One of the most commonly discussed goals of the GeT Support Project is working collectively to improve the instructional capacity for high school geometry. It makes sense for this to be a point of common discussion for us, as it is the goal to which the Get: A Pencil community is collectively committed. There is, however, a second, equally important goal of the GeT Support Project: developing an inter-institutional network of support for instructors of the undergraduate GeT course. As conveners of the GeT: A Pencil community, the GRIP lab has been keenly aware of our responsibility to observe and support the community’s progress toward this second goal. After all, without the establishment and maintenance of the GeT: A Pencil community, it will be quite difficult to make progress toward the goal of improving the instructional capacity for high school geometry. Because of this, many of our internal reflections, conversations, and decisions at the GRIP lab have been animated by this second goal. 

Internally, we have found the forming–storming–norming–performing model of group development (Tuckman, 1965) useful for trying to understand both what we are observing in the community, as well as what changes in the community we should anticipate to be on the horizon. When we first began together as a community in June of 2018, Tuckman’s forming stage described our community well—with individuals engaging in introductions with a certain amount of eagerness and excitement as well as anxiety. Similarly, our first year together was fairly well accounted for by Tuckman’s storming phase of development. In this phase, it is typical for a group to experience some amount of conflict, competition, and drop offs in participation. This is because a storming group has moved past simply exchanging pleasantries into the identification of real issues facing the group. While these issues have a way of surfacing conflict, they also have a way of getting a group ready for the norming phase—with individuals electing to work together, in spite of their differences, to collectively seek the resolution of the issues they have identified.

In the norming phase of development, a group learns to resolve the kinds of personality conflicts that characterize the storming phase by learning to accept one another as they are in order to work collectively towards a common goal. Until recently, I felt pretty confident that the GeT: A Pencil community had been mostly operating within this phase. But in some of our recent reflections about the work people are doing within the GeT: A Pencil community, I felt it quite likely that we have turned the corner in some crucial ways—with the group engaging in activities more akin with what Tuckman described as the performing stage of a group. 

In the performing stage, a group benefits from previously established norms and is able to achieve high levels of success towards meeting the goals they set out for themselves. Such a group is now able to operate in ways that are fairly autonomous, needing less of the kinds of supervision or organization they originally could not muster on their own—with the organization hierarchies that may have been crucial in the early stages being much less visible and prominent. I’d like to take this opportunity to illustrate my point by taking a brief tour of some of the work that is happening in the community.

In the last year, the Teaching GeT Working Group has elected to set aside differences in their individual courses to work together towards a common set of student learning objectives (SLOs) for the undergraduate GeT course. Although the processes the group has used have been marked by consensus-seeking from the beginning, the group’s interactions make it clear that dissent is not only an allowable part of the process but a necessary and crucial aspect of their work for the continued refinement of the SLOs for broader dissemination and consumption. Some of the artifacts this group has produced can be seen in this issue’s articles entitled GeT Course Student Learning Outcome #8 and GeT Course Student Learning Outcome #10, as well as the Working Group Update provided by the group’s facilitator, Dr. Nat Miller. This group also recently gathered to find avenues to disseminate their work—managing to submit two conference proposals and one handbook chapter proposal in the last six months.

Similarly, the Transformations Working Group has brought together individuals to think together what it might mean to teach geometry using a transformational approach. In this group we have seen the members grow in greater intimacy as they have voluntarily elected to open up their classrooms to one another through a series of virtual classroom observations. More than that, the group elected to do this using a process called lesson study in which the group collaboratively developed, implemented, observed, reflected on, and refined a set of lessons for teaching transformational ideas using the Adinkra patterns (see Babbitt et al., 2015). Remarkably, the choice to center a set of lessons on the Adinkra patterns emerged from an idea in the group, rather than from an area of expertise that any of the faculty members had previously developed. We see this as an important indicator of the group’s willingness to be vulnerable with one another and take risks—moving past the more typical norms of competing and showcasing that can sometimes go along with lesson study in the U.S. (Rappleye & Komatsu, 2017). Like the other working group, this group has begun to disseminate about their work—producing two conference proposals and posting a note on one of the AMS Blogs (Boyce et al, May of 2021). Dr. Julia St. Goar provides an update about the current happenings of the group in this issue’s Working Group Update.

We also note that for the first time since the GeT: A Pencil community formed, we, as members of the GRIP lab, have been able to make time to facilitate a series of workshops within the community. Up until now, we have had our hands full handling the administration and organization of the community—expending most of our effort making sure that things are running smoothly. But this past year, at the request of the community, we engaged in the development of items for assessing the SLOs—piloting those items with a set of GeT students this spring. This summer, we felt the other two working groups were operating autonomously enough for us to have the needed bandwidth for our team to run a series of workshops focused on engaging instructors with those items as well as the responses we gathered to them this spring. More information about those items and what we are learning through those workshops can be found in this issue’s articles entitled “From Theory to Practice: Development of the SLO Items”(Ion & Herbst, 2021) and “A Deeper Dive into an SLO Item: Examining Students’ Ways of Reasoning about Relationships between Euclidean and Non-Euclidean Geometries ” (Herbst & Ion, 2021).

Finally, alongside the evidence we see in these bodies of work, the interactions between instructors also provide evidence that we have, indeed, turned a corner as a community. In this issue, Dr. Carolyn Hetrick, a recent graduate whose research focuses on community organization and a postdoctoral scholar at the GRIP lab, shares about some of the changes she has observed in her re-entry into the community after being away for several years. 

Our community’s shift into the performing stage of development has some important implications for our future work—including the creation of some exciting opportunities we see emerging on the horizon. One of the opportunities that we envision is a conference with a different kind of participation from GeT instructors than we envisioned for the June 2018 conference. For example, we can imagine a future conference that is organized by a committee made up of members from the GeT: A Pencil community, rather than planned solely by the GRIP. If you are interested in potentially playing a role to help shape a future conference, let us know. 

References

Babbitt, W., Lachney, M., Bulley, E., & Eglash, R. (2015). Adinkra mathematics: A study of ethnocomputing in Ghana. Multidisciplinary Journal of Educational Research, 5(2), 110-135.

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.

Herbst P. & Ion M. (2021, November). A Deeper Dive into an SLO Item: Examining Students’ Ways of Reasoning about Relationships between Euclidean and Non-Euclidean Geometries. GeT: The News!, (3)1.

Ion M. & Herbt P. (2021, November). From Theory to Practice: Development of the SLO Items. GeT: The News!, (3)1.

Tuckman, B. (1965). Developmental sequence in small groups. Psychological Bulletin. 6(3), 384-399.