About

Manipulative Calculus is a project at Harvard University in which we are constructing 3D models and manipulatives to be used in active learning lessons in our calculus course sequence. In these lessons, we put models into students' hands, and they are asked to make geometric sense of the concepts learned in the course through problems requiring them to handle, discuss, and sketch on the models.

The current focus of the project is on Math 21a -- Multivariable Calculus. In the Spring 2018 semester, we piloted several lessons and activities with small groups of students. Using what we learned, we carefully refined our lessons and model designs, and spent the summer scaling production to approximately fifty of each model, enough to accommodate all of the students who take Math 21a each semester.

In the 2018-19 academic year, the models and lessons were fully integrated into Math 21a. With a typical enrollment of 300-400 students, the course is taught by graduate students and faculty in coordinated sections of approximately thirty students each. During the semester, the instructional team is trained in using the models in the active learning lessons we have planned.

For the Fall 2019 semester, we are adding models and lessons to support Math 1b -- Integral Calculus.

To learn more about the design and production of the models we are using in the course, visit the Models page.

For sample lessons and instructor reflections from the Fall 2018 semester, visit the Lessons page.