The cost of calculus texts

As fall semester begins and students return to campus, I can’t help but reflect on the cost of textbooks, and challenge myself to think about how this affects my students and me.

Data from the Conference Board of Mathematical Sciences (CBMS) show that in Fall 2005, there were over 600,000 students enrolled in calculus on university campuses in the United States (http://bit.ly/SFeU8h).  This appears to be an increase of about 100,000 students from an estimate made in 1994 (http://bit.ly/SFegrp).

That’s a lot of calculus students.

If there are 600,000 again this fall, I am teaching 0.01% of those: 60 students in 2 sections of 30 students in calculus II.  Because my ongoing project only has the text for differential calculus complete so far, I will be using what my colleagues and I have traditionally used for the past decade or so:  the text by Hughes-Hallett et al that is often termed “the Harvard Calculus.”  Which is a really good text: well-written, intuitive, and with interesting problems.  But I just looked at my university bookstore’s web page.  New, the text is $189.95.  Used, $99.95.  Students can buy a solutions manual for $56.95 (new) or $34.95 (used).  Holy freaking cow.

I just checked on Amazon, where the same text sells new for $134, and used from $65.  As an aside, I wonder how many students actually pay the $50 markup over Amazon.  Crazy.  I imagine university bookstores are going to go the way of for-profit publishers.

I’m sure that by now my reader is thinking about the total expenditure by my 60 calculus students this fall, or perhaps by the roughly 600 calculus students at my university, or even by the 600,000 taking it nationally.  For round numbers, say that an average student spends $100 on a calculus text: the national college calculus cohort thus spends 60 million dollars.  As I said above: holy cow.

Now, the students I teach this fall will, I believe, each get $100 in value from their text.   (Also notable: most of my students took calculus I at GVSU, and each will have already purchased the text for that course.)  For nearly every class meeting, they will have a reading assignment to complete, and they will be consistently urged (required!) to read and study the text.  And, of course, there will be exercises; but, somewhat ironically, I will likely not assign any exercises from the text.  Instead, I’ll be using WeBWorK and its National Problem Library, in which nearly all of the Harvard text’s exercises are available.  So, because my department now has a WeBWorK server, I could actually assign my students exercises even if they didn’t have a text.

In closing, some questions:  how often have we instructors of mathematics used calculus textbooks primarily as a source of exercises?  And if so, is that worth $100?  Even as a well-used resource, is such a text really worth $100?  As we require our students to undertake these expenses, it behooves each of us to think carefully about how and how well we use these resources to impact our students’ learning.  In light of the exciting developments in free and open texts, as well as the ease of self-publishing, I’m inclined to think that the $100 expense is not nearly as worthwhile as it used to be.  Maybe that figure should be at most $10 or $20.

Coming up in my next post: a brief survey of existing free (or nearly free) calculus texts that follows up on a couple mentioned in Open Textbooks.

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Initial Public Offering: Differential Calculus

[Update in January 2013: in addition to an updated version of the differential portion of the text, I’m pleased to publicly share four additional chapters for integral calculus.  See the download page at my GVSU site and/or this post here on the blog.]

After working in seclusion throughout my sabbatical and sharing early drafts with a small and select group of colleagues, the past couple of weeks have marked a big change for me.  With this blog, a new Twitter account, an email to a major listserv I’m on, and a talk at Mathfest, I’ve been fortunate to have news of this project to reach a much greater number of people.  My sincere thanks to everyone who has shown interest so far, as well as to everyone who has helped spread the word.

Initially, I intended to make the materials available at this point in time by request only.  That is, rather than post the full .pdf, I’d just post a sample.  Folks could request the full version by direct email to me.  I suppose I wanted to maintain some semblance of control over who had access to the text, plus my curiosity pressed me to have some way to know who wanted to look at it and possibly use it.

In one of my conversations with Rob Beezer about his own free and open linear algebra text, he urged me: “Put it out there.  Even if it’s only half-baked.  Post the .pdf online.”  Even only a quarter-baked?  Sure.

So, here it is:  [Update in January 2013:  as noted above, the links below are not to the most up-to-date files, and they obviously don’t include integral calculus.]


The links are to shared Google docs and should open in your browser.  From there, you should be able to choose “download” from the File menu if you wish to download the actual .pdf to your own machine.  Anyone who has the link can access.

So, a very different sort of initial public offering.  But one I’m excited to have out there and for the conversation that hopefully follows.  If you choose to download the text or activities workbook and use one of them in any substantial way, I’d very much appreciate hearing from you in either a comment on this post or by direct email at boelkinm at gvsu dot edu.

Again, thanks for your interest.  May it be a great fall semester ahead.

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Open Textbooks

At Mathfest, I had the pleasure of meeting Rob Beezer and having some extended conversation with him.  Rob is a longtime proponent of free and open textbooks, as well as the author of one himself.  After my talk he said “You’re where I was 5-6 years ago.  We should talk.”  After sitting and listening and peppering him with questions for an hour, I’m immensely grateful to have someone in the same field with rich experience to turn to for counsel.

Rob works at the University of Puget Sound and is a leader in the free and open textbook movement.  He first shared a version of his linear algebra text in 2004.  About a year ago, he reached 750,000 page views for his website.  His story is a fantastic one.  And now he’s doing amazing work in terms of the digital delivery of his text; he told me that while he long used .pdf as his main delivery format, his big project of late has been to convert the entire project to html so that his primary output target can be “a web version, enabled by MathJax, knowls and XML source.”  The result is impressive, and the use of “knowls” is especially cool, as these provide a way for text to expand and retract seamlessly with the simple click of a mouse.

(When I look at Rob’s work, I think: what have I gotten myself into?  Clearly a lot of learning and hard work ahead … with much to aspire to.)

Beyond this one great example, everyone should know that the American Institute of Mathematics has a growing open textbook project.  One of the goals for the book I’m working on is eventually to get it endorsed by AIM.  At AIM’s open textbook site, you can find links to some of AIM’s approved texts, including Rob’s linear algebra text.  There are also two for calculus.  One is a long out-of-print text by Gilbert Strang of MIT, as well as a more modern one by David Guichard at Whitman College.  Strang’s text is free in .pdf format, but the source is not open.  Guichard’s .pdf is free, and the source is open.  Neither of these books suits my own personal tastes, particularly for engaging students actively in class, but both are great contributions to the diverse options out there for the teaching and learning of calculus.  And again:  both are free.

Strang’s text has long been posted online as one of the early contributions to the MIT Open Courseware Project.  My understanding is that MIT was one of the very first elite universities to make such resources available for free, which in some cases include video lectures.  For instance, you can watch Strang’s lectures from teaching linear algebra.  This is a spectacular free resource, not unlike the idea of Coursera and a previous post I wrote about Robert Ghrist’s upcoming calculus class.

All of these contributions are working to remove “access” as the limiting resource, and to bring the opportunity to learn deep, interesting, and important mathematics to anyone who has the time and the talent for it.

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Keith Devlin on Self-Publishing

“The procedure is so ridiculously straightforward, I can see no reason why anyone should ever publish another textbook a different way, given the huge expense of textbooks.”

Read the whole thing:  http://devlinsangle.blogspot.com/2012/08/the-future-of-textbook-publishing-is-us.html

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“The limiting resource should not be access, but rather time and talent”

On Saturday morning in Madison at Mathfest, I attended a fantastic talk by Robert Ghrist, titled “Putting Topology to Work”.  He has apparently given versions of this lecture in several other locations, including the Young Mathematicians’ Conference at Ohio State; from their site at http://www.ymc.osu.edu/2011/speaker1.php, you can watch a video of the talk.  Highly recommended.

The version of the talk that he gave at Mathfest had a different ending.  After sharing a bunch of really cool, cutting edge applications of algebraic topology, Robert said a question had plaguing him: “How do we bring these ideas to the people who can and need to use them?”  It seemed like he first had in mind engineers, but also undergrads, who both (in his opinion) should learn to think topologically, early and often.  He spoke about how when linear algebra was first introduced as a discipline, people derided it as abstract, arcane, and useless.  Some of the biggest early critics (physicists), are now the biggest end users of the subject.  And now we teach linear algebra to freshmen and sophomores (and sometimes even HS students).

Robert made the argument that he thinks algebraic topology will be a similar discipline; and stated that one of his goals is that within the next decade or two, students will have the opportunity to start thinking topologically much earlier in their education.  He has a plan for how he will try to impact that change through an effort to bring algebraic topology to the masses (ok, the really bright masses, but more masses than just math grad students).

To that end, he closed his talk by discussing his plans to start teaching calculus “the right way” (by which, he clarified, he meant “the topological way”) so as to start to engender sophisticated and topological thinking in his students.  He is teaching a Coursera class this fall (I think he said 26000 students (!!) are already enrolled — you can learn more at https://www.coursera.org/course/calcsing) and he is going to put some of his new ideas to work.  He has a very brief, very unusual, but very entertaining calculus book (FLCT – fun little calculus text) that you can find online at his website (and the book is very free!) at http://www.math.upenn.edu/~ghrist/FLCT/index.html.

There are a whole bunch of game-changers here.  Like other Coursera courses, the “masses” can study, for free, under the tutelage of a spectacular professor from one of the world’s top universities; calculus is being taught with way different goals and perspective, goals that are relevant for the 21st century and far afield from the relatively traditional calculus goals that most schools abide by; and Prof. Ghrist is making his written resources available free of charge.  Traditional universities and traditional textbook companies are both going to have to wrap their minds around this new reality if they wish to survive.

He closed his talk with a statement to the following effect (I’m paraphrasing, as I didn’t record it): “The limiting resource should not be access, but rather time and talent.”  I like that a lot.

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Updated Mathfest slides

Here’s a better link to the slides: .  (Thanks @mathhombre.)  And thanks to everyone who attended the talk.

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Mathfest Talk Slides

I am speaking in a contributed paper session at Mathfest today on the teaching and learning of calculus.  If you’d like to see the slides from my presentation, they can be found at http://faculty.gvsu.edu/boelkinm/Mathfest.2012.pdf.

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Where have we come from and where are we going?

While on sabbatical during the winter semester of 2012, I began drafting a free, open-source calculus text.  I undertook the project in part because I felt like there wasn’t an activity-driven text available, as well as because I don’t think anyone should make millions by selling a calculus text.

The book that is underway is different from most existing texts in at least the following ways:

– the text will be free for download by students and instructors in .pdf format;
– due to the electronic format, graphics are in full color and there are live html links to java applets;
– the text will (eventually) be open source — interested instructors can gain access to the original source files upon request;
– the style of the text requires students to be active learners … there are very few worked examples in the text, with there instead being 3-4 activities per section that engage students in connecting ideas, solving problems, and developing understanding of key calculus ideas;
– each section begins with motivating questions, a brief introduction, and a preview activity, all of which are designed to be read and completed prior to class;
– the exercises are few in number and challenging in nature.

The interested user should know at least the following things before adopting the text:

– this is very much a work in progress; the materials have not yet been piloted or reviewed.  I began the project essentially in January 2012.  I am learning about a variety of key issues as the work progresses.
– there is not a traditional set of exercises included; for now, it is essential to have access to WeBWorK or some other source of routine problems.
– I have not yet completed materials for integral calculus; these are currently in progress (in collaboration with two of my colleagues), with the goal of having a usable draft of the material for integral calculus in time for Winter 2012.

While I think the text could be used in place of a traditional differential calculus text for the coming semester, a more realistic alternative might be to use it as a supplemental text for students, or to just use the activities workbook:  the text is arranged so that all of the activities are embedded in the text, but can also be compiled in a separate document that provides students room to work.  An instructor could use as many or few of the activities as she found useful.

See the page on my website devoted to the text, or this earlier post, where you can find a link to download a sample chapter of the text (which includes the table of contents).

I will be using the blog as a place to post user feedback and gain further ideas/suggestions/edits through the comments that readers and users of the text provide, and hopefully this site will become home for a community of users who decide to use the text in some way.  I’ll also, of course, post updates regarding how the project is progressing.

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Project CAPABLE at USNA

Several professors at the US Naval Academy have an ongoing project of developing in-class and out-of-class activities and projects for students.  CAPABLE stands for Calculus Acquisition through Project and Activity Based Learning.  Check them out at https://sites.google.com/site/temporarycapablesite/, including the link to “syllabus by day”, for a host of possible activities and projects.

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Talk at Mathfest: “Toward a Freer Calculus”

I am speaking at Mathfest in Madison, WI, this Friday, August 3, at 1:45 in Meeting Room Q, as part of the contributed paper session on Teaching or Learning Calculus.

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