Introduction to Abduction in Mathematics

Abstract

The five chapters that comprise this section of the book illustrate in both theory and empirical research how the nature, activity, and practice of mathematics could be grounded in inquiry, (surprising) observation, imagination, insight, creativity, invention, and everything else that emerges from abductive thinking and reasoning. These five chapters help make the case that the trivium of abduction, induction, and deduction is the core of inference making and validation in mathematics. de Freitas explores the process of creative abductive reasoning in the context of an ecological, anthropocentric view of mathematical practices, where mathematical activity involves using eco-cognitive processing and imagination in mathematical reasoning. Campos describes mathematical activity as a type of scientific abduction in inquiry and heuristic investigative contexts. Ernest describes ways in which abduction may occur in creative work among students in school mathematical contexts and among research mathematicians and underscores cognitive activities, metacognitive activities, and abductively driven intuitive activities in mathematical problem-solving. Using student data, Meyer illustrates how the meaning and context of discoveries are mediated by different types of abductions. Pedemonte illustrates ways in which an instructor’s abductive interventions may help decrease the distance between students’ argumentation and solutions to a problem.