EJC: PUBLICATIONS
~Eric Bach
•Articles in Refereed Journals (with abstracts)
•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
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
Abstract. This research continues the longstanding tradition of investigating relative likelihood comparisons. Respondents are presented with sequences of heads and tails derived from flipping a fair coin five times, and asked to consider their chances of occurrence. An iteration of the task, which maintains the ratio of heads to tails in all of the sequences presented, provides unique insight into individuals’ normatively incorrect relative likelihood comparisons. In order to reveal the aforementioned insight, this research, based upon participants’ response justifications, presents unconventional partitions of the sample space, which are organized according to switches, longest run and switches and longest run. In doing so, it will be shown that normatively incorrect responses to the task are not necessarily devoid of correct probabilistic reasoning. To accurately render the data gathered from 239 prospective mathematics teachers, an original theoretical framework (the meta-sample-space) will be used with a new method (event-description-alignment) to demonstrate, that is model, that certain individuals base their comparisons of relative likelihood according to a subjective organization of the sample space, that is, a subjective-sample-space.
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
Abstract. In mathematics education, there are (at least) two seemingly disparate and unethical issues that have been allowed to continue unresolved for decades: the math wars (traditional versus reform teaching and learning of mathematics) and the marginalisation of Indigenous students within K-12 mathematics. Willie Ermine, an Indigenous scholar, has proposed the use of ethical spaces to explore and analyse occurrences of unethical situations arising between the “intersection of Indigenous law and Canadian Legal systems” (Ermine, Indigenous Law Journal 6(1):193–203, 2007). This paper brings Ermine’s notion of ethical spaces to the field of mathematics education research as the theoretical framework for analysing the aforementioned issues. The result of this analysis is a potential single theoretical resolution to both dilemmas that can also serve as a significant factor in the processes of decolonisation.
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.
Abstract. The objective of this article is to contribute to research on prospective teachers’ probabilistic knowledge. To meet this objective, prospective mathematics teachers were presented with a novel task, which asked them to identify which result from five flips of a fair coin was least likely. However, unlike previous research, the participants were presented with events, that is, sets of outcomes, as opposed to sequences, which have dominated previous literature on relative likelihood comparisons. Recognizing that previous changes to the task have resulted in new areas of research, a new lens – the composition fallacy – was utilized when accounting for participants’ responses. Use of the new lens bolsters the contention that logical fallacies are a viable avenue for future investigations in comparisons of relative likelihood and research in probability.
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
Abstract. The general objective of this article is to contribute to the limited research on teachers’ probabilistic knowledge. More specifically, this article aims to contribute to an established thread of research that investigates relative likelihood comparisons. To meet these objectives, prospective mathematics teachers were presented two different answer keys to a ten question multiple-choice quiz and were asked to determine and justify which of the two was least likely to occur. Unlike previous research, this article does not employ the representativeness heuristic, but, instead, utilizes the attribute substitution model—which stems from the genericism of the heuristics and biases program—to account for specific responses to relative likelihood comparisons. This new perspective demonstrates that certain individuals, when presented one question, answer a different question instead. Results demonstrate that participants substitute a variety of heuristic attributes instead of making the intended relative likelihood comparison of the answer keys presented.
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
Abstract. The purpose of this article is to address the lack of research on teachers’ knowledge of probability. As has been the case in prior research, we asked prospective mathematics teachers to determine which of the presented sequences of coin flips was least likely to occur. However, instead of using the traditional perspectives of heuristic and informal reasoning, we have utilized logical fallacies for our analysis of the results. From this new perspective, we determined that certain individuals’—those who provided normatively incorrect responses—utilized the fallacy of composition when making comparisons of relative likelihood. In addition, we discuss how our findings impact models established in the research literature (e.g., the representativeness heuristic) and, further, we suggest that logical fallacies should supplement heuristic and informal reasoning as potential perspectives for research investigating comparisons of relative likelihood.
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.
Abstract. In this article, we discuss how acknowledging and embracing that the sample space is one of many ways to partition the set of all possible outcomes impacts the teaching and learning of sample space and proba- bility. After recounting an exchange surrounding two viable answers to a probability question, we detail how developments arising from mathematics education research investigating the partitioning of all possible outcomes can be integrated into the mathematics classroom. As a result, we present a unique perspective to normatively incorrect responses.
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
Abstract. This article is a systematic reflection on a sequence of episodes related to teaching probability. Our central claim is that reducing problems to a consideration of the sample space, which consists of equiprobable outcomes, may not be in accord with learners’ initial ways of reasoning. We suggest a “desirable pedagogical approach” in which the solution builds on the set of outcomes as identified by learners and serves as a bridge towards mathematical convention. To explore prospective high school mathematics teachers’ ideas related to addressing a potential learner’s mistake and their reactions towards the suggested approach, we presented them with two tasks. In Task I, participants (n = 30) were asked to suggest a pedagogical remedy to a frequent mistake found in dealing with a standard probability problem, whereas in Task II, they were asked to solve a probabilistic problem, which they had not encountered previously. We discuss participants’ mathematical solutions to Task II in reference to their pedagogical approaches to Task I. The presented disparity serves in extending the convincing power of the suggested pedagogical approach.
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.
Abstract. Zero is a complex and important concept within mathematics, yet prior research has demonstrated that students, pre-service teachers, and teachers all have misconceptions about and/or lack of knowledge of zero. Using a hermeneutic approach based upon Gadamer’s philosophy, this study examined how two elementary mathematics teachers understand zero and how and when zero enters into their teaching of mathematics. The results of this study add new insights into the understandings of teachers and students related to zero and the origins, relationships between, and consequences of those understandings. Significant gaps and misconceptions within both teachers’ understandings of zero suggest the need for pre-service education programs to bring attention to the development of a more complete and meaningful understanding of zero.
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
Abstract. In this study subjects are presented with sequences of heads and tails, derived from flipping a fair coin, and asked to consider their chances of occurrence. In this new iteration of the comparative likelihood task, the ratio of heads to tails in all of the sequences is maintained. In order to help situate participants’ responses within conventional probability, this article employs unconventional set descriptions of the sample space organized according to: switches, longest run, and switches and longest run, which are all based upon subjects’ verbal descriptions of the sample space. Results show that normatively incorrect responses to the task are not devoid of correct probabilistic reasoning. The notion of alternative set descriptions is further developed, and the article contends that sample space partitions can act as an investigative lens for research on the comparative likelihood task, and probability education in general.
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
Abstract. In this article the three dominant philosophical interpretations of probability in mathematics education (classical, frequentist, and subjective) are critiqued. Probabilistic explorations of the debate over whether classical probability is belief-type or frequency-type probability will bring forth the notion that common ranges, rather than common points, of philosophical reference are inherent to probability measurement. In recognition of this point, refinement of subjective probability, into the dual classification of intrasubjective and intersubjective, and frequentist probability into the dual classification of artefactual and formal objective, attempts to address the nomenclatural issues inherent to subjective and frequentist probability being both general classifiers and particular theories. More specifically, adoption of artefactual and intersubjective probability will provide a more nuanced framework for the field to begin to heed the numerous calls put forth over the last twenty-five years for a unified approach to teaching and learning probability. Furthermore, the article proposes that “artefactual period” be adopted as a first approximation descriptor for the next phase of probability education.
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
Abstract. In this paper we describe two episodes of instructional interaction, in which examples are used in order to help students face their misconceptions. We introduce the notions of pivotal example and bridging example and highlight their role in creating and resolving a cognitive conflict. We suggest that the convincing power of counterexamples depends on the extent to which they are in accord with individuals’ example spaces.
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
Abstract. Acknowledging students’ difficulty in generalizing in general and expressing generality in particular, we assert that the choice of examples that learners are exposed to plays a crucial role in developing their ability to generalize. We share with the readers experiences in which examples supported generalization, and elucidate the strategies that worked for us in these circumstances, presuming that similar strategies could be helpful with other students in other settings. We further share several pitfalls and call for caution in avoiding them.
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
Abstract. In this article we introduce a usage-goal framework within which task design can be guided and analyzed. We tell a tale of one task, the Pentomino Problem, and its evolution through predictive analysis, trial, reflective analysis, and adjustment. In describing several iterations of the task implementation, we focus on mathematical affordances embedded in the design and also briefly touch upon pedagogical affordances.
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. (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).