Publications

Collapsing dimensions, physical limitation, and other student metaphors for limit concepts

This study identified basic metaphors used by introductory calculus students to reason about limits and characterized how those metaphors influenced students' understanding of fundamental concepts throughout calculus. Approximation metpahors emerged as a potentially productive approach to supporting powerful student reasoning.

Layers of abstraction: Theory and design for the instruction of limit concepts

[preprint] [journal link] [reference]

This article reviews research literature about students' understanding of limits and various approaches to calculus instruction based on interpretations of this literature. It then outlines the instructional approach guiding the CLEAR Calculus project based on developing the central limit concepts in terms of approximations and error analyses.

Problems and solutions in students’ reinvention of a definition for sequence convergence

[preprint] [journal link] [reference]

This study engaged a pair of students in a "guided reinvention" of the formal definition of sequence convergence. They first constructed as many qualitatively different examples of sequences that converge to 5 and of sequences that do not converge to 5. We then engaged the students in multiple cycles of i) attempting to write a definition that included all of the examples and excluded all of the non-examples, ii) testing their definition against the examples and non-examples, iii) identifying problems with their definition, and iv) attempting to resolve those problems as they revised their definition.

Reinvention six months later: The case of Megan.