About CLEAR Calculus
Publications
Collapsing dimensions, physical limitation, and other student metaphors for limit concepts
[preprint] [journal link] [reference]
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.
[preprint] [journal link] [reference]
The use of dynamic visualizations following reinvention
[preprint] [journal link] [reference]
From intuition to rigor: Calculus students’ reinvention of the definition of sequence convergence
[preprint] [journal link] [reference]
Students’ reinvention of formal definitions of series and pointwise convergence
[preprint] [journal link] [reference]
Part / whole metaphor for the concept of convergence of Taylor series
[preprint] [journal link] [reference]
Strong metaphors for the concept of convergence of Taylor series
[preprint] [journal link] [reference]
Calculus students’ assimilation of the Riemann integral into a previously established limit structure
[preprint] [journal link] [reference]
Student understanding of accumulation and Riemann sums
[preprint] [journal link] [reference]
Approximation as a foundation for understanding limit concepts
[preprint] [journal link] [reference]
Strong and weak metaphors for limits
[preprint] [journal link] [reference]
Mixed metaphors: How students reason about limits in the calculus classroom
[preprint] [journal link] [reference]
Students’ reinvention of pointwise convergence for Taylor series
[preprint] [journal link] [reference]