An Intellectual Need for Relationships: Engendering Students’ Quantitative and Covariational Reasoning

Abstract

Drawing on Harel’s construct of “intellectual need” (1998, 2008b, 2013), I propose an expansion in possible categories of such needs, to include an “intellectual need for relationships.” This is a need to explain how elements work together, as in a system. Broadly, I offer Freudenthal’s (1973) term, “mathematizing,” to describe a category of a way of thinking that can emerge from an intellectual need for relationships. I argue that this need can engender students’ quantitative and covariational reasoning, important not only for their mathematical development, but also for being informed citizens. I put forward four facets of an intellectual need for relationships, addressing task design considerations for each: attributes in a situation (What are the things?), measurability of attributes (How can things be measured?), variation in attributes (How do things change?), and relationships between attributes (How do things change together?). I conclude with implications for theory and practice.