Teaching Philosophy
My primary goal as an educator is to facilitate students' academic and personal growth.
To do so, it is important that students encounter new experiences, be exposed to new ideas and perspectives, and learn how to constructively challenge their preconceptions.
The principles that guide the decisions I make include setting and supporting high expectations, active engagement, broadening perspectives, and continued personal development.
Recently, I have worked to incorporate social topics into my mathematics classrooms as examples of how mathematical thinking skills can help navigate our complex world.
If you are interested in more details, the most recent iteration of my teaching philosophy is available
here.
(Last updated Feb 2022)
Current Efforts
I am currently working to transition my assessment methods to a standards based grading system that emphasize grades reflecting understanding of concepts and motivates learning for the sake of learning.
When I have time to wonder, I think about what a mathematics major might look like without such a heavy emphasis on Calculus and how that could open new pathways into mathematics that no longer exacerbate inequities established by the K-12 education system.
Latest Approach for Courses Taught
- Mathematics for Liberal Arts: a smattering of mathematical topics covered primarily to explore non-computational mathematics in the world around us (i.e. partly for funsies) but also to support a student philanthropy project through NKU's center for Civic Engagement; topic discussions from Our World In Data lay groundwork for a course project where students find a dataset and create a vizualization to help analyze the data (as of spring 2022)
- Precalculus: a read-explore-practice cycle where students read sections of OpenStax textbook in Perusall prior to class, engage with Desmos interactives in class to explore topics covering algebraic, trigonometric, and exponential and logarithmic functions, and then practice through homework in WeBWorK; assessment via standards-based grading through small, frequent quizzes with opportunities for reassessment where a base grade during the semester is modified by understanding demonstrated on a cumulative final exam (as of spring 2022)
- Calculus 1: a read-explore-practice cycle where students read sections of OpenStax textbook in Perusall prior to class, engage with clicker-questions from the GoodQuestions Project at Cornell in class to explore topics covering limits, derivatives, and integration, and then practice through homework in WeBWorK; assessment via weekly quizzes with throwback questions and a final exam (as of fall 2019)
- Calculus 2: a read-explore-practice cycle where students read sections of OpenStax textbook in Perusall prior to class, engage via Socratic Lecture and individual/group work in class, and then practice through homework in WeBWorK; assessment via standards-based grading through small, frequent quizzes with opportunities for reassessment where the final exam period is used as a final opportunity to reassess standards (as of fall 2021)
- Calculus 3: a read-explore-practice cycle where students read sections of OpenStax textbook in Perusall prior to class, engage via Socratic Lecture supported by Mathematica vizualizations and individual/group work in class, and then practice through homework in WeBWorK; assessment via standards-based grading through small, frequent quizzes with opportunities for reassessment where the final exam period is used as a final opportunity to reassess standards (as of spring 2022)
- Linear Algebra: socratic lecture supported by homework practice and supplemented with exploratory Mathematica projects; "traditional" assessment structure of 3 midterms and a final (as of spring 2018)
- Intro to Proofs: a read-present-explore-write cycle where students read sections of open-source textbook in Perusall prior to class, present and peer-review proofs written in LaTeX, engage in more open-ended questions regarding topics/definitions from advanced mathematics courses, and then write proof for presentation in next class; assessment of proof presentations based on "journal referee recommendation" with semester culminating in proof portfolio written using LaTeX (as of fall 2021)
- Number Theory: an IBL problem-oriented approach where students "discover" theorems and prove them in class; "traditional" assessment structure of 3 midterms and a final (as of spring 2017)
- Discrete Mathematics: a read-engage-practice cycle where students read sections of the textbook before class, generate a list of topics to focus class discussions on, and then practice via homework; assessment via weekly, cumulative quizzes (as of spring 2020)
- Graph Theory and Combinatorics: an IBL problem-oriented approach where students are given definitions and work to "discover" theorems and prove them in class; assessment via frequent cumulative quizzes with semester culminating in proof portfolio written in LaTeX (as of spring 2020)
Previous Experiences
