Focus: SLO 9 and SLO 4 (tangentially)

by Bob Bell

The Wednesday GeT Working Group has been discussing SLO 9: Non-Euclidean Geometry and SLO 4: Axioms & Models. The group consists of five community members (S. Greenwald, R. Bell, T. Mingus, D. Dumitrascu, and K-H. Roh). We are working towards common goals of (1) creating activities (to be published open-access) for the community and (2) revisiting the SLOs on a deeper level. We met three times this semester, once to organize and twice to respond to specific prompts. In our November meeting, we shared the topics and activities that we use when we first introduce GeT students to non-Euclidean geometries. In our December meeting, we shared how we communicate to future geometry teachers the reasons why we study non-Euclidean geometries and why the study of such geometries is important. We are next scheduled to meet on January 15, 2025.

Please reach out to the facilitator, Bob Bell (be****@*su.edu), for more information.

Focus: SLO 9 and SLO 4

by Mara Markinson

In fall 2024, we convened the Thursday Working Group on the third Thursday of every month. This group is composed of pure mathematicians, mathematics teacher educators, and high school mathematics teachers. We are building on the work of the ESLO group, which met over the 2022-2023 and 2023-2024 academic years to first read and provide commentary on each of the ten SLOs, and then propose and examine geometry tasks specifically targeting SLO 3. This collection of tasks was saved in an online folder and is serving as an instructional resource for the members of the group. This year’s group is primarily focused on SLO 6, and is revisiting each of the tasks proposed and analyzed by the ESLO group from an “SLO-6 lens”. For each task, we are discussing ways to implement the use of dynamic geometry environments and, when applicable, digital proof tools. For our first meeting, we discussed the Midpoint Quadrilateral Task which leads to Varignon’s Theorem and for our next meeting, we will discuss a paper folding reflections task. Our group is always open to new members – reach out to the facilitator, Mara Markinson (ma************@*****ny.edu), for more information.

Focus: SLO 8 (construction) along with SLO 1 (proof)

by Tuyin An

Our working group meets bi-weekly on Friday afternoons from 2-3 PM. Due to the availability of our group members, our working group has met twice so far and will meet one more time by the end of this semester. During the first two meetings, we established the focus of the group: geometry constructions (SLO8) along with proofs (SLO1).

We have set the following tasks for the rest of this semester: gather resources related to geometric constructions (articles, books, websites, tools, etc.), and brainstorm a possible scholarly product to support our publication needs. Additionally, we attended Dr. McDaniel’s GeT seminar in November to learn more about his construction-focused work.

Starting as a relatively small group, we aimed to expand our membership to include more expertise. We reached out to a few GeT community members who we know have a passion and expertise in geometry constructions and invited them to join us. We are now a group of six members (listed alphabetically): Tuyin An, Erin Krupa, Michael McDaniel, Nathaniel Miller, Laura Pyzdrowski, and Steve Szydlik (who will join us next semester). We are hopeful to establish more concrete goals in our next meeting this month. The meeting time is Dec. 13 from 2-3 PM. We will resume our group meetings next semester in January. Anyone interested in this topic is welcome to join us!

Please reach out to the facilitator, Tuyin An (ta*@*************rn.edu), for more information.

Winter 2024 – Transformation Group Update

by Julia St. Goar

In the summer and fall of 2024, the transformation group mainly focused on creating a sequence of lessons that GeT instructors could insert into their course to teach the proof of the Side-Angle-Side (SAS) triangle congruence criterion from a transformation perspective. Work on this front has proceeded in several ways. First, the transformation group reviewed several ways that the SAS proof could be written, especially based on the axiomatic structure and context of the course. The initial goal here was to select one axiomatic structure and proof approach that our lesson sequence would focus on, but since then the group has settled on the idea of creating at least two versions of the lesson plan that would accommodate some of the different ways of structuring previous properties and axioms. Second, the transformation group has worked on viewing different ways instructors and various sources have taught the SAS proof and some of the background material in these contexts. One interesting concern that came up here was that some instructors made extensive use of technology, while others indicated they wouldn’t reasonably be able to incorporate a lesson with such significant technology without extending the length of the sequence of lessons. Currently, a version of the lesson that doesn’t involve technology is more extensively developed, but the group plans to look into ways to incorporate more technology, either as a separate version of the lesson or as one that accommodates a variety of needs.

This semester, Kevin McLeod is incorporating a version of the SAS lesson sequence into his GeT course, so the group will discuss how this iteration of the lesson went for the purposes of modifying the SAS sequence. The group plans to work to accommodate further instructors in the group who may be interested in incorporating a version of the lesson sequence into their GeT courses as well. Furthermore, group members have been writing reflections after each meeting so that the group can later take a broader look at how the process of collaborating to create the SAS lesson sequence has gone.

In the upcoming semester, we plan to continue the above-described directions of work.

Please reach out to the facilitator, Julia St. Goar (st*****@*******ck.edu), for more information.