Employing Digital Tools for Collaborative and Flexible Mathematical Proving

Abstract There is a clear disconnect between the linear and deductive presentation of written proofs and the non-linear and messy process of constructing one. This disconnect poses challenges for students who do not often have opportunities, or the necessary supports, to navigate the transition between the two, quite often contributing to feelings of exclusion. It is therefore important to design learning environments with increased epistemic transparency, so that students can flexibly work on mathematical problems while learning and failing together. In this article, I present an instructional design for online collaborative proving activities for secondary school students. I discuss how the use of digital post-it notes and digital shared workspaces can create opportunities for multiple ways of participating for youth, support the navigation of different reasoning patterns, and provide space for extended across-group knowledge sharing. I share a classroom example of how this could look like in practice and discuss main implications of some of the affordances and constraints of the tools used for equitable and respectful student participation in mathematical epistemic practices.