Joseph Antonides

My research maintains three interrelated research agendas. First, I am interested in how students construct mathematical concepts, particularly with the domains of combinatorics, geometry, and logic. To frame this aspect of my work, I draw heavily on constructivist theories, especially action-object theories and theories of abstraction. Second, I am interested in how students’ constructions of mathematical concepts can be supported through equitable, inquiry-oriented instruction, particularly at the undergraduate level. I build, test, and refine learning trajectories (LTs) where qualitatively distinct ways of thinking about mathematical ideas are linked to specific instructional tasks and strategies hypothesized to support student thinking about that mathematical idea. Third, I am interested in comparing and unifying compatible theoretical perspectives on students’ mathematical thinking. In doing so, I aim to (a) build bridges across differing perspectives and potentially leverage each theory to the enhancement of the other, and (b) apply unified theoretical perspectives to develop increasingly accurate and reliable explanations of students’ reasoning.