My earliest memory of mathematics was my father teaching me to count in binary when I was six. I was raised by an astronomer and an elementary school teacher, so education was highly valued in my family. At one point I was planning on becoming an elementary school teacher, and in my senior year of high school I performed a study on motivation in young children. At the same time, I took AP Calculus and remembered how much I used to like math. I had coasted through precalculus with little interest, but calculus engaged and challenged me in a way that was newly exciting. I decided to stick with my goal of teaching in public schools, but shifted to high school math.

Teaching Experience

     I taught high school and middle school for three years, but I was unable to handle the disciplinary requirements of teaching a K-12 class and left the profession despondent. On a whim, I applied for a position at Trident Technical College and was hired as an adjunct with a full-time class load. I threw myself into this job and discovered I enjoyed it more than I ever did middle school. I had numerous students tell me that they understand algebra or statistics for the first time because of me.

     At Trident I learned to help struggling students overcome their pessimism. I have had many students who wanted to graduate but were uninterested in math or convinced they cannot do it, and I help them see things in a new way. I have an especially strong rapport with “non-traditional” students who are returning after a long absence, but I also introduce more advanced concepts for students who plan to go further in math.  In more recent years, I have taught Multivariable Calculus primarily to engineering majors, and so I use a lot of physical examples to introduce mathematical concepts.  I differentiate my instruction to appeal to all students and make it a point to check on them regularly during class.

Teaching Philosophy

My teaching philosophy can be described as constructivist.  I believe almost all students are capable of learning, but learning is only meaningful if it is something they construct for themselves.  The most important question in learning is “what does this remind me of?”  We must always make connections between what we know and what we are trying to learn.  I tell my students that confusion is the first step to learning.  All humans form a framework to understand the world.  When they are presented with something new, it disrupts that framework and they become confused.  This is known as cognitive dissonance.  They can then either reject the new information or rework their existing framework to accommodate it.  I believe a teacher’s role is to catalyze that process, helping speed along what would naturally happen on its own given enough time.  Biologically, modern humans are no more intelligent than those who lived millennia ago, but we can draw on the accumulated knowledge of our ancestors to reach understanding more quickly.

Teaching Methods

My main technique in the classroom is “scaffolding.”  I will start with an example of something students have seen before and connect it to something new.  I tell my Multivariable Calculus students “don’t reinvent the wheel” on the first day of class.  When teaching how to find extrema of a multivariable function on a region, I will lead in with an example from Calculus I on finding extrema of a single-variable function on an interval.  Most of my students are engineering majors, so I try to use as many practical examples as possible.  I particularly enjoy teaching Green’s Theorem.  In researching Potential Theory, I have learned a lot about the life of George Green and his pioneering work on electrostatics, so I talk about how that subject is connected to Calculus.  For computer engineers, I point out how linearization and Taylor polynomials are a way of reducing the number of flops a computer program needs.  The most important thing about teaching is to always meet students where they are, and that is what I will always strive to do.

Teaching Experience II

     My experience as instructor of record includes teaching most subjects from College Algebra through Multivariable Calculus.  I have also taken on additional teaching roles when possible.  The math department hires experienced graduate students to lead small groups of newer graduate students in studying for qualifying exams.  In Summer 2023, I led the Real Analysis study group and tried to give context to theorems they may have not fully understood- for example, one student did not understand the concept of “one-sided inverses” until I showed him a counterexample.  In Summer 2024, I did much the same thing but for Complex Analysis.  I wish these groups had been around when I was preparing for qualifying exams, and I would love to start something similar in my new role.

     I also participated in the school’s Directed Reading Program- one of my Calculus students showed interest in Analysis and so I offered to assist him in working through some basic Real Analysis.  I chose Stephen Abbott’s Understanding Analysis and assigned him weekly readings that we discussed together.  I have also worked as a grader for both Real and Complex Analysis, and I hold regular office hours for students to ask questions about my grading choices.  Someday I would like to develop and teach a special topics course in Potential Theory using Thomas Randsford’s textbook, assuming there was sufficient interest among the student body.

Further Education

     I am always looking for new techniques to improve my teaching.  In Spring 2023, I attended a conference at University of New Mexico on teaching methods.  It inspired me to attempt some more innovative ideas.  I had considered using “flipped classrooms” in the past, in which students read textbook passages at home and do practice problems in class under the teacher’s supervision.  I was attracted to this method because it gives me the opportunity to correct errors in real-time, but on the other hand I did not know if students would have the skill and discipline for such a self-directed style.  The ability to record video lectures was a game-changer.  I began devoting one class a week to in-class problem-solving in groups, making up for the lost lecture by recording a video lecture to be watched over the weekend.  This has given students opportunities to get more help in class and work together on problems, and according to anonymous evaluations several students appreciated the experience.  Many of them exchanged contact information to continue working together out of class.
 

     At the Joint Mathematics Meeting in San Francisco (January 2024), Monroe Community College demonstrated how 3D printed models were used in Multivariable Calculus courses.  Drawing three-dimensional functions is notoriously difficult, and models give students a tactile understanding of subjects like local maxima, contour lines, and Lagrange Multipliers.  I took notes on the subject, and when I returned to Albuquerque I reached out to the Health Sciences school at UNM about using their 3D printer.  The manager showed me how to use it and I printed six models over the next couple of weeks.  The first lesson was on partial derivatives.  Students were engaged and seemed to understand the ideas in question.  I enjoyed listening to them discuss with each other, saying things like “it needs to go up as you go right” or “this one should be a peak, and that should be a trough.”  More details are available on my professional website.

     This year I was chosen to participate in the Graduate Teaching Scholars program, a paid monthly workshop where graduate teachers meet to discuss teaching and learn new concepts.  In the Spring, we will each design a pilot study to conduct with our students as subjects.  While I have not yet worked out the details, I plan on trying to address student attrition rates.  UNM provides many resources to help struggling students, plus my own individual offers of assistance, so it is frustrating when students drop the course without taking advantage of any of these opportunities.  I am hoping this will be yet another tool in my arsenal while working with my students.