall)

 

University of Saskatchewan (2008-2009)

ECUR 819.3 (02) Trends and Issues in Mathematics Education (Summer)
ECUR 318.3(02) Mathematics Secondary 1 (Winter)
ECUR 316.3(30) Teaching K-9 Mathematics: Part II (Winter)
ECUR 316.3(G78) Teaching K-9 Mathematics: Part II (Winter)
ECUR 898.3(10) Research Trends and Issues in Mathematics Education (Winter)
ECUR 898.3(08) Social Construction of Knowledge (Winter)
ECUR 311.3(29) Teaching K-9 Mathematics: Part I (Fall)
ECUR 311.3(G77) Teaching K-9 Mathematics: Part I (Fall)

 

University of British Columbia (2008)

MAED 320 Curriculum and Instruction in Mathematics: Middle Years.

 

Simon Fraser University (2007-2008)

EDUC 864 Research Designs in Education.
EDUC 415 Designs for Learning: Secondary Mathematics.
EDUC 475 Designs for Learning: Elementary Mathematics.
EDUC 211 Mathematical Experience I: Numbers and Beyond.

 

Simon Fraser University (2006-2007)

EDUC 415 Designs for Learning: Secondary Mathematics.
EDUC 475 Designs for Learning: Elementary Mathematics.
EDPR 523 Thinking Like a Mathematician.
EDUC 211 Mathematical Experience I: Numbers and Beyond.
EDUC 864 Research Designs in Education.

 

Simon Fraser University (2005-2006)

EDPR 564 Contemporary Issues in Mathematics Education.

 

Vancouver School Board: Killarney Secondary School (2003-2006)

Essentials of Mathematics: 8, 9, 10
Principles of Mathematics: 8, 9, 10, 11, 12
Principles of Mathematics (Honours): 10, 12

 

Vancouver School Board: Lord Byng Secondary School (2001-2003)

Essentials of Mathematics: 9, 11
Applications of Mathematics: 11
Principles of Mathematics: 8, 9, 10, 11
Principles of Mathematics (Honours): 10

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SERVICE

Academic Community Service

Manuscript reviewer (2013). Nordic Studies in Mathematics Education (NOMAD).

Manuscript reviewer (2012-4). The Canadian Journal of Science, Mathematics and Technology Education.

Manuscript reviewer (2012-2). The International Journal of Science and Mathematics Education.

Manuscript reviewer (2012-3). The Canadian Journal of Science, Mathematics and Technology Education.

Manuscript reviewer (2012-2). The Canadian Journal of Science, Mathematics and Technology Education.

Team member (2012, July). Topic Study Group 11: Teaching and learning of probability. 12th International Congress on Mathematics Education (ICME-12). Seoul, Korea.

Manuscript reviewer (2012-1). The Canadian Journal of Science, Mathematics and Technology Education.

Manuscript reviewer (2012-1). The International Journal of Science and Mathematics Education.

Editorial team member (2012-present). Fields Mathematics Education Journal (FMEJ).

Editorial board member (2012-present). Canadian Journal of Science, Mathematics and Technology Education (CJSMTE).

Editorial board member (2012-present). Vector: Journal of the British Columbia Association of Mathematics Teachers (BCAMT).

Manuscript reviewer (2011). Journal for Research in Mathematics Education.

Manuscript reviewer (2011). Topic Study Group 11: Teaching and learning of probability. 12th International Congress on Mathematics Education (ICME-12). Seoul, Korea.

Manuscript reviewer (2011). Journal of Mathematical Behavior.

Manuscript reviewer (2011). ZDM: The International Journal on Mathematics Education.

Manuscript reviewer (2011). Division K Section 1: STEM Teacher Education. 2012 Annual Meeting of the American Educational Research Association (AERA). Vancouver, BC, Canada.

Manuscript reviewer (2011). Division C - Learning and Instruction/Section 3: Mathematics. 2012 Annual Meeting of the American Educational Research Association (AERA). Vancouver, BC, Canada.

Manuscript reviewer (2011). Special Interest Group: Research in Mathematics Education. 2012 Annual Meeting of the American Educational Research Association (AERA). Vancouver, BC, Canada.

Manuscript reviewer (2011). Canadian Journal of Education.

Editorial Team: Reviewer (2012-2013). World Journal of Education.

Manuscript reviewer (2011). Educational Studies in Mathematics.

Manuscript reviewer (2011). Asia Pacific Education Review.

Manuscript reviewer (2011). Seventh Congress of the European Society for Research in Mathematics Education (CERME7). Working Group 5: Stochastic Thinking.

Manuscript reviewer (2009). Journal of Mathematics Teacher Education.

Member secretary (2008-2011). North American Chapter of the International Group for the Psychology of Mathematics Education.

Steering Committee member (2008-2011). North American Chapter of the International Group for the Psychology of Mathematics Education.

Manuscript reviewer (2008, 2010). The Canadian Journal of Science, Mathematics and Technology.

Manuscript reviewer (2007-present). The International Group for the Psychology of Mathematics Education.

Manuscript reviewer (2007-present). The North American Chapter of The International Group for the Psychology of Mathematics Education.

University Service

Internal reviewer (2012-present). SSHRC College of Reviewers. University of Saskatchewan. Saskatoon, Canada.

Chernoff, E. J. (2011, November). Are you sure you’re supposed to be here? Presentation for the U of S Department of Psychology’s Basic Behavioural Science Research Seminar (Psyc 900). Saskatoon, SK, Canada

Dean’s Designate Chair (2011, April). PhD defence in the Department of Electrical and Computer Engineering. College of Graduate Studies and Research. University of Saskatchewan. Saskatoon, Canada.

Dean’s Designate Chair (2011, April). PhD defence in the Department of Plant Sciences. College of Graduate Studies and Research. University of Saskatchewan. Saskatoon, Canada. 

Panel member (2010, February). Careers in Education panel. St. Thomas Moore’s (STM) 2010 Plan your career week. University of Saskatchewan. Saskatoon, Canada. 

Committee member (2009-2010). University of Saskatchewan, 2010 Whelen Lecture Planning Committee.

Group member (2008). University of Saskatchewan, High School Mathematics Curriculum Working Group.

Faculty Service

Committee member (2011). University of Saskatchewan, College of Education, Department of Curriculum Studies, Salary Review Committee.

Committee member (2011-2012). University of Saskatchewan, College of Education, Department of Curriculum Studies, Admissions Committee.

Committee member (2009-2012). University of Saskatchewan, College of Education, Department of Curriculum Studies, Academic Advisory Committee.

Committee member (2009). University of Saskatchewan, College of Education, Department of Curriculum Studies, iUsask Education App Committee.

Chair (2009-2012). University of Saskatchewan, College of Education, Faculty Policy and Planning Committee.

Committee member (2009). University of Saskatchewan, College of Education, Department of Curriculum Studies, Salary Review Committee.

Program coordinator (2009-present). The M(ath)Ed Master’s Cohort.

Committee member (2008-2010). University of Saskatchewan, Department of Curriculum Studies, Graduate Programs Committee.

Public and Community Service

Committee member (2011-present). The SMTS awards committee.

Committee member (2011-present). The SMTS 50th Anniversary (planning) committee.

Chair (2010). Merry Christmath! Organizing committee of the Saskatchewan Mathematics Teachers’ Society’s float entry in the 20th annual Saskatoon Santa Claus Parade.

Committee member (2009-present). Saskatchewan Math Challenge organizing committee.

Committee member (2009-present). Saskatchewan Ministry of Education Provincial Level Mathematics Committee.

Committee member (2009-present). Saskatchewan Ministry of Education Secondary Mathematics reference committee for curriculum revision.

Committee member (2008-present). Saskatchewan Understands Math (SUM) conference organizing committee.

NCTM Affiliate Editor (2008-present). vinculum: Journal of the Saskatchewan Mathematics Teachers’ Society

Editor (2008-present). vinculum: Journal of the Saskatchewan Mathematics Teachers’ Society.

University of Saskatchewan Representative (2008-present). Saskatchewan Mathematics Teachers’ Society Executive Committee.

Committee member (2008-present). Saskatoon Public School Strategic Committee for K-12 Mathematics.

Committee member (2008-present). Saskatoon Public School Secondary Mathematics Working Committee.

Digital Service

Pinterest (2012-present). http://www.pinterest.com/matthewmaddux

MatthewMaddux Education (2011-present). http://www.matthewmadduxeducation.com

Second Life (2011-present). MatthewMaddux

StumbleUpon (2010-present). http://http://www.stumbleupon.com/stumbler/MatthewMaddux

LikendIn (2009-present). http://ca.linkedin.com/in/matthewmaddux

Delicious (2009-present). http://www.delicious.com/matthewmaddux

Facebook (2009-present). http://facebook.com/matthew.maddux

Twitter (2009-present). http://twitter.com/MatthewMaddux

Personal Website (2008-present). http://www.eganchernoff.com

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AWARDS

Academic Prizes

Dean of Graduate Studies Convocation Medal (2010). Simon Fraser University, Faculty of Education, Vancouver, British Columbia, Canada.

Fellowships

Simon Fraser University Graduate Fellowship (2008). Simon Fraser University, Faculty of Education graduate student award ($6,250), Vancouver, British Columbia, Canada.

Simon Fraser University Graduate Fellowship (2007). Simon Fraser University, Faculty of Education graduate student award ($6,000), Vancouver, British Columbia, Canada.

Simon Fraser University Graduate Fellowship (2006). Simon Fraser University, Faculty of Education graduate student award ($6,000), Vancouver, British Columbia, Canada.

Stipends

Simon Fraser University President’s Research Stipend (2009). Simon Fraser University, Faculty of Education graduate student award ($6,250), Vancouver, British Columbia, Canada.

Scholarships

Lis Welch Graduate Scholarship in Education (2007). Simon Fraser University, Faculty of Education graduate student award ($3,345), Vancouver, British Columbia, Canada.

Rotary Club of Burnaby Scholarship (2006). Simon Fraser University, Faculty of Education graduate student award ($1,000), Vancouver, British Columbia, Canada.

Grants

University Conference Fund Grant (2011). University of Saskatchewan, Programs and Initiatives of the Office of the Provost and Vice-President Academic ($2000). Saskatoon, SK, Canada.

New Faculty Research Grant (2008). University of Saskatchewan, Office of the Provost and Vice-President Academic ($5000). Saskatoon, SK, Canada.

Simon Fraser University Graduate Studies Travel Grant (2008). Simon Fraser University, Faculty of Education graduate student grant ($800), Vancouver, British Columbia, Canada.

Simon Fraser University Graduate Studies Travel Grant (2007). Simon Fraser University, Faculty of Education graduate student grant ($800), Vancouver, British Columbia, Canada.

Graduate Studies Travel Grant (2006). Simon Fraser University, Faculty of Education graduate student grant ($700), Vancouver, British Columbia, Canada.

Simon Fraser University Graduate Studies Travel Grant (2006). Simon Fraser University, Faculty of Education graduate student grant ($400), Vancouver, British Columbia, Canada.

Merit Awards

1.0 Special Increase (2012). Awarded by College Review Committee (CRC). College of Education, University of Saskatchewan. Saskatoon, SK, Canada.

1.0 Special Increase (2012). Awarded by Department Review Committee (DRC). Department of Curriculum Studies, College of Education, University of Saskatchewan. Saskatoon, SK, Canada.

1.0 Special Increase (2011). Awarded by Department Review Committee (DRC). Department of Curriculum Studies, College of Education, University of Saskatchewan. Saskatoon, SK, Canada.

1.0 Special Increase (2010). Awarded by President's Review Committee (PRC). Office of the Provost and Vice-President Academic, University of Saskatchewan. Saskatoon, SK, Canada.

1.0 Special Increase (2010). Awarded by College Review Committee (CRC). College of Education, University of Saskatchewan. Saskatoon, SK, Canada.

0.5 Special Increase (2009). Awarded by Department Review Committee (DRC). Department of Curriculum Studies, College of Education, University of Saskatchewan. Saskatoon, SK, Canada.

Nominations

USSU Teaching Excellence Award (2012-2013, Winter). University of Saskatchewan Students’ Union, University of Saskatchewan, Saskatoon, Saskatchewan, Canada.

USSU Teaching Excellence Award (2012-2013, Fall). University of Saskatchewan Students’ Union, University of Saskatchewan, Saskatoon, Saskatchewan, Canada.

USSU Teaching Excellence Award (2009-2010). University of Saskatchewan Students’ Union, University of Saskatchewan, Saskatoon, Saskatchewan, Canada.

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GRADUATE STUDENT SUPERVISION

Senior supervisor (completed)

Leanne Lomax-Forden, MEd (2012). 
Connecting 
the 
classroom
 to 
First 
Nation’s culture:
 practical ethnomathematics education. The M(ath)Ed Cohort, Department of Curriculum Studies, College of Education, University of Saskatchewan.

Lindsay J. Shaw, MEd (2012). Beyond the grade: an examination of why we grade and how to implement a grade-less program in a secondary mathematics classroom. The M(ath)Ed Cohort, Department of Curriculum Studies, College of Education, University of Saskatchewan.

Ronald Georget, MEd (2012). The M(ath)Ed Cohort, Department of Curriculum Studies, College of Education, University of Saskatchewan.

Brian Crawley, MEd (2010). Mathematics lessons using learner generated examples. Department of Curriculum Studies, College of Education, University of Saskatchewan.

Stephen Vincent, MEd (2010). Mathematics appreciation: connections in context. Department of Curriculum Studies, College of Education, University of Saskatchewan.

Senior supervisor (in progress)

Lisa Eberharter, M(ath)Ed cohort, Department of Curriculum Studies, College of Education, University of Saskatchewan.

Terry Johanson, M(ath)Ed cohort, Department of Curriculum Studies, College of Education, University of Saskatchewan.

Randi-Lee Loshack, M(ath)Ed cohort, Department of Curriculum Studies, College of Education, University of Saskatchewan.

Michelle Naidu, M(ath)Ed cohort, Department of Curriculum Studies, College of Education, University of Saskatchewan.

Gale Russell, Phd. Department of Curriculum Studies, College of Education, University of Saskatchewan.

Tamara Schwab, M(ath)Ed cohort, Department of Curriculum Studies, College of Education, University of Saskatchewan.

Committee Member (in progress)

Claire McTavish, M(ath)Ed cohort, Department of Curriculum Studies, College of Education, University of Saskatchewan.

Jacqueline Johnson, M(ath)Ed cohort, Department of Curriculum Studies, College of Education, University of Saskatchewan.

Simin Sadat Chavoshi Jolfaee, PhD. David Wheeler Institute for Research in Mathematics Education, Faculty of Education, Simon Fraser University.

Stavros Stavrou, PhD. Department of Mathematics and Statistics, College of Arts and Science, University of Saskatchewan.

Cognate Member (in progress)

Anna Maslany, MSc. Department of Psychology, College of Arts and Science, University of Saskatchewan.

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MEDIA EXPOSURE

Chernoff, E. J. (2013, February). Relative Likelihood Comparisons: A Comparative Overview of the Research. Colloquium of the School of Mathematical and Statistical Sciences, Arizona State University. Phoenix, Arizona, USA. Video available on YouTube: http://www.youtube.com/watch?feature=player_embedded&v=dHOXcaZjoyI

Chernoff, E. J. (2013, February). Calculating climate change. Pocket Mulch with Dwayne Keir. CFCR 90.5FM. Saskatoon Community Radio. Saskatoon, Saskatchewan, Canada.

Chernoff, E. J. (2013, January). Egan Chernoff of MatthewMaddux Education. The Math-Frolic Interviews. Interview available here: http://math-frolic.blogspot.ca/p/blog-page.html

Chernoff, E. J. (2013, January). How we measure. The environment around us. Pocket Mulch with Dwayne Keir. CFCR 90.5FM. Saskatoon Community Radio. Saskatoon, Saskatchewan, Canada.

Chernoff, E. J. (2012, November). How we measure. The environment around us. Pocket Mulch with Dwayne Keir. CFCR 90.5FM. Saskatoon Community Radio. Saskatoon, Saskatchewan, Canada.

Chernoff, E. J. (2012, October). "Egan Chernoff and MatthewMaddux: How we're related" video now available online. Carnival of Mathematics 91. Retrieved from http://matheminutes.blogspot.co.uk/2012/10/91st-carnival-of-mathematics.html (and also found here: http://aperiodical.com/carnival-of-mathematics/)

Chernoff, E. J. (2012, October). Recognizing the aesthetic (and, in this case, practical) appreciation of triangular numbers. MAA Found Math for the Week of October 1, 2012. Mathematical Association of America. Available: http://www.maa.org/FoundMath/12week38.html

Chernoff, E. J. (2012, September). Alternative Base Representation. Carnival of Mathematics 90 (Category: Art and Mathematics). Retrieved from http://www.walkingrandomly.com/?p=4558 (and also found here: http://aperiodical.com/carnival-of-mathematics/)

Chernoff, E. J. (2012, September). Bill, you had me at "arithmetic". Carnival of Mathematics 90 (Category: Commentary). Retrieved from http://www.walkingrandomly.com/?p=4558 (and also found here: http://aperiodical.com/carnival-of-mathematics/)

Livestream Lecture: Egan Chernoff and MatthewMaddux: How we're related. Inaugural lecture: Second Life Lecture Series on Wheeler Island. David Wheeler Institute for Research in Mathematics Education (Simon Fraser University, Vancouver, BC, Canada). Second Life, Wheeler Island (139, 28, 30). [http://blogs.sfu.ca/research/davidwheeler/projects/]

The StarPhoenix (2011, December 2nd). Proponents say new math adds up. [http://www.thestarphoenix.com/technology/Proponents+math+adds/5799774/story.html]

The Morning Edition with Sheila Coles (2011, September 26th). How teachers are taught math: The controversy continues!

CBC News (2011, September 25th). Math education plan worrisome, U of S prof says. [http://www.cbc.ca/news/canada/saskatchewan/story/2011/09/25/sask-teachers-math-education.html]

CBC News: Saskatchewan at 6 (2011, September 23rd). Bad Math?

CBC News: Saskatchewan at 5 (2011, September 23rd). Bad Math?

CTV Saskatoon (2010, December 20th). 20th Annual Saskatoon Santa Claus Parade.

On Campus News (2010, September). Specific approach to randomness. [http://www.usask.ca/communications/ocn/10-sept-24/8.php]

SFU News (2010, June). 2010 Convocation medal roundup. [http://www.sfu.ca/sfunews/news/2010-convocation-medal-roundup.shtml]

CMS Notes (2010, June). Education notes. [http://math.ca/notes/v42/n3/Notesv42n3.pdf]

On Campus News (2008, October). Around the bowl. [http://www.usask.ca/communications/ocn/08-sept-05/aroundthebowl.php]

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