`Teaching
Philosophy & Strategies
Catherine A. Roberts`

I am committed to a career of effective teaching and scholarly activity. I have an established record of quality teaching, publications in mathematics education, as well as extensive involvement of students in research projects. Relating the significance of mathematics as a tool for understanding and explaining the world is a fundamental component of my approach to teaching.

As a Master Teacher for the Massachusetts Department of Elementary and Secondary Education and a member of the Leadership Team for the Intel Math program, I am actively engaged in state and national efforts to "move the needle" on mathematics learning.

I teach courses in Calculus, as well as a variety of courses in applied math (Numerical Analysis, Differential Equations, Mathematical Modeling, Environmental Math). My courses are web and email enhanced. I check email throughout the day and evening to respond to student questions. My web site includes scanned lecture notes, special hints and guides, and both blank (for practice) and solution copies of multiple versions of each assessment. Student grade records are posted under secret-code names so that my students always know precisely where they stand in the course.

Quizzes, problem sets and special assignments are tallied together as Activity Points. Students are able to earn credit for a certain number of activity points -- corresponding to 10% - 20% of their course grade (depending on the course). They are provided with an extensive suite of choices -- activity point options far exceed the number that students may choose for credit. A quiz may count 10 points, a problem set may count 20, attending a math seminar may count 15 points and a substantial group project may be worth up to 40 points. For example, students can write a two page mathematical autobiography or critique an editorial from the Notices of the American Mathematical Society for 10 activity points. This approach serves a dual purpose. First, students are able to maximize their activity points by choosing multiple activities to ensure that a portion of their course grade is locked in as an A+. This results in a grade scaling of sorts -- one that rewards consistent work throughout the semester. Students who do poorly on problem sets can still maximize this component of their grade by doing additional activity point assignments. Next, students are exposed to a broad variety of activities, although they aren't forced to participate in any one in particularl. Whereas some students gravitate towards the group activities, others enjoy the writing assignments. As an instructor, I enjoy providing multiple paths towards success. Moreover, as I do not accept any late assignments, the responsibility is placed upon the student to pace him or herself wisely throughout the semester. What holds particular meaning to me is the special opportunity to get to know students individually. I enjoy the challenges of helping to guide students toward making appropriate choices during this critical time of learning and personal growth.

Prior to joining the faculty at Holy Cross in 2001, I worked at Northern Arizona
University in Flagstaff, AZ (1995 - 2001). While there, my teaching at the
undergraduate level consisted of multiple sections of Calculus, Mathematical
Modeling, Partial Differential Equations and Applied Mathematics. I also conceptualized
and developed an interdisciplinary course for our Honors Program titled The
Science of Art. This course was team taught by myself, an art historian and
a chemist (details available in an article in *A Liberal Arts Course Linking Art, Art History, Mathematics and Chemistry*, C. Kelley, A. Jordan and C. A. Roberts, J. Clg. Sci. Teaching, Vol. 31, 2001, 162-166). At the graduate level, I have taught courses in Partial Differential
Equations, Integral Equations and Applied Mathematics. The latter course was
taught completely on the web for the M.S. program in engineering. During my
three years on the faculty at the University of Rhode Island (1992 - 1995),
I taught similar courses.

My first years of teaching were a time of evolution and revolution in the development of my teaching style and philosophy. I consider my efforts during this time to have solidified my devotion to promoting student inquiry and student engagement through active learning. I support curriculum reform efforts -- even if these efforts are not as successful as we may hope -- because they require faculty to converse, analyze and reflect upon the way we teach. This process is a valuable exercise that improves student learning outcomes.

For example, I learned Calculus traditionally, and then taught with a reform text for four years. I then taught for two years with a hybrid traditional/reform text. My experience with a broad spectrum of philosophies in teaching calculus has resulted in my being a more effective teacher in all of my courses.

To illustrate my early commitment to teaching creatively and thoughtfully, I would
like to elaborate on some of the experiences that have shaped my philosophy.
My exposure to reform concepts regarding teaching began with my involvement
as co-editor for the Rhode Island Calculus Consortium's NSF funded project.
This project developed instructional modules adapted from the calculus reform
efforts. During my second year at the University of Rhode Island, I served
as a Teaching Fellow. In this program, twenty select faculty met twice a month
to examine current pedagogical issues in concert with professional instructional
development staff. We addressed issues such as diversity in the classroom,
accommodation of different student learning styles, stages of moral development,
and writing across the curriculum. I attended an MAA Short Course on calculus
reform offered by Ithaca College. After incorporating some of their projects
into the standard calculus curriculum, I remain impressed by the ability of
such activities to enrich conceptual understanding and to enhance students'
communication skills. I also served as co-editor for the Creative Math Teaching
newsletter for five years. This newsletter invites faculty to share their
experiments in creative mathematical instruction and also serves as a forum
to discuss challenges faced by teachers. I was invited to present some of
my ideas at the Third Conference on the Teaching of Calculus and at the Future
of Education Symposium at Bowdoin College (details available in *How to Get
Started with Group Activities*, C. A. Roberts, Creative Math Teaching, Vol.
1, No. 1, 1994 and *A Mathematics Buffet: Introducing Choice In Calculus*, C.
A. Roberts, UME Trends, Vol. 6, No. 5, Nov 1994.).

While on the faculty at Northern Arizona University, I continued to engage
in local conversations about effective teaching. I share some of my experiences
with alternative assessment techniques in MAA Notes (*Group Testing*, C. A.
Roberts, in Assessment Practices in Undergraduate Mathematics, eds. B. Gold,
S. Keith and W. Marion, MAA Notes, Mathematical Association of America, Washington
DC, 1999, 137-139.). I am an engaged teacher who is devoted to achieving excellence
in every aspect of my teaching. In 1999, I established the Modeling and Simulation
Lab in the Department of Mathematics and Statistics at Northern Arizona University.
I personally mentored twelve undergraduates and three graduate students in
Flagstaff (note: I had a doctoral student at URI early in my career). My students
receive undergraduate research credit and/or salary from one of my research
grants. Projects have included designing and programming the Grand Canyon
River Trip Simulator, assisting the University Space Management Team by creating
analytical methods to understand space utilization on campus, and assisting
the Department of History through the creation of an optimized course rotation
schedule. Two other faculty also used the lab as a resource to support their
student projects. As a result of their positive experiences, three of my students
have decided to become math minors, one became a double major with physics
and another switched his major to mathematics. One completed a master's degree in applied mathematics at the University of Colorado and another completed her doctorate in applied mathematics at Northwestern University in 2009. My students have
been successful in garnering grants to support both their research and their
travel to conferences to present their results. Their names have appeared
on some of my research publications (such as *Intelligent Agent Modeling for Simulating and Evaluating River Trip Scheduling Scenarios for the Grand Canyon National Park*, H. R. Gimblett, C. A. Roberts, T. Daniel, M. Mitner, S. Cherry, D. Kilbourne, M. Ratliff, D. Stallman, R. Bogle, J. Bieri in __Integrating GIS and Agent based modeling techniques for Understanding Social and Ecological Processes,__ ed. H. R. Gimblett, Oxford Press, 2000, 245-275.).

On a more practical level, I would characterize my teaching as organized and enthusiastic. I encourage student collaboration on homework and during short classroom group activities. I demand student accountability by insisting on attendance and by frequent assessments. Students learn best when they actively work through a wide variety of problems -- students work hard in my classes. Here at the College of the Holy Cross, I have had three opportunities to teach a course sequence in Differential and Integral Calculus aimed at under-prepared students. These students are often minority or are from under-resourced high schools. These courses meet an extra one-hundred minutes per week. With this extra time, we are able to incorporate more discussion and more group work. This year, my students do a warm-up problem in a composition book at the start of class that is collected almost daily. I provide detailed feedback on their work - without a grade - to provide a low-stakes method for the students to learn how to communicate mathematically prior to the assessments. This is a helpful addition to the online homework that we use, since it provides an opportunity for students to receive feedback about their writing of mathematics, which is, after all, a second language.

I have taught a number of sections of a course called Topics in Mathematics: Environmental Mathematics. This introductory liberal-arts course promotes the development of quantitative reasoning among students who are not studying math or science. These courses are Community-Based Learning courses. Each semester, a variety of environmental nonprofits from Worcester visit class to describe their mission and their needs. Students then form groups and work on projects as mathematical consultants. These projects benefit the nonprofit agencies and provide students with the opportunity to work with clients one a real-world problem. I also taught the upper-level math majors course in Mathematical Models as a Community-Based Learning course. Students did projects that relied on advanced mathematical techniques and made stunning presentations to the local nonprofit agencies that were all viewed as remarkably helpful to the agencies. This work was described in *Perspectives on Modeling Applications in a Service-Learning Framework*, C. A. Roberts, in __Mathematics in Service to the Community: Concepts and Models for Service-Learning in the Mathematical Sciences__, edited by Charles R. Hadlock, MAA Notes #66, Mathematical Association of America, Washington DC, 2005.

My approach is an involved one. I actively recruit math majors and minors through private conversations and letters to promising students. I am particularly devoted to mentoring female and minority students in the sciences. I volunteer and present at Career Days at a local high school. I helped organize a Sonia Kovelevsky Day for high school girls to learn about careers in mathematics at NAU. Starting in 2007, I became a Master Teacher for the MA Department of Education. In this capacity, I teach courses based on the Intel Math Initiative to elementary- and middle-school teachers from urban locations, such as Springfield and Worcester. As a member of the Intel Math leadership team, I have been fortunate to help train new faculty instructors for Intel Math in a number of states around the country. I have also taught a course in environmental mathematics to high school teachers through the MA Improving Teacher Quality grant. This fall, I am developing a Mathematics Learning Community for a group of K-6 teachers from the Worcester Catholic Diocese schools. In my view, it is essential that college and university faculty contribute to improving the mathematical teaching of our K-12 teachers so as to improve mathematical learning for our children.

I believe that as a mathematics professor, I positively impact students on three fronts. First, I expose them to the subject in a creative, enthusiastic fashion that reveals both the utility and beauty of mathematics. Second, as an applied mathematician, I am well suited to encourage exploration of the connections between mathematics and other subjects. Finally, by continuing my own research, I remain an active participant in the wider mathematics community and give students opportunities to engage in the world of mathematical research.

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