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.

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, calculator programs, special hints and guides, and both blank (for practice) and solution copies of multiple versions of each exam. 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 up to 250 activity points -- corresponding to 25% of their course grade. They are provided with an extensive suite of choices -- over 500 activity points are available. 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 25% 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 generating assignments. Next, students are exposed to a broad variety of activities, although they aren't forced to participate in them all. 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 has held particular meaning to me during this, my first year of teaching, is the special opportunity to get to know students individually. I have enjoyed the challenges of helping to guide students toward making appropriate choices during this critical time of learning and personal growth. The ability of the College to support students and faculty in this regard has impressed me.

Prior to teaching at Holy Cross (2001 - present), 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 the Journal of College Science Teaching). 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. Student evaluations of my teaching are consistently high (average of 4.4 on a scale of 1.0 - 5.0) and peer evaluations of my teaching have placed me in the meritorious or outstanding categories every year.

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.

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 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. He is now finishing his graduate degree in applied mathematics at the University of Colorado. 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.

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 quizzing. Students learn best when they actively work through a wide variety of problems -- students work hard in my classes. For example, I oftern use graphing calculators and Mathematica for multiple technology based laboratory activities in my Calculus sections.

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.

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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