Rob Ely

Student reasoning in mathematics, and also it relationship with historical reasoning in mathematics, particularly with respect to the infinite and the infinitesimal.

• Ely, R. (2019). The torpedo’s shock. For the Learning of Mathematics.
• Bair, J., Blaszczyk, P., Ely, R., Heinig, P., & Katz, M. (2018). Leibniz’s well-founded fictions and their interpretations. Matematychni Studii, 49(2), 186-224.
• Ely, R. (2017). Reasoning with definite integrals using infinitesimals. Journal of Mathematical Behavior, 48, 158-167. 
• Bair, J., Blaszczyk, P., Ely, R., et al. (2017). Cauchy, infinitesimals, and ghosts of departed quantifiers. Matematchni Studii, 47(2), 115-144.
• Bair, J., Błaszczyk, P., Ely, R., Henry, V., Kanovei, V., Katz, K., Katz, M., Kutateladze, S., McGaffey, T., Sherry, D., & Shnider, S. (online 2016, print 2017). Interpreting the infinitesimal mathematics of Leibniz and Euler. Journal of General Philosophy of Science, 48, 1-44.  
• Adams, A., Ely, R., & Yopp, D. (2016). Making arguments viable: Using generic examples. Teaching Children Mathematics, 23(5), 292-300.
• Yopp, D., & Ely, R. (2016). When does an argument use a generic example? Educational Studies in Mathematics, 91:37–53. 
• Yopp, D., & Ely, R. (2015). Generic example proving criteria for all. For the Learning of Mathematics, 35(3), 8-13.
• Bialostocki, A., & Ely, R. (2015). Points on a line that maximize and minimize the ratio of the distances to two given lines. Forum Geometricorum, 15, 177-178.
• Brendefur, J., Hughes, G., & Ely, R. (2015). A glimpse into secondary students’ understanding of functions. International Journal for Mathematics Teaching and Learning. 1-22.
• Bair, J., Błaszczyk, P., Ely, R., Henry, V., Kanovei, V., Katz, K., Katz, M., Kutateladze, S., McGaffey, T., Sherry, D., & Shnider, S. (2013). Is mathematical history written by the victors? Notices of the AMS, 60 (7), 886-904.
• Ely, R. (2012). Loss of dimension in the history of calculus and in student reasoning. The Mathematics Enthusiast, 9(3), 303-326.
• Ely, R. & Adams, A. (2012). Unknown, placeholder, or variable: What is x? Mathematics Education Research Journal, 24, 19–38.
• Ely, R. (2011). Envisioning the infinite by projecting finite properties.  Journal of Mathematical Behavior, 30(1): 1-18. 
• Ely, R. (2010). Nonstandard student conceptions about infinitesimal and infinite numbers. Journal for Research in Mathematics Education. 41(2): 117–146.
• Ely, R. & Cohen, J. S. (2010). Using student work: The double-spin game. Mathematics Teaching in the Middle School, 16(4), 208-215.

• Making Mathematics Reasoning Explicit (MMRE) -- a 5-year, $5 million, NSF Math Science Partnership Grant (2011-2016) collaboration between Washington State University, University of Idaho, and a consortium of rural districts in eastern Washington and northern Idaho. The goal is to develop teacher leaders in Grades 4-12 who promote mathematical reasoning, generalization, and justification in their classrooms, schools, and districts.