Types of Epistemological Justifications, with Particular Reference to Complex Numbers

Epistemological justification is one of the essential constructs of DNR-a conceptual framework for the learning and teaching of mathematics. In this chapter, I distinguish among three types of epistemological justification: (1) Sentential epistemological justification (SEJ). This refers to a situation when one is aware of how a definition, axiom, or proposition was born out of a need to resolve a problematic situation. (2) Apodictic epistemological justification (AEJ). This pertains to the process of proving. It is when one views a particular logical implication, a > b, in causality, or explanatory, terms-how a causes b to happen. This can take place in two forms. One might observe a, asks what are its possible consequences, and finds out that b is a consequence of it. Or one might observe b, asks about its causes, and finds out that a is a cause of it. (3) Meta epistemological justification (MEJ). This refers to a situation when one not only possesses SEJ and AEJ, but also he or she is aware of how the sentence or the implication came into being. These three types will be illustrated with examples from the field of complex numbers.