''It has been well said that the highest aim in education is analogous
to the highest aim in mathematics, namely, not to obtain results but
powers, not particular solutions, but the means by which endless
solutions may be wrought.''
George Eliot, in an essay about Thomas Carlyle
I am a preceptor in the Mathematics Department at Harvard University. Some courses recently taught include Math 1a: Introduction to Calculus I, Fall 2012
Math 152: The Math of Symmetry, Topics in Discrete Math and Abstract Algebra, Fall 2011 .
I have also worked as co-coordinater of the Calculus Course Assistant Program and
the dinner-time seminar for undergraduate math concentrators.
Scholarly and Professional Work
My two main areas of scholarly and professional work are mathematics teaching and learning at the introductory undergraduate level and the professional development of middle and high school mathematics teachers. These areas have obvious interest to both the education and mathematics community and the potential impact of such work has grown with recent nationwide recommendations about what mathematics to teach, who should teach it, and how.
For the first area, I am interested in the gains calculus students make in their conceptual understanding of the subject and how their knowledge of calculus, and math in general, can connect to and support their primary academic interests, specifically in STEM (Science, Technology, Engineering and Mathematics) and quantitative social science fields. This is an important challenge, as reflected by the recent report by the President's Council of Advisors on Science and Technology which seeks ``new approaches to [...] the mathematics bottleneck that is currently keeping many students from pursuing STEM majors."
For the second area, I am interested in the professional development of mathematics teachers around mathematical habits of mind and how these translate to classroom practice and ultimately their students' success. This work has become especially important with the advent in 2011 of the Common Core State Standards for Mathematics (CCSSM) which emphasize using and assessing ``mathematical practices" across content areas in the K-12 grades. Some examples of this follow.
Here are slides from an invited talk ''Making Sense of the Standards for Mathematical Practice'' presented at MassMATE 2012 Symposium: Teachers Leaders Making It Happen: Bringing the Guiding Principles and Standards for Mathematical Practice into Mathematics Classrooms, at Bridegwater State Universtity, May 2012.
Here are slides from a talk ''Designing Professional Development around the Common Core Standards for Mathematical Practice A Mathematician-Teacher Collaboration'' presented at the MAA Session The Mathematical Preparation of Teachers: The Impact of the Common Core State Standards Initiative at the Joint Math Meetings in Boston, January 2012.
Here are slides from a session I co-organized for the AWM's 40th Anniversary Conference on Intersections of Mathematics and Math Education: Research and Practice K-20 at Brown University in September 2011.
Here are slides from a talk '' 'Mathematician' Meets 'Math Educator': The Experience of Co-teaching a Math Inquiry Course Course'' presented at the Mathematics Colloquim at the University of New Hampshire, April 2009.
Here are slides from a talk at the Joint Math Meetings in DC, January 2009, on the same course as above, a mathematical inquiry course for math educati\ on doctoral students.
Mathematical Research: Select Papers and Talks
My mathematical research interests are in algebraic number theory and arithmetic geometry, with an eye towards cryptography. I completed my PhD in Mathematics in May 2008 at the University of Maryland , working with Professor Larry Washington, on number theoretic algorithms for elliptic curves. A copy of my thesis is here.
Pairings on Hyperelliptic Curves , with Jennifer Balakrishnan, Sarah Chisholm, Kirsten Eisentrager, Katherine Stange, and Edlyn Teske. Proceedings of the Women in Numbers (WIN) Workshop, Banff International Research Station, Banff Canada, Fields Institute Communication Series, 2009
Talk ''Computing the Hilbert Class Polynomial Using p-adic Lifting'' at M.I.T. STAGE: Seminar on Topics in Arithmetic, Geometry, Etc., May 2009.
For more on my past talks, teaching and publications, check out my old University of Maryland website.