Abstract:

Tall and Vinner’s (1981) theory of concept images and concept definition, that is grounded in Piaget’s (1971) theories of knowledge acquisition and cognitive development, provides a modified and a more suitable approach to students’ learning of Mathematics. According to Tall and Vinner concept images included the “conceptual conglomerations” associated with a student’s previous experiences with the concept. These personal, mental images of a concept are often at odds with its concept definition that is accepted by the mathematics community. The misconceptions influenced by such concept images continue until these images align with the concept definition. Different students attain concept equilibrium at different paces with the scaffold of unique, but achievable further involvements with the concept. These diverse involvements with concepts could mitigate the inequalities posed by the cognitive and affective domains associated with mathematics learning (Oehrtman, 2008, 2009, 2020; da Fonseca, 2020; Czocher, 2014; Nair, 2010; Elstak, 2008). This talk will highlight certain calculus concept images held by university sophomore students and how concept modification was accomplished through equitable and inclusive methods of instruction that every instructor could easily adapt to. The research discussed here is informed by the teaching experiment methodology as described by Steffe (2000).

Keywords:

Math inclusiveness, math equity, math teaching experiment, concept images, concept definition.