I have been in the trenches of undergraduate education in the Mathematics Department at UC Santa Cruz since 1994 when I was first hired as a Unit-18 lecturer. Since then I have taught a large number of courses up and down the curriculum of the undergraduate program. I have developed a number of undergraduate courses over the years. Without a doubt the most consequential such work was the development of the ground-breaking online calculus sequence for UC with my colleague and friend, Distinguished Professor Anthony (Tony) Tromba. Over these last few years, we have co-taught well over 23,000 students in online calculus, including students from all nine undergraduate-serving campuses in the UC system. More on the online calculus project can be found here.

In addition to teaching college classes at UC, I have also extensively taught enrichment courses in K-12. I taught for COSMOS (California Summer School for Mathematics and Science) at UC Santa Cruz. I have also taught enrichment courses at local middle and elementary schools. In fact, the most difficult class I ever taught was an enrichment class for a group of about ten motivated and talented elementary school students at San Lorenzo Valley Elementary school. It was very difficult for me to keep these fifth graders on task, and I have gained a lot of respect for K-12 teachers in the process.

Here are some thoughts on teaching I wrote up as part of my teaching statement for my 2014 excellence in teaching award. They very much reflect my philosophy about teaching mathematics at UC Santa Cruz, and have guided me in the way I teach and structure my classes, in person or online.

• Mathematics is NOT a spectator sport: Getting students engaged with the material to get them to think and do problems on their own is crucial for success in any math class. Courses need to be structured to give students ample opportunity to engage with the material and with other students, TAs, and the instructor about the material. This is the key ingredient for a successful course.
• Mathematics is a difficult subject: Many students struggle with abstract concepts and may feel inadequate if they don’t get something immediately. Students need to give themselves the time to understand the material, and teachers need to be patient and reassuring that it is not a personality defect if one doesn’t grasp a concept immediately. It is important to tell students that mathematics was not developed over night! For instance, it took several thousands of years for a suitable system of arithmetic to be developed (try multiplying with roman numerals).
• Mathematics is the language of science and nature: Mathematics plays a crucial role in many students’ course of study. Our students deserve carefully designed courses and curricula, well prepared lectures and excellent instructors that in addition to being experts in the subject matter are able to differentiate students’ backgrounds, motivations, and abilities.
• Structure is important but so is flexibility and compassion. Life happens! Deadlines and a clear syllabus for the course are needed, particularly in large lecture courses. But this should not become an excuse for not considering exceptions such as illness or family emergency.
• Teachers and good teaching matter: A teacher’s attitude toward teaching and towards his or her students can have a profound effect on students’ willingness to engage with the material. As a parent I regularly saw the reflections of my children’s teachers in their attitudes toward a subject, both good and bad.
• Teaching is a great learning opportunity: We have so much more to learn about how students learn. Paying attention to this fact and to your students is as important as ever to be able to be an effective teacher.