Why the proverbial "light bulb" moment isn't always the best moment for a student:
Teaching is my passion and the reason I went into academia; watching students grow and develop into adults capable of asking--and answering--insightful questions are highlights of my career as a professor. It isn't about the "light bulb" moments. It's about students knowing the current is on and that moment just before the switch flips--where students struggle to find the answer, but have faith there is a way. If teaching was all about that moment the switch worked, we'd miss so many moments where students would go back to the circuit board, determine where the wires were crossed, and ultimately make a more efficient wire diagram that worked. The reason I teach is to watch students believe there is an answer (of some sort, even to unsolvable problems) and determine what is necessary to reorganize and rework the problem to get there.
So what do I do that makes my classes work?
Through using a variety of means of assessments--which may include exams, quizzes, projects, and short in-class polls--my goal is to allow students to best demonstrate their knowledge in the modality that both works for them and allows me to equitably assess the class as a whole. Understanding that not every student comes in with the same background or the same life circumstances requires flexibility in the types of assessments. The level of course can also impact the level of "math phobia" a student brings to the classroom--just because a student is in an upper-level course doesn't mean they aren't afraid of the content. Through the use of different modalities of teaching and allowing students to take responsibility for their own learning, my goal is to educate students not only with the content of the course, but also with content for life.
Particular projects of interest:
There are several projects that I have done in recent years with one of my general education courses, Heart of Mathematics, at Southern New Hampshire University. This course is a survey-level course designed to introduce high-level mathematical concepts (e.g., topology, number theory, or dynamical systems) at an accessible level to the student looking for a "one and done" course for this university's mathematics requirement. In Spring 2020 (with modifications in subsequent semesters), I introduced the Automathography, where students gave me a little background at the beginning of the semester so I could better understand where and how they approached the course. This idea is the subject of a manuscript with Ron Buckmire (Occidental College), currently under review. Spring 2020 also brought Real Life Mathematicians (RLMs) to light, and an article highlighting this project was published in MAA Focus. I switched up the RLM project in Fall 2020 to focus on Mathematicians of the Non-Standard Type to encourage students to explore the histories and accomplishments of a more diverse set of mathematicians than those typically discussed. Links to each of these projects can be found either within this paragraph or the subheading below.
I teach using a variety of projects to help illuminate ideas that may not be fully explored in classes. Previous projects include:
Heart of Mathematics (No coding language necessary)
Automathography (links to subpage with examples from various semesters)
Biography of a REAL LIFE MATHEMATICIAN! (links to subpage with poster from Spring 2020 semester)
Mathematicians of the Non-Standard Type (links to subpage with examples from various semesters)
Graph Theory on Campus Maps
Traveling Salesman Problem with Local School Districts
Fractal Art Creation
Calculus III (No coding language necessary) [using Carmen Sandiego as a theme]
Equations of Motion
Curl, Flux, and Divergence
Linear Algebra (uses basic Matlab code)
Difference Equations and Markov Chains
Condition Numbers of Matrices
Google Page Rank
Differential Equations (uses basic Matlab code, some projects updates incorporate live scripts)
Duffing's Equations (Chaos theory)
In addition to the projects I have developed at Southern New Hampshire University and Fort Lewis College, I returned to the NCSU REU in 2014 and 2015 to introduce students to the typesetting language LaTeX and the mathematical language MATLAB. Resources for these introduction courses can be found the Resources page.