PROCEEDINGS OF THE 16TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION (Vol 2)
2013
Denver, Colorado
Entity versus Process Conceptions of Error bounds in Students’ Reinvention of Limit Definitions
Page: 2-234
We report results from a guided reinvention of the definition of sequence convergence conducted in three second-semester calculus classes. This report contributes to the growing body of research on how students come to understand and reason with formal limit definitions, focusing on the emergence of students’ understanding of the epsilon quantity, conceived in terms of error bounds. Using Sfard's framework of the condensation of processes to entities, we mapped the possible conceptual trajectories followed by the students in the study. In this report, we detail our map, these trajectories and students’ reasoning about other aspects of the formal definition, and the influence of reasoning about approximations and error analyses in students’ progression.