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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.)
Publications
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.
Also:
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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