Operationalizing authentic mathematical proof activity using disciplinary tools

Many educators advocate for students to engage in authentic mathematical activity – activity reflective of the discipline. In our respective design studies, we had a common goal of engaging students in authentic mathematical activity in relation to proof. However, we identified a need to better operationalize “authentic” and characterize student activity in relationship to the discipline in the undergraduate proof setting. We introduce the Authentic Mathematical Proof Activity (AMPA) framework 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.