Is Calculus MOOCable?

There’s been lots of discussion in higher education regarding the emergence of MOOCs:  Massively Open Online Courses.  These courses are free to anyone interested and are taken in an entirely online format; they are typically taught by well-known professors from elite universities.

Among many questions about MOOCs that are being asked on the campuses of good, but not elite, universities such as mine: “Could these MOOCs replace the education we provide?”

There are many directions from which to approach this question.  A fundamental one is economical.  Matt Yglesias has an insightful recent post, inspired by a much longer article by Kevin Carey in the Washington Monthly about the “disruptive technology” in academe that is emerging out of Silicon Valley.  Like lots of articles in the Washington Monthly, this one by Carey is packed with interesting tidbits, and is worth the longer read when you have the time.  One lesson to take away from the WM article is:  venture capitalists are investing large sums of money in companies whose intent is to challenge (overthrow?) traditional colleges and universities.  And there are lots of avenues by which higher education will be challenged.

Yglesias’s main point is:  while colleges and universities are not businesses, they have a business model.  And the basic gist of that model is that low-level, high-volume courses generate lots of revenue and enable institutions to do some of its most valuable, but least efficient work in small, upper-division classes.  He thinks that MOOCs have the potential to “compete away” this “low quality” but high-dollar-producing stuff that colleges do.  That would pose real problems for how they’d be able to afford the high quality, low volume (and likely money-losing) services they currently offer.

Mike Caufield goes further, claiming that MOOCs could actually kill higher education, due to the structure of American colleges’ business model, piggy-backing on the point of Yglesias.  He points to particular classes that are “MOOC-able”, ones that can be replicated in high volume at low cost, where literally tens of thousands of students could take a single course.  His example is Intro Psych; Yglesias’s example is an intro course on the French Revolution.  But these examples, and these lines of reasoning, beg the question: are these classes really MOOC-able?  And, hitting closer to home, is calculus MOOC-able?

A few short thoughts, as I still need to think more about these questions:

– if a college class merely consists of going to lectures, listening to an expert, and taking a handful of exams, then I don’t think the class is promoting much in the way of learning.  Such a course deserves to be replaced by a MOOC.  It’s ridiculous to think of paying $1000 for such a class (rough cost for 3 credits at GVSU for a full-time student taking 15 hours a semester), much less the almost $4500 that a school like Williams College charges (I took the annual tuition and divided by 30 credits to get an approximate cost per credit hour).  Sitting passively in large lectures is easily replaced by watching said lectures on YouTube.

– if college generally is mainly about information transfer from faculty to student, then it, too, deserves to be MOOCed.  But as far as I’m concerned, we’re way past the 19th century model of education as information transfer, and have been for some time.  If we are teaching our classes in the form of “here is some information that I have that I want to share with you; write it down,” well, then here, too, we deserve to be run out of business.  There are way more important things to learn and do, and information transfer is free, easy, and completely searchable.

– I’m likely biased, since part of the way I make my living is by teaching calculus, but I think calculus is hard to MOOC.  To help me understand the issues better, I’m going to take Robert Ghrist’s Coursera Calculus class this coming January.  I’m really curious to see how that goes.  But I think there’s lots of evidence that calculus is hard to learn, and even harder to learn in a large lecture setting.  One of our mathematical professional societies recommends that undergraduate courses in mathematics have at most 30 students.  In my experience, I see students achieve the most significant gains in learning through interacting directly with me and with one another (under my supervision).  I don’t understand how a person of average collegiate aptitude trying to learn calculus for the first time can be one of 25,000 students in an online class and, without the opportunity to ask questions and get some human feedback on mistakes, be able to make real progress in gaining deep understanding.

But maybe calculus is MOOCable.  And that would make it really, really free.  More than any book.

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Opening Week

(This post was originally titled “Opening Day.”  Given that the entire week rushed by before I could post it, I updated.)

Classes started this past Monday at GVSU.  It has been the usual whirlwind getting things organized and started for my three classes.  Besides it being the usual exciting time of year, there’s been an added sense of anticipation in the air for me as I know some of my colleagues (near and far) are using some of the materials I’ve developed for this project.  In particular, three GVSU math faculty are using the text in place of our traditional book.  On Monday, I walked into one of my classes and, as the professor before me was wrapping up, I saw Active Calculus displayed on the screen.

As people use the text and share feedback, I hope to have some discussions of their reactions here on the blog.  If you happen to be using either the text or activity workbook and haven’t told me, I’d appreciate hearing from you: boelkinm at gvsu dot edu.

According to my GV colleagues, the early student reaction is very appreciative.  I’m sure that the price contributes significantly to that reaction:  free for the .pdf, $12 from the bookstore for a printed copy totaling about 250 pages.

Two other short thoughts about the start of the semester:

– at one of the startup meetings I attended, the director of admissions at GVSU gave a presentation on who our students are.  A whopping 42% of them are first generation college students.  For many of them, college is something approaching a financial hardship.  I am certain that purchasing several $100-$200 texts adds to that challenge in significant ways.

– two of my 62 students in calculus 2 have talked to me about challenges they’ve faced in purchasing the text.  The main issue seems to be waiting for some financial aid matters to be wrapped up so they have the cash available to make a purchase.  I so badly wish I could say “Here’s a .pdf.”

Working on it.

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Existing Free (or Very Low Cost) Calculus Texts

One of the overwhelming things about the Internet (to me, at least) is just trying to keep track of what’s out there.  With this post, I invite readers to contribute to a list of free (and where fitting, open) calculus texts that are available on the web; I’ve added two that are very low cost (under $20 per student).  If people want to offer testimonials or other observations in the comments, that would be especially appreciated.

As noted in an earlier post, there are a couple of calculus texts posted online as part of the American Institute of Mathematics’s Open Textbook Project (those by Strang and Guichard, respectively).  Again, Strang’s book is free, but not open, while Guichard’s is open.

Here are some others.  The first two have some modest costs associated with them; the remaining ones are all free.  None of these, to my knowledge, is open source.

  • David Massey, Worldwide Differential Calculus.  Massey is the founder of the Worldwide Center of Math; I believe that originally, this text was free.  Massey now charges $10 for the .pdf, or $30 for a bound copy.  In reviewing earlier versions (when it was posted online), I was struck by how complete the text is (differential calculus is 565 pages!), and how vast the included resources are for students, with even lengthy video tutorials.  So not free, but not $189.95 either.  Massey’s site has a growing collection of similar books.
  • David Smith and Lang Moore, Calculus: Modeling and Application.  I was (am) a huge fan of the print version (1st edition) of this text.  Smith and Moore have converted the text to an entirely .html platform.  Now hosted and endorsed by the MAA, schools can purchase a license agreement to gain access to the full text online for their students.  From the order form on the page, it costs roughly $15-$20 per student, depending on the number of students enrolled.  This is a great, low-cost alternative, and again the text and materials are extremely high quality.  I’m not as big a fan of the .html format and how each link leads to a new window, but I do see advantages of this format.
  • Miklos Bona and Sergei Shabanov, . “From the University of Florida Department of Mathematics, this is the first volume in a three volume presentation of calculus from a concepts perspective.”  The other two volumes (for integral and multivariable calculus) are available from the Florida Digital Repository.  At under 200 pages, this is a nice, comprehensive introduction to standard concepts in calculus.  Exercises are included.   Text is free and in .pdf format.  (As an aside, the Florida Digital Repository seems to be one of the better online “warehouses” for free texts with a reasonably good search feature.)
  • William Smith, The Calculus.  Free, but copyrighted (the author doesn’t want any of the text even copied to other locations).  The typesetting is poor and hard to read online, and the text has two unusual features (as noted by the author): (a) proofs for everything are included, and (b) the text introduces ideas in one and two variables simultaneously.
  • Dan Sloughter, Difference Equations to Differential Equations.  Clearly the author has more in mind than calculus, but there’s quite a lot of calculus content available; the table of contents is presented in html, with the links leading the reader to .pdf files that are essentially short individual chapters.  Sloughter also offers Yet Another Calculus Text, written from the perspective of the hyperreal numbers.
  • Jerome Keisler has a text that seems similar in spirit to Sloughter’s, using infinitesimals, titled Elementary Calculus: an Infinitesimal Approach.
  • Paul Garrett, Calculus Refresher.  A brief (approximately 80 page) review of some key calculus ideas (with some exercises).  This book seems designed for students who’ve had calculus and need some review, rather than for students encountering the ideas for the first time.

What am I missing?  Are there other good texts out there that people have used?  Testimonials for any of the above?

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A different challenge to publishers

From Insider Higher Ed, an interesting article on the startup “Boundless Learning”, which endeavors to provide text-like materials to students free of charge.

“It does so, essentially, through reverse engineering — identifying widely used textbooks in certain fields (three last year, seven now) and then stitching together the best freely available material it can find and presenting it to students as an alternative (without charge, at least for now).”

I’m not sure I like this model (and I can understand why the textbook publishers are suing them), but I see this approach as further evidence that the traditional, high-expense model of publishing is crumbling.

Among the interesting items in this piece, I was particularly intrigued by the college textbook market being estimated as a $4.6B (as in billion) annual industry, and the statement that approximately a third of college students choose not to buy the textbook for their course at all.  The latter figure sounds questionable to me, but there is no question that textbooks form a major expense to students and that for many students who struggle financially, it may be an expense they strive hard to avoid.

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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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