Secondary Public Offering: thru integral calculus

As promised last week, here is , now with four additional chapters that can be used for the second semester of university calculus.

The link above is to the full text, all of chapters 1-8, as a Google document that should be embedded in your browser.  From the new Active Calculus download page on my GVSU faculty website, you can find links to this file, as well as to just chapters 1-4, or to just the activities workbook for either the whole text or just chapters 1-4; in addition, there you can also find links that will allow to directly download the .pdf version of any file, rather than viewing it as a Google doc.

If you are interested in some sort of other custom arrangement of the files, please contact me at boelkinm at gvsu dot edu.

A couple of other notes:

  • You’ll observe that Section 6.6 on Probability is not yet included.  I will be working on this section early in 2013 and expect to post it by early February as an addendum.  At the end of winter semester, this section will get fully incorporated into the latest version.
  • We do not yet have hints or answers for the activities in chapters 5-8.  Working towards the January 1, 2013, deadline made us focus on getting the exposition finished, so hints and solutions will have to follow later.  The same is true for most of the exercises throughout the text.  (If you are interested in the hints or solutions to activities in chapters 1-4, please contact me directly.)
  • Again, my deep thanks to David Austin and Steve Schlicker for each contributing a chapter (David on Differential Equations, Steve on Sequences and Series).

If you will be using any part of Active Calculus in your classes this winter, I would appreciate hearing from you about how you plan to do so.

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One year later

A year ago at this time, I was about to embark on my sabbatical.  I had drafted a couple of brief sections of what would become Active Calculus, but had almost nothing of substance written.  By May, I had a working draft of four chapters of material, essentially the standard topics of university calculus I; in August, I posted that publicly, and a handful of folks adopted it for use in their fall semester courses.

As I noted in a couple of earlier posts, it became almost immediately clear to me that a free, open source text for only calculus I was nearly useless without the corresponding chapters for calculus II.  Realizing that my sabbatical was exhausted, I set about recruiting some helpers:  my GVSU colleagues David Austin and Steve Schlicker, both accomplished mathematicians and authors, each volunteered to write a chapter (David on differential equations, Steve on sequences and series).  Personally, I worked at length over the summer on a chapter on constructing antiderivatives, and then spent much of my “free” time during fall semester pounding away at a chapter on applications.

The result is that, in spite of my frequent thinking that a January 1, 2013, deadline was totally unrealistic, we’re ready to unveil next week the next four chapters of Active Calculus.  The combined materials provide a sufficient base for a two-semester calculus course.  I’m excited to share it, to have a couple of my GVSU colleagues use it in our second semester course, and to start getting feedback.  With this big deadline met, I’m also enthusiastic about having the chance to blog about some of the feedback from students and peers who used the differential portion of the text during fall semester.

So, consider this post a promise and a celebration.  The promise: calculus II materials join those for calculus I on Wednesday, January 2, to ring in 2013.  The celebration: 500+ pages in just under a calendar year (with deep thanks to David and Steve).

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From fall to winter, from differential to integral: news and updates

So things have been pretty quiet here on my blog since early in fall term.  While there are all of the usual reasons for being busy, the main source of my nonposting has been that I’ve tried to devote much of my available spare time to writing a couple of new chapters for the text.  Here’s an update on where things stand with the Active Calculus project.

Several of my colleagues used the and the corresponding in their calculus I classes this fall; another handful of peers at other institutions used it, too, sometimes in conjunction with other materials.  Most of these users have sent me editorial feedback, and I’m deeply grateful for all that commentary.  I am presently working on implementing many of the suggested edits, including all of the corrections, and expect to have an updated version of the differential portion of the text posted by December 22.

While I was teaching integral calculus this fall, I also invested considerable time in writing material for the integral portion of Active Calculus.  My colleagues David Austin and Steve Schlicker also volunteered to contribute to the project: David is writing a chapter on differential equations,  and Steve is writing a chapter on infinite series.  Along with the two chapters I’ve been developing (one focused primarily on finding and using antiderivatives, the other on applications of the definite integral), we look forward to having a draft of the next four chapters of the text posted online by early January.

If you are interested in using the integral calculus portion of the text in the upcoming semester and want to see the table of content for it or get a preview of the not-yet-ready-for-public-consumption version, please email me directly at boelkinm at gvsu dot edu.

And now: back to work on the text.  More posts to follow soon.

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Holy cow … it’s Thanksgiving

So today my blog got hacked.  Someone out there seems to want to use my site to advertise getting paid for something, and now they’ve managed to do it to my Twitter feed (3 weeks ago) and the blog.  I wasn’t even using Michael Scott’s password (1234).

Anyhow, I guess this is fitting punishment for not posting lately.  I owe news about usage this fall and resulting feedback, as well as an update on material for integral calculus.  Soon — by early December — I promise.

For the record:  the calculus text is still free.  And I’m not getting paid.  And loving it.

Apologies for any nuisance for the hacked post.  And Happy Thanksgiving to all.

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Reflections at 1/3-term

Each of the past several weeks has started with “write new post” high on my to-do list.  With 90 students in 3 classes, working on new sections for the second semester of Active Calculus, and the usual laundry list of life and work, the weeks have flown by.  Here are three things I’ve been thinking about regarding the teaching of calculus at the end of week 5 in a 15-week semester.

1.  In my two calculus II classes, I have 60 students.  We meet 4x a week in person, and I provide a substantial out-of-class workload that includes reading, WeBWorK exercises, team homework exercises, graded lab activities, and exams.  I expect students to work 8-12 hours a week on assignments related to the class.  A short anonymous poll I conducted this week revealed that well over a third of respondents say they normally spend 4-6 hours a week or less on work for my course.

2.  Geogebra and Wolfram Alpha are awesome.  Long live free software.  In calculus 2, we’ve been using a mix of Maple, Wolfram Alpha, and Geogebra to support our technological needs.  For single variable calculus, there’s no question to me that a combination of Wolfram Alpha and Geogebra is more than sufficient to replace a traditional computer algebra system.  Added bonuses:  both run in a browser, have limited syntax requirements for use, and are genuinely intuitive to use.  I see my students doing good things with each of them to aid their understanding and computation.  And again: they’re free.

3.  Mike Caulfield continues a great discussion of Massively Open Online Courses over at hapgood.us.  In one of his many posts, he notes that in a recent survey of students taking a circuits and electronics course, 80% reported taking a similar course previously.  80%.  Mike has a great point here:  MOOCs may prove to be an outstanding way for students to refresh or expand a topic they’ve studied in the past.  He wonders, like I do, how well they can function for introducing students to new material for the first time.

Connecting (3) back to (1), I would say:  if working face to face with my calculus students 4x a week and giving them meaningful graded assignments to complete on a regular basis leads to only 4-6 hours of outside work, it’s clear to me that many students are working to minimize their workload for my course, or at least to minimize it in light of other commitments they are choosing.  Imagine if such a student were one of 26,000, with name unknown to the instructor, and not paying a dime for the course.

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Textbook Inflation

A recent US News and World Report article focuses on the high rate at which textbook costs have been rising and explains how the costs are divided among bookstores and textbook companies.

While overall inflation is currently low, not so for textbooks: “According to the Labor Department, textbook prices as of July were 8.1 percent higher than in July 2011, while prices for all goods only grew by 1.4 percent overall.”  This contrast is striking, particularly in light of longstanding trends which show an already high rate of text inflation: “A 2005 Government Accountability Office report showed that college textbook prices grew at twice the rate of inflation from 1986 to 2004.”

The article provides other interesting points:  college bookstores only reap about 20% of the cost of the text, most of which goes toward human and facility costs.  More than 75% of the cost accrues to the publisher.  There are some crazy large dollar figures cited, too.

On page 2, the conversation shifts a bit to e-books and related technologies.  There, a person from the National Association of College Stores makes the assertion that “the cost of bringing textbooks into the digital age may even push costs higher.”  To that, I basically say: “baloney.”  These technologies should make nearly all of these expenses less, largely because of all the wonderful free resources out there.  Consider Geogebra and WeBWorK as two prominent examples, much less LaTeX itself.

From my perspective, textbook companies are furiously developing software add-ons that are tied to books in an effort to increase their business:  they create products that are tied directly to texts, and then charge premium fees to students for this software, in addition to the text itself.  Personally, I think it would be crazy to require students to purchase the software Geometer’s Sketchpad ($69.95) when they can use Geogebra for free.  On a similar note, I think we’re nearing a point where WeBAssign ($19.95 per student per course) is a far less appealing option than WeBWorK (free, in the right circumstances, though there’s some institutional cost if you run your own WeBWorK server).

And the point about bringing textbooks into the digital age pushing costs higher is even crazier in light of the point that many have already made:  it is incredibly easy and inexpensive (other than human time and effort) to self-publish a text.  Instead, we can and must make these costs go down.  It’s no longer tenable to ask the average college student to spend $1168 a year on textbooks.

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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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