In the spring of 2021, the transformation working group created a lesson in the context of transformation geometry, taught and observed the lesson in a group members’ online course, and reflected on the implementation of the lesson. This effort resulted in a publication in the AMS Blogs (Boyce et. al., 2021). The lesson created by the group reflected a variety of content goals including that it should contribute to student understanding of mathematical definition, emphasize mathematical precision, and help develop a culture of sense-making, exploration, and justification.. A further goal was to create an introductory-level, inquiry-based learning lesson that could be easily adapted to be placed into a variety of different types of GeT courses and contribute to student understanding of transformation geometry. The lesson used Adinkra, which are symbols created in Ghana, from the resource created by Eglash et. al. (n.d.). 

Moving forward, the group will likely teach different versions of the above lesson in the GeT courses taught by transformation group members, reflect on how it went as a group, and modify the lesson accordingly. More broadly, the group will continue focusing on collecting and creating activities that support student understanding of foundational topics in transformation geometry. 

Parallel to the above goals the group has an ongoing goal of 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. However, instead of formulating the system from scratch, the group is currently exploring various existing axiomatic systems and definitions in transformation geometry (e.g., Douglas & Picciotto, 2017; Venema, 2006) and discussing their appropriateness and applications in the diversity of GeT courses currently represented in the transformation group.

References

Boyce, S., Ion, M., Lai, Y., McLeod, K., Pyzdrowski, L., Sears, R., & St. Goar, J. (2021, May 6). Best-Laid Co-Plans for a Lesson on Creating a Mathematical Definition. AMS Blogs: On Teaching and Learning Mathematics. https://blogs.ams.org/matheducation/2021/05/06/best-laid-co-plans-for-a-lesson-on-creating-a-mathematical-definition/ 

Douglas, L. & Picciotto, H. (August, 2017). Transformational proof in high school geometry: A guide for teachers and curriculum developers. Retrieved from https://www.mathedpage.org/transformations/proof/transformational-proof.pdf.

Eglash, R., Bennet, A., Krishnamoorthy, M., Sawyer, S., & Adali, S. (n.d.) Adinkra Background. Culturally Situated Design Tools. https://csdt.org/culture/adinkra/index.html 

Venema, G. A. (2006). Foundations of geometry. Pearson.