Authentic Mathematical Proof Activity: What is it and how might we study it?

Many educators advocate for students to engage in authentic mathematical activity—activity reflective of the discipline.  This has been a substantial guiding pillar of the design-based research of myself and my colleagues. However, we did not find that “authentic” in proof based settings was operationalized in a way to guide fine-grained design and analysis decisions. In this talk, I will share the Authentic Mathematical Proof Activity (AMPA) framework developed as a theoretical tool for researchers interested in taking a multi-dimensional approach to documenting authenticity in students' proof-related activity. The framework provides both a means to deconstruct activity systems in terms of tools and objectives of the professional mathematician community and a set of dimensions (agency, authority, alignment, complexity, variety, and accuracy) to account for differing elements of authenticity related to both student and disciplinary aims.