Epistemological Justification

"Epistemological justification" is a way of thinking that manifests itself through perturbation-resolution cycles revolving around the question "why and how was a piece of mathematical knowledge conceived?" The paper offers a conceptual framework for constituent elements of epistemological justification. The framework provides: (a) a theoretical basis for epistemological justification, (b) criteria for its occurrence, and (c) analysis of its relation to "mathematical explanation." The criteria are illustrated by a series of learning-teaching events taken from teaching experiments aimed at investigating the learning and teaching in linear algebra. The contribution of the proposed framework is three-fold: (a) it addresses a critical aspect of proof understanding not explicitly addressed in the literature; (b) it goes beyond the traditional treatment of mathematical understanding and production into questions about learners' conceptualization of the origins of mathematical knowledge; and (c) it theorizes instructional approaches that can advance this conceptualization among students.