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Mathematics Education at UI

About Me 



Rob's Home Page 



Rob Ely's Research Page


I am interested broadly in the relationship between historical reasoning in mathematics and student reasoning.  In particular I am studying how students think about the infinite and the infinitesimal.


What is the relationship between the internal cognitive rules that govern the construction of (locally) consistent sets of conceptions and our external socio-mathematical rules that govern the construction of consistent mathematics?


I am also researching how to develop student reasoning, through explicit generalization and justification in the classroom.  This is what our NSF grant is about.  Making Mathematical Reasoning Explicit (MMRE) is a $5 million 5-year MSP grant in collaboration between UI, Washington State University, and a consortium of rural districts in eastern Washington and northern Idaho. (See the "Mathematics Education at UI" link to the left.)



Ely, R. (in review). Dynamic reasoning with limit, function, and continuity. Research in Mathematics Education.

Ely, R. & Radu, I. (to appear 2012). Promoting students’ object-based reasoning with infinite sets. Online proceedings for the 15th SIGMAA on Research in Undergraduate Mathematics Education Conference. Portland, OR: Portland State University, OR.

Ely, R. (to appear July 2012). Loss of dimension in the history of calculus and in student reasoning. The Mathematics Enthusiast.

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.

Ellis, A. & Ely, R. (2011). The Case of the Mystery Table.  Mathematics Teaching in the Middle School.

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.

Ely, R. & Boester, T. (2010). Point/Counterpoint: Should we teach calculus using infinitesimals? Online Proceedings for the 13th SIGMAA on Research in Undergraduate Mathematics Education Conference. Raleigh, NC: North Carolina State University.

Ely, R.  (2007). Nonstandard models of arithmetic found in student conceptions of infinite processes.  In Lamberg, T., & Weist, L. R. (Eds.) Proceedings of the 29th Annual Conference of the North American Chapter of the International Group for the Psychology of Mathematics Education. Stateline (Lake Tahoe), NV: University of Nevada, Reno.



Ely, R. (2010). Review of Theories of Mathematics Education. Educational Studies in Mathematics.

Webb, N. L., Alt, M., Ely, R., Cormier, M., & Vesperman, B.  (2006).  The Web Alignment Tool: Development, Refinement, and Dissemination.   In Aligning Assessment to Guide the Learning of All Students: Six Reports on the Development, Refinement, and Dissemination of the Web Alignment Tool, Council of Chief State School Officers, Washington, D.C.


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