Teaching

Teaching Methodology. You learn mathematics by experiencing mathematics, not by copying off a board or reading a book.

This claim is based upon both extensive documented research in undergraduate mathematics education as well as over a decade of my own experiences teaching. Consequently, my job as an instructor is to foster a safe and welcoming environment of exploration, and within that environment, create opportunities for students to experience the material. In the classroom I am committed to making class time a time of learning, and to this end, I use evidence-based active learning strategies. An average day of class with me is composed of a mixture of short lectures, group activities, and group discussion. Outside of class, I assign several hours of homework that build upon the ideas developed in class.

Depth. Understand simple things deeply.

As a strategy to help students achieve deep understanding, I am an adamant believer in the "Rule of Four," by which I mean every concept should be understood verbally, numerically, visually, and symbolically. Students are often habituated to conceiving of mathematics as symbolic formulas and believe the activity of mathematics to be pushing symbols around the page. Emphasis and repetition of the Rule of Four helps student develop habits of mind to understand concepts deeply. As I always say to my students, "you can be so much more than just a symbol pusher."

Breadth. All of mathematics is connected.

In addition to emphasizing depth of understanding, it is one of my teaching goals to convey the interconnectedness of mathematics. The divisions between sub-disciplines of mathematics are artificial and the more students see how ideas from one area of mathematics can be leveraged in another, the more equipped they will be to solve mathematical problems. In my own research, I constantly use ideas from all areas of mathematics, and it is for these reasons that during my time at CSUSB, I have taught courses in every sub-discipline of mathematics and at every level, from GE to graduate level.

Technology. As mathematicians, we are problem solvers. A fundamental component of problem solving is being able to effectively use the best tools at our disposal.

Over the past several years, I have become very involved in the use of free computer programs and programming languages that enable students to most effectively visualize concepts, perform computations, and experiment with content in ways that were previously inaccessible. Every class I teach, I both use and teach students to use the most powerful technological tools, from spreadsheets to GeoGebra to the python-based Sage programming language.