The transformation group has two ongoing complementary goals of 1) collecting and creating activities that help support foundational concepts in a transformation geometry context and 2) formulating an axiomatic system such that (a) its statements are accessible to both college geometry students and high school students and (b) the axioms lead to an efficient system of lemmas and propositions that can be used to deduce major congruence and similarity results. At its start over a year ago, goal (2) was the primary objective, but since then the group has been shifting its focus more towards goal (1). 

To advance goal (1) over the summer of 2020, members of the group presented activities from transformation geometry they had already created or seen. In the fall of 2020, the group read Transformational proof in high school geometry: A guide for teachers and curriculum developers by Douglas and Picciotto and decided for the spring of 2021 to try to use the structure of axioms, definitions, and basic properties in the document as a foundation for collecting and creating a coherent set of activities. It is our intent that using this document will provide a way to more clearly organize and sequence activities, including those that the group has already collected. This process will likely start with working on activities that support future teachers’ understanding of the early postulates and definitions in the document and move later to more complex proofs and properties. However, the group will also continue its discussion of ways to expand on the early structure of the document, including the addition of more axioms, definitions, and notation to support certain teaching goals. A long-term goal of this process would be to create a shareable document to aid instructors who currently use or want to use transformations in their GeT courses. 

The Transformations group meets every other Wednesday at 11:00 AM ET. The group welcomes new members.

References

1. Douglas, L. & Picciotto, H. (March, 2018). Transformational proof in high school geometry: A guide for teachers and curriculum developers. Retrieved from https://www.mathedpage.org/transformations/proof/transformational-proof.pdf