PROCEEDINGS OF THE 23RD ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2020
Boston, Massachusetts
Framework for characterizing students’ reorganization of school mathematics understandings in their collegiate mathematics learning
Page: 358
In an attempt to address the problem of discontinuity between school mathematics and collegiate mathematics, the current study aimed at characterizing how university students’ previous knowledge constructed in school mathematics can be reorganized in their learning of collegiate mathematics. To this end, a construct called transformative transition and its accompanying categorical framework were developed and explained with student data. A transformative transition involves a qualitative leap in existing understandings as an individual encounters a new construct and integrates it into his/her cognitive system. Its four categories—extending, deepening, unifying, and strengthening—delineate different ways in which that qualitative leap might take place. Results from the analysis of interviews with six mathematics-intensive majors revealed that the context in which the participants could actively revisit, observe, reflect on, and interrelate their existing understandings at a higher level and from a different angle helped them to reorganize their school mathematics understandings.