Calculus and sustainability

I saw a number of interesting talks while at the Joint Mathematics Meeting last week. Hopefully I’ll find the time to write about some of them here.

One of the presentations that got me the most excited was the minicourse that I attended, Educating about the state of the planet and sustainability while enhancing calculus, run by Tom Pfaff of Ithaca College.

Tom uses real-world data, Excel, and a little bit of modeling to enhance his traditional Calculus I class—the theme is sustainability (climate change, energy usage, etc.).

His idea is very slick. At the beginning of the semester he gives his students data in Excel spreadsheets. In a lab they find mathematical models to fit the data—mostly linear, quadratic, cubic, and exponential functions. Even this process is enlightening. It is wild to check out some of this data. For example, look at how China’s CO2 emission changes at the turn of the 21st century:


(He maintains a website with all of his data and assignments. He is always updating them and adding to them. Tom got this CO2 data from the Energy Information Administration.)

At the end of the lab the students decide on what the “right” function is for each data set. Then they have these functions in the bank for use all semester. Each time they learn a new idea in calculus they apply it to one of their functions and draw conclusions about what this mathematics implies.

What I like most about this approach is that it does not require a major re-design of the calculus course, nor does it push out other material. We can teach about derivatives, rates of change, integration, and as usual, but have the exercises come from this collection of functions. At our college we have a calculus lab each week. I could certainly see having a sustainability focus for all of these labs.

Tom says that he has gotten a lot of good feedback from his students about this approach. (By the way, he said that tries to be as politically neutral as possible and lets the data and the mathematics speak for itself.)

His website is set up for use with a Calculus I course. He said that he is working on doing something similar for a statistics course.

His website: Tom Pfaff’s Sustainability Page


  1. Gene Chase says:

    Read my first lab in Calculus 1, Part III.B, and my response. First lab is here. Answer key is

  2. samjshah says:

    Wow. Thanks so much for posting this. DEFINITELY worth investigating further for use next year.

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