Before each section students are assigned a Preview Activity to complete at home. This is an idea lifted directly from Active Calculus. These activities are designed to introduce the main ideas of the next section in an intuitive and understandable way. Each class period begins by a debrief of the Preview Activity.
The majority of class time is dedicated to students working in groups on Activities. These activities lead students through the definitions, theorems, formulas, and strategies in each section of our textbook. It builds upon the work students already have completed in the Preview Activities, and usually culminates with some challenging problems.
All Preview Activities and Activities can be found below. They are sorted by textbook sections of Calculus 2nd Ed. by Jon Rogawski.
The most compelling way to explain most ideas in calculus is through geometric demonstrations. There are a few examples that are primarily algebraic (like derivative rules). As such, I have replaced most proofs with Geogebra demonstrations. Sometimes the Activity will instruct students how to create their own, but for more complicated demonstrations I will provide students with the file. You can find all my Geogebra demonstrations here. Keep in mind these include Calculus 1, Calculus 2, and Multivariable Calculus.
In order to give students exposure to some applications of calculus, I assign a simple group project. Each group is assigned a specific application selected from the textbook. Usually these are pulled from sections of the text not covered in class. The goal of the project was for each group to produce a video lesson introducing their application and going over some examples. To ensure all group members contribute, each group member was required to record a portion of the video. To encourage collaboration, they received a a single grade based on the overall accuracy and quality of the video. These videos were posted on the course Moodle for others to watch. To incentivize students watch these videos, I assigned extra credit WeBWorK assignments corresponding to each topic.
For example, in a recent Calculus 2 class the topics were:
Linear and Radial Density
Average Value
Flow rate
Fluid Pressure
Arclength