Two years ago in calculus, when I only had one section and only 7 students were in that section, I had each student work on an individual project during the 4th quarter. I helped each student choose a project based on their own interests and then they had a few weeks to work on them, and I would sometimes give them classtime to work on them.
Last year, I was given two calculus sections with many, many more students in it — and I couldn’t come up with a feasible way to ramp up this project idea. That year was devoted to trying to figure out how I could effectively teach to so many more students, who were all so varied in ability. (I did, however, had my kids do some amazing multivariable calculus projects.)
This year I still am teaching two calculus sections, but I feel like I have the course content way more codified. And my algebra boot camps are really working!  So I’m already contemplating what a final project would look like for my kids.
I think I will have students pick a partner and work on the project in a pair. And unless they come to me with a specific topic they are dying to investigate, I am going to give them a list of 3 or 4 projects they can choose from. I’ve been wondering what these projects might be, and I am leaning towards a few things that might appeal to those who are more artsy farsy. (Okay, who knows, I might give them 15 project ideas and have them make their own rubric.)
Some ideas that have popped in my mind (clearly they need to be really fleshed out):
1a. Write and illustrate a children’s book explaining calculus to someone in lower school (or, if you want, middle school). You then will present/read your story to actual lower school or middle school students
1b. Write and illustrate an “ABC”s of calculus book (e.g. L=Leibniz! Limit! L’Hopital!), explaining each term graphically or visually.
1c. Write a cogent response (with graphics) to this metafilter post. Be literary.
2. Research the uses of calculus in (architecture, physics, electrical engineering, chemistry, statistics, etc.). Interview someone who uses calculus in their work. Present your findings.
3a. Knowing what you know about calculus now, re-design the course. Explain what order you would teach things in, how you would introduce each unit, what sorts of assessments you would have and why, would you would expand upon, what you would reduce, etc.
3b. Rewrite a 3 day unit from the course. Make the smartboards, handouts, and assessments.
4. Create a visual map tracing the course from our origins (limits) to the end (surface area of revolutions). Explain in your map how various ideas and skills connect.
5. Now that you know more about calculus, revisit the ideas you briefly encountered studying the history of calculus. Do a more thorough and scholarly investigation of Newton and Leibniz and write a short paper explaining the similarities and differences in their philosophical approach to calculus.
6. Create video tutorials for 5 topics you found the most challenging in the course. You may use the SmartBoard. (This harks back to my Algebra II video project from two years ago.)
The point of this blog is for me to jot down ideas. (Some of them are terrible! But that’s brainstorming!) Let’s hope I can get a calculus project actually happening this year!
 How I know this first semester of calculus has been a success? I gave my kids their midterm last week, and the grades were way higher than expected. I was shocked that so many students were getting As. Good job kids! Good job!