Discussions in Calculus

I stumbled across this book called Paradoxes and Sophisms in Calculus when looking through my newsfeed on facebook. One of my college math professors had shared it from Mathematical Association of America website.

It includes difficult and interesting problems in Calculus. Many of the problems look false, but are in fact true. Although some may look true, but have some minor flaw. This makes students focus on common misconceptions and help them eventually deal with them. Many of the problems were historically important to the development of calculus. I think these problems can help students have a deeper understanding of Calculus.

Some teachers commented on the post saying they thought this would just make an already difficult subject more confusing. I could see this really confusing and not correcting misconceptions of American students. However these problems are just the challenging questions my Chinese students need. Now I think they may confuse some of the lower students that struggle, but I think the majority of my students will benefit from these questions. The top students that are constantly asking questions that go beyond the course basics would extremely benefit from these questions.

I hope to buy this when I am home in the States and bring it back to China. I am thinking of using the questions as a discussion piece. Where students will do a think, pair, share over the question. I think there are plenty of questions to fit in the curriculum. I may have them write down their answer to the question after the discussion and include it their in-class grade. They will be definitely good time killers and a good resource for in-class activities. I would like to maybe add them to the homework load, but I think I already have enough to grade. I may add them as homework in the second semester where I usually don't have enough things to grade because most of second semester is spent reviewing. I might have to look over the questions to see if one would make a good journal entry and make them journal entry questions. I could also periodically put them on quizzes or tests as extra credit.

I could use them in a multitude of ways, but I think it could really enhance the curriculum. It would allow the course to go beyond the AP test, but still give them a solid foundation of calculus that will only help them when the test comes.

I got invited to be a part of the curricular development team that  supports the math teachers that work for our company this June. I will share this resource with the team and try to make this available to the other calculus teachers that work for our company. I am planning to apply to work with the curricular development team next year and hope that I can use that time to make resources like this book available to my fellow coworkers.