This talk will discuss the role of diagrams in geometric proofs.  I will discuss some of the history of the use of diagrams in proof, leading up to a twentieth century bias against the use of diagrams.  More recent work reveals that we can understand precise rules by which diagrams can be used in geometric […]

I started teaching geometry for teachers course in 2006 and taught it on and off for the following 10 years. When I first started teaching the course, I had no formal training or knowledge of teaching, other than two workshops I went through as a graduate student and a postdoc. Over those ten years, I worked with […]

The nature of geometry makes it an ideal subject to introduce students to the fascinating ideas that underlie mathematics. In the Topics in Geometry course at Juniata, we build Euclidean geometry from the ground up using the 15 axioms formulated by Hilbert. Though the course follows a traditional axiomatic approach to geometry, it utilizes active […]

In our presentation, we share details about the MKT-G instrument we administer to GeT students before and after they take the GeT course offered by instructors in the GeT Support community. So far, the instrument has been taken by 518 students from 31 GeT courses. Among the 518 students, 380 students took both pre- and […]

How can we help our students begin to grasp the idea(s) of hyperbolic geometry, specifically a geometry with constant negative curvature—everywhere—that strongly shows the independence of Euclid’s Fifth Postulate for Euclidean geometry. There have been several models of hyperbolic geometry that mathematicians use—Poincare disk, Poincare half plan, Beltrami pseudosphere, and others, but students just beginning […]

In this seminar Gloriana González and Christine Rinkerberger will share teachers’ perspectives about geometry problems that are situated in visual arts contexts. They will engage the participants to consider geometry teachers’ knowledge of students, mathematics, and pedagogy that they bring to bear in their evaluations of textbook problems. The aim of this seminar is to […]