We offer an analysis of calculus assessment items that highlights ways to evaluate students' application of important meanings and support their engagement in generative ways of reasoning. Our central aim is to identify characteristics of items that require students to apply their understanding of key ideas. We coordinate this analysis of…

We present adaptable activities for models of drug movement in the human body -- pharmacokinetics -- that motivate the learning of ordinary differential equations with an interdisciplinary topic. Specifically, we model aspirin, caffeine, and digoxin. We discuss the pedagogy of guiding students to understand, develop, and analyze models,…

This article presents an extended analogy that connects infinite sequences and series to the science of genetics, by identifying power series as "DNA for a function." This analogy allows standard topics such as convergence tests or Taylor approximations to be recast in a "forensic" light as mathematical analogs of genetic concepts such as DNA…

Discusses and provides sample lessons of learning by discovery and weekly problem sets, which are presented as alternative methods for teaching college calculus. Both approaches stress conceptual understanding and guide the students to explore the ideas of calculus in small groups in a computer laboratory setting. (JJK)

Discusses the rationale and a method for the instructional use of graphing calculators as an intermediary step between the intuitive notion of the concept of a limit and its formal epsilon-delta definition. (JJK)

This paper describes a sequence of lessons from two Calculus I classes for teaching the epsilon-delta definition of a limit. In these lessons, the author elicited students' misconceptions and perceptions of this definition through a reading/writing lesson and then used these student ideas to design a lesson aimed at addressing these misconceptions…