“*Leveraging Students’ Intuitive Knowledge About the Formal Definition of a Limit*“

Presented by Aditya ‘Adi’ Adiredja

Graduate Group in Science and Mathematics Education (SESAME)

University of California, Berkeley

The formal definition of a limit, or the epsilon-delta definition, is a critical topic in calculus for mathematics majors’ development. It is typically the first opportunity for students to engage with rigorous and formal mathematics. Research has documented that the formal definition is a roadblock for most students but has de-emphasized the productive role of students’ prior knowledge and sense making processes. This presentation discusses the productivity of an instructional analogy called the Pancake Story, which was specifically designed to leverage students’ knowledge about *quality control*,* *in instruction. Data is drawn from videos of semi-structured interviews with 25 elementary calculus students. diSessa’s Knowledge in Pieces theoretical framework guides the study in uncovering the structure of students’ prior knowledge and its role in learning about the formal definition. A detailed case study of one student illustrates the ways by which many students in the study engage with the analogy to overcome a well-documented learning difficulty with the definition. Broadening access to this central idea in calculus and analysis is part of a larger effort to address the shortage of mathematics majors and STEM majors generally.

Refreshments at 4 p.m., Thursday, Feb. 6

Talk at 4:30 p.m. in Ed Ad 110