My typical mode of teaching is through Inquiry-Based Learning, aka IBL for short. The Academy of Inquiry Based Learning is a great resource on this subject. There's not one right way to teach with IBL -- it depends on the course and my students -- but the four pillars of IBL are:
Student Inquiry: Students engage deeply in rich mathematical sense making.
Collaboration: Students have regular opportunities to collaborate with peers and instructors.
Instructor Inquiry: Instructors inquire into student thinking.
Equity: Instructors foster equity in their design and facilitation choices.
Mathematicians work in axiomatic systems. We first state axioms and then build the rest of our theory, modeling, and practice from there. I like to think of axioms as a deep enduring feeling about what must be true.Â
I have incorporated the following four axioms for teaching, learning, and doing mathematics. The axioms below are originally attributable to Prof. Frederico Ardila.
Mathematical potential is distributed equally among different groups, irrespective of geographic, demographic, and economic boundaries.
Everyone can have joyful, meaningful, and empowering mathematical experiences.
Mathematics is a powerful, malleable tool that can be shaped and used differently by various communities to serve their needs.
Every student deserves to be treated with dignity and respect.
MTH106. Calculus Foundations (stretch calculus, part 1)
MTH121. Linear Algebra.