The emergent consensus our community has reached on the student learning outcomes for geometry courses for teachers allows us to come back to one of the aspirations of the initial working groups in GeT: A Pencil–the creation of a task repository. Indeed, the collaborative curation of resources for teaching GeT courses could be a next step for our community to cooperate toward the goal of increasing capacity for high school geometry instruction. Along those lines, we hope to submit a grant proposal to support this work; this essay describes some initial thoughts on how that work could be framed. 

The notion of resources is key in this proposal. Trouche et al. (2020) elaborate what is meant by resources in the field of mathematics education thus:

a resource [is] anything likely to ‘re-source’ the teacher’s practice. It can be a textbook or a website …. Teachers search for resources, select resources and modify them; they use them in class, and this can lead to further modifications. … [T]his work is called teachers’ documentation work. (p. 1244)

Resources are tied to technologies inasmuch as they may be produced and modified with technologies. They are also tied to curriculum, inasmuch as curricula are canonical examples of resources, but the concept of resources in the context of instructional practice is more general. Furthermore, the resources approach spearheaded by Luc Trouche and his colleagues differs from approaches to curriculum use that emphasize central planning by authors and fidelity of implementation by teachers. It points to the dynamic interactions between teachers and resources⸺the latter informing the former, and the former modifying the latter, in ways similar to how Remi Llard (2005) had described some teachers’ interaction with curriculum materials as “participating with” curriculum materials (and contrasting with following, subverting, drawing on, or interpreting curriculum materials). Trouche et al. (2020) refer to the work that instructors do with resources as documentation, noting that the interaction with resources is projected in documents that, for example, attest to changes they made to resources or add observations made in the context of use that might inform future uses. 

With the assistance of the concepts of resources and documentation, we can describe more concretely what we could be producing in the next few years. First, rather than producing a textbook, I argue that we should shape a system that can support the documentation of resources for GeT instruction. Further, we should begin to make that system work by putting out resources that might enable individual instructors to pick and choose what would be serviceable for the course they want to teach and support the work of documenting instructors’ use. Second, to support the discretionary use of resources and their documentation, I argue that the final destination for the publication of those resources needs to be a digital platform that permits both instructors tinkering with, editing, and augmenting resources, the use of those resources with their students, and the observation of patterns of instructors’ and students’ use by the community, particularly by those of us interested in understanding how instructors shape resources. Third, the digital publication of these resources also permits us to conceive of the resources that get put out as supporting various kinds of documentation. The customization of a set of curricular resources to compose a course of studies is one canonical documentation, but other traversals of the set of resources are possible to envision as we realize that the documentation process may generate other resources, derivative of the curricular resources. 

To be clearer, if we think of a problem as a case of a resource that an instructor could choose to include in their course, other resources that support the use of that problem in class might be developed, linked, and consulted. For example, a set of tags that connect the problem to different SLOs can be one such secondary resource; hints for students that the instructor might provide access to are another example of a secondary resource. Information from research on students’ cognition that appraise the instructor of errors to be prepared to see in the context of GeT students’ work on the problem can be a third kind of secondary resource. Furthermore, materials derived from early uses of the resource (e.g., students’ work) can also be among these secondary resources, supporting other instructors’ anticipation of what students could produce. 

This brings us back to the design of a system that can support this documentation work: The work the community may get to do includes specifying the workflows and task descriptions needed for the community to produce all of these resources. This may include many of the activities often thought of as part of curriculum development process (e.g., drafting, disseminating, piloting, assessing outcomes, revising, etc.) but with a focus more on community and systems development through the production of resources than on the production of a final set of resources. A community like ours can organize itself for the work of continuously improving its instructional resources; this can be our next step in the trajectory toward improving capacity for high school geometry instruction.

References

Remi Llard, J. T. (2005). Examining key concepts in research on teachers’ use of mathematics curricula. Review of Educational Research, 75(2), 211-246.

Trouche, L., Rocha, K., Gueudet, G., & Pepin, B. (2020). Transition to digital resources as a critical process in teachers’ trajectories: the case of Anna’s documentation work. ZDM–Mathematics Education,  52,1243–1257. https://doi.org/10.1007/s11858-020-01164-8