Dr Cantley’s research has focused on mathematics education and the mathematical and philosophical foundations of educational measurement.

This research has included investigations into the influence of teacher attributes and organisational/societal factors on the pedagogical practices of mathematics educators and students’ mathematical learning. This has entailed research into aspects of mathematics education using the anthropological theory of didactics (ATD). A central pillar of ATD is a 'scale of levels of didactic co-determination', which represents a hierarchy of levels that govern how mathematics is actually taught in classrooms, premised on the fact that mathematics learning and teaching cannot be divorced from the broader organisational, societal and cultural contexts within which they occur. 

Recent work in this area has focused on the application of ATD, and Dewey’s theory of experiential learning, to investigate factors influencing curricular and pedagogical continuity during the transition from primary to post-primary mathematics education. Dr Cantley’s work has also included empirical research to investigate the influence of active learning approaches on students’ attitudes to mathematics, and some research into the theoretical foundations of educational measurement.

The principal objective of Dr Cantley’s research activity is to investigate ways of improving student achievement in, and attitudes towards, mathematics, while taking cognisance of the inherent limitations imposed by current assessment paradigms.