Nested syntheses: a complexity-informed approach to incommensurability in mathematics education

Abstract

We address the challenge of theoretical fragmentation in mathematics education research by proposing nested synthesis as a complexity-informed approach for working with incommensurate discourses. We focus on situations in which theories are aligned in treating learning as a complex, multi-level phenomenon, yet differ in their objects, data, and explanatory commitments. We argue that theories such as commognition and conceptual metaphor theory can be construed as complexity-aligned discourses, each attending to distinct emergent aspects of mathematics teaching and learning. Through analysis of a classroom episode involving elementary students learning about decimal numbers, we demonstrate how commognition illuminates the development of shared routines and meta-rules, while conceptual metaphor theory reveals the role of metaphorical resources in shaping the understanding of number . Bringing these perspectives into relation, we show how interpretations generated within one discourse can constrain and re-specify those of another, without reducing their differences. We conclude by articulating preliminary guidelines for nested synthesis and discussing its implications for theoretical work in mathematics education.