For the past three years Occupy Math has been working on a calculus text for the integrated first-year math and physics course he co-designed. The regular books did not have the right topics in the correct order. This post announces that the book is ready. It is the second edition (now with far fewer errors!) We used the book last year and found a need to revise and extend. The book is not a standard calculus book and the rest of the post is about that. The big points are: we got the cost down to less than half that of the book it replaces. It covers all the topics of a standard first year calculus course for science majors. The presentation is different based on decades of experience with what does and does not work.
What goes in a calculus book?
The whimsically minded among Occupy Math’s readers will have already muttered “calculus?” Correct, but there are a lot of choices to make. The big issues you need to look at are these:
- How much will the students need to review their algebra?
- What sort of student is the book for?
- Do we present the elegant but daunting theory underlying calculus?
A number of recent articles have explained that mathematics teaching is in disarray. In fact we have a fairly serious problem with math teachers not being well trained in math. Given this, Occupy Math has always found a need for a brisk review of the basics and the first (long) chapter reviews lines, quadratics, equation solving, logs, exponentials, and the trig functions. In the present situation a large algebra review is usually needed.
The students: threat or menace?
The question “what sort of students is the book for” is a key one. There are several flavors of calculus course. Occupy Math’s least favorite is the course for people in majors that don’t use much math; many of these students are terrified of math. Next up the ladder of fun courses is business calculus where the students vary from people who should major in math to people who are in real danger of being indicted for fraud if they don’t fix their attitude. The business courses have the highest percentage of students that will do any amount of work to avoid doing a little work. The topics for this class are also pretty different. Geometric series for finance and derivatives get called “marginals”.
The third major group is biology students. Occupy Math has been the course coordinator for a biology calculus course at Iowa State University. He was hired into an endowed chair to do bioinformatics at Guelph. The students in these courses are typically willing to work and have tolerable to excellent organizational skills. They are, unfortunately, enriched with people that are terrified of math and who incorrectly imagine that math is not used in biology. This course is also different from standard calculus. It often has topics, like difference equations, that don’t show up in other calculus courses.
The fourth group is math and science students — that is the group Occupy Math’s current book is for.
A harder course that students pass more often?
Occupy Math’s book is entitled “Fast Start Calculus for Integrated Physics.” The physics department used to complain that we taught calculus techniques a year after they were needed for physics courses. They also taught the calculus they needed in a somewhat whimsical manner that caused a need to help our students un-learn some bad habits. Occupy Math teamed up with physics instructors to design a course where the calculus is taught just-in-time for the physics course and the physics serves as a coherent anchoring example for the calculus. The course is double credit and covers three semesters of calculus in two semesters to meet the needs of physics.
Sound terrifying? Normally between 20% and 40% of the students either drop or flunk first year calculus. Occupy Math’s much harder course has run six times. The median number of students lost is three, the maximum is seven. A loss of 20% would be twenty-four students. This suggests that the integration of calculus and physics, the new topic order for the calculus, and the increased speed make the course far easier to pass. A big part of this is that people attend the course and keep up with the work. There is no “I’m bored” zone — and that zone is the biggest enabler of starting to skip class and then flunking.
When do we make the mandatory trip to hell?
The general purpose, business, and biology courses either avoid or slight the underlying weirdness and power that makes calculus work. There is a quite unintuitive type of proof called an epsilon-delta proof that is the core of the theory behind calculus. In math it is traditional to present topics in the order in which they logically arise, moving from understanding to understanding in a defensible logical chain. While, in general, this has served us well, it leads to an act of insanity: teaching people epsilon-delta techniques in the first two weeks of their University career.
Occupy Math has done the experiment. Eighteen-year-olds, newly freed from parental control, in an environment with enhanced access to alcohol, no curfew, and lots of other people the same age looking to explore the possibilities have diminished mental capacity until they calm the heck down. In service of this issue, the theory of calculus has been moved to week eight of Occupy Math’s course — substantially increasing the chance people will get it. The other topics have been re-ordered as well and there is far more emphasis on making topics work together. This shows both in the integration with the physics taught by Occupy Math’s co-instructor and in having lots of call-backs in the homework and examples that show how topics are connected.
The battle against insane textbook prices
One of Occupy Math’s big goals in writing this book is price control. A university education is expensive and, because it is viewed as a pre-requisite to success, people will pay. This has tempted textbook companies to go too far. Occupy Math paid $17 for the book he used to learn calculus from. Last time Occupy Math assigned a calculus book, the new book price was $140 and a used book was $90 (a better used price was available at the co-op bookstore, see if your campus has one). Occupy Math’s book is $60 Canadian and $50 US through the Amazon Createspace store. This allows us a profit that will help get the cheap textbook initiative in the air, but it is less than half what it was before. Support the revolution! Buy my book! Or, at least, see if your institution is interested in dropping costs and making students (and their parents) a little happier.
Occupy Math is a little unhappy that the price point we arrived at by rational calculation is three times what he paid as a student. There has been inflation and we are trying to put the money to work in service of good goals, but it still feels a little bit wrong. It’s also true that a solid but reasonably priced book is only a small part of effective teaching.
Is Occupy Math a hypocrite?
Readers of Occupy Math may well have seen the TED talk about why we should be teaching most students something other than calculus. It is linked at the bottom of the about Occupy Math page. This book is for the science majors who should be taking calculus. Beyond that, rolling back the “advanced math is calculus” band-wagon will take years if it happens at all. Occupy Math promises that the profits from this book will be used to help the crusade. To be specific, they fund the start up of the consulting company that writes cheap textbooks and helps Occupy Math keep things going. In the meanwhile, this book will substantially improve the student experience in Occupy Math’s own course — financially and pedagogically.
The creation of this book has been an adventure — but we are well started on the next one, an inexpensive business math and calculus text. This is also for a course developed by Occupy Math in collaboration with five faculty from the College of Business. Occupy Math is doing reasonably priced basic math books through his consulting company and advanced books via his publisher Morgan and Claypool. One big goal is to get textbook prices headed back in the direction of sanity. Do you have a text that you would like to see written? Do you have stories about outraageoouus book prices? Do not be shy, please comment or tweet!
I hope to see you here again,
University of Guelph,
Department of Mathematics and Statistics