''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 currently am a Professor of Practice in Mathematics at Boston College, teaching Multivariable Calculus and Foundations of Mathematics for Elementary Educators. Through BC, I am also a mathematician mentor for early-career teachers in high-needs districts as part of the BC-Math-for-America-Boston Noyce Teaching Fellowship.
From 2013-2015, I worked as project coordinator and principal investigator for a grant from the Harvard Initative on Learning and Teaching entitled Curricular Innovation in Calculus: Meeting the Changing Needs of Our Students and Client Disciplines. This work is motivated in part by the ''mathematics bottleneck that is currently keeping many students from purs uing STEM majors'' (in the words of a 2012 report by the President's Council of Advisors on Science and Technology) and involves collaborating with other disciplines on online multi-media modules to supplement existing calculus curriculum. These modules feature videos of practitioners discussing questions in their field which are informed by calculus, interspersed with interactive problems designed for students to connect the calculus and the context in a hands-on way. We are examining whether these modules shift student beliefs on the relevance of calculus to STEM and quantitative social science disciplines and increase persistence in mathematics courses.
From 2008-2013, I worked as 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 main area of scholarly and professional work is mathematics teaching and learning at the undergraduate level and the professional development with middle and high school mathematics teachers. I did my graduate work in the area of algebraic number theory and cryptography, topics which are still some of my favorite in mathematics (see papers and talks below for more).
At the undergraduate level, I am currently focused on early course experiences, specifically examining students' conceptual understanding and knowledge and beliefs about calculus and how these connect to their past experiences, their course performance and their primary academic interests in STEM (Science, Technology, Engineering and Mathematics) and quantitative social science fields. Part of this work is related to the grant project mentioned above.
In the area of teacher education, I am interested in professional development with mathematics teachers focused on mathematical investigations and mathematical habits of mind. This work is very much in line with the recent Common Core State Standards for Mathematics (CCSSM) which emphasize using and assessing ''mathematical practices ''across content areas in the K-12 grades as a way to deepen students' appreciation and understanding of the structure and concepts of math and build their capabilities for problem-solving and communication in mathematics and other fields. Some examples of this follow.
Mathematics Education: Talks
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 education doctoral students.
Mathematics Research: 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.