- What did you enjoy about teaching geometry?
I taught geometry to two different audiences:
Math majors with some inclination to proceed to secondary teaching or a graduate program in mathematics.
Students taking mathematics to fulfill some general education requirements for a bachelor’s degree.
In different ways, what I enjoyed in teaching both these groups was seeing the positive energy and enjoyment when these students would see something deeper in the topic under discussion.
For the math major, it might be in seeing the power and generality of projective and hyperbolic geometries and their transformations both synthetic and algebraic connecting the axioms of Euclid to Descartes and Hilbert.
For the general education student, it might be in realizing the ability to use transformations to classify symmetries or projective geometry to understand perspective in art, or the freeing experience of beginning to comprehend the nature of dimension.
- What was it like for you to teach future secondary teachers?
Teaching future secondary teachers was a challenge because some of them had only a minimal background and experience with geometry. Seeing them make progress in understanding the many complex interrelations between the manifold approaches to geometry and the rigorous axiomatic underpinnings made me hopeful that they had learned more in being able to explore geometry and mathematics further beyond this single course.
- What are you most interested in learning/achieving through participating with the GeT: A Pencil community?
I am most interested in seeing that the SLO’s being articulated for the GeT courses are a rich resource for instructors of these courses to draw upon as they design their own courses to fit into their programs to educate future secondary teachers.