PROCEEDINGS OF THE 21ST ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2018
San Diego, California
Generalisation, Assimilation, and Accommodation
Page: 1128
This paper builds theory by connecting Piaget’s assimilation and accommodation constructs to Harel and Tall’s (1991) framework for generalisation in advanced mathematics. Based on what they imagined to be the cognitive processes underlying generalisation, Harel and Tall proposed that generalisation might be expansive (occurring when a student expands the applicability range of an existing schema without reconstructing it), reconstructive (occurring when a student reconstructs a schema to widen its range of applicability), or disjunctive (occurring when a student constructs a new, disjoint schema to deal with a new context). I contend that expansive and reconstructive generalisation align with assimilation and accommodation, respectively. I provide ‘proof of concept’ using data from a study of students’ generalisation of graphing from R2 to R3. Further, I show how linking Piagetian constructs to Harel and Tall’s work provides a theoretical explanation for other empirical findings about generalisation