PROCEEDINGS OF THE 23RD ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2020
Boston, Massachusetts
Development of students’ shared understanding in guided reinvention of a formal definition of the limit - from commognitive perspective
Page: 458
This paper examines the mechanism behind students’ guided reinvention process of a formal definition of the limit of a sequence by looking at how students’ shared understanding develops and what discursive rules enable such development using the commognitive approach focusing on the relationship between routines (discursive rules) and changes in endorsed narratives (shared understanding). A Calculus II instructor conducted a teaching experiment in which 11 students reinvented a formal definition of the limit starting from their initial statement about the sequence convergence, mainly including dynamic language such as “approaching.” In our analysis, we identified the routines about the application of the definition in examples and non-examples, and the consistency between written and illustrated form of their definition, and the readers of the definition, and how those routines contributed to the changes in students’ endorsed narratives about sequence convergence during the guided reinvention.