- Ph.D., Curriculum & Instruction, University of Wisconsin-Madison, 2007
- Master's, Mathematics, University of Wisconsin-Madison, 2004
Student reasoning in mathematics, and also it relationship with historical reasoning in mathematics, particularly with respect to the infinite and the infinitesimal.
- Adams, A., Ely, R., & Yopp, D. (to appear). Making arguments viable: Using generic examples.
- 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.