In the spring of 2022, the transformation geometry working group advanced several of its on-going goals. One of the major goals of the past year has been collecting and creating activities and sequences of activities that contribute to student understanding of the topic of transformations. In the spring of 2021, the working group created a lesson that engaged students in an activity focused on the creation of mathematical definitions in a transformation context (Boyce et. al., 2021); this semester members of the working group presented on and retaught the lesson. Additionally, the working group continued its exploration of existing transformation teaching materials.

This spring, in 2022, several members of the transformation group collaborated on and completed the following presentations on the lesson study (Boyce et. al., 2021): 

• a GeT: a Pencil seminar on January 21st titled “Engaging Prospective Teachers in Defining Mutuality” by Steven Boyce, Laura Pyzdrowski, Ruthmae Sears, and Julia St. Goar;
• a presentation with the same title at the AMTE conference on February 10 by presenters Steven Boyce and Laura Pyzdrowski; and
• a presentation at the RUME conference on February 24 about the lesson study by Steven Boyce, Mike Ion, Ruthmae Sears, and Julia St. Goar within the context of the GeT: a Pencil working group, Improving Teaching and Learning in Undergraduate Geometry Courses for Secondary Teachers.

On April 14 of this year, Steven Boyce remotely re-taught the lesson in Matthew Shraeder’s class at West Virginia University, while several other members of the transformation group attended remotely. The transformation group discussed the outcomes of this iteration of the lesson and is currently considering new options moving forward with this lesson to make it a better fit for different types of GeT courses and to further deepen some of the lesson content.

Additionally, this semester the transformation group decided to focus on considering several different sets of existing course materials involving transformational geometry. This is a continuation of previous work considering course materials from sources like those by Douglas and Picciotto (2017). This semester, two different members of the transformation group, Priya Prasad and Yvonne Lai, volunteered their course materials related to transformation geometry for the purposes of discussion in the working group. Additionally, the group began discussing some of the materials on transformation geometry produced by MODULES(S²) (Alibegovic et. al., n.d.). In each case, one to two full meetings were devoted to each set of materials. Focuses of the discussions included a.) working to understand the teaching goals of each set of materials under discussion, as well as b.) (when applicable) considering the definitions and possible axiomatic structure used by the materials for both their mathematical accuracy and appropriateness in an undergraduate or high school setting. This second point of discussion relates to the transformation group’s ongoing interest in axiomatic systems based on transformations. These meetings on existing course materials were especially fruitful and, due to the large amount of content present in several of these sets of materials, will likely be the source of future ongoing discussion within the working group. 

References

Alibegovic, E., Anhalt, C., Aubrey, J., Casey, S., Cortez, R., Czap, L., Gobstein, H., Hart, J., Kohler, B., Lai, Y., Lischka, A., Maddox, S., Patterson, C., Ross, A., Strayer, J., Tuttle, J., & Weiss, M. (n.d.) Our Project. MODULES(S²): Mathematics of Doing, Understanding, Learning and Education for Secondary Schools. https://modules2.com/our-project/ 

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.