Screencasts for Active Calculus and the Inverted Classroom

Posted on August 5, 2013 by Matt Boelkins

It’s time to gear up for fall semester.  Over the month of August ahead, I look forward to sharing some news and updates about Active Calculus and related matters here on the blog.

I’m excited that among the many sections of calculus I and II we’ll be offering at GVSU this fall, about half of the instructors have decided to use Active Calculus.  Two of those folks, Robert Talbert and Marcia Frobish, have decided to structure their courses on the model of the inverted classroom.  Robert used AC this past spring, and Marcia did this past winter, and each thinks the text is well-suited to use in this manner of instruction.  A few others who’ve worked with the text find that it aligns well with many inquiry-based learning goals.

Robert and Marcia decided that to support their mode of instruction this fall, a sequence of screencasts was in order.  After we had a meeting in early July, they drafted a list of about 75 topics (!), an average of 3 screencasts for each of the 25 sections in chapters 1-4 for first semester calculus.  They’ve been very busy for the past month, and are now pushing the halfway point of this list with over 30 such videos already produced.  You can find the full list in the Math 201 playlist on the GVSU Math YouTube Channel.

Huge thanks to Robert and Marcia for these great contributions to Active Calculus.

As I teach our first-semester calculus class this fall using AC, I will also be using these videos as a resource for students to support work they do outside of class with assigned reading and preview activities.  I look forward to writing more about that experience as the semester progresses.

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On work-life balance

Posted on July 23, 2013 by Matt Boelkins

This has little to do with calculus, but everything to do with the profession that typically delivers calculus.  If you haven’t read this wonderful post by Radhika Nagpal, who teaches computer science at Harvard, you should.

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Active Calculus is not like the NSA

Posted on June 28, 2013 by Matt Boelkins

So there’s a new brand of e-book out there, and it has an NSA-like flavor:  an e-reader that tracks what students have read.

From a recent NYT article, “They know when students are skipping pages, failing to highlight significant passages, not bothering to take notes — or simply not opening the book at all.”

They know this due to a new startup called CourseSmart, which is apparently owned by several major players in the publishing industry and who, in the words of the article, “see an opportunity to cement their dominance in digital textbooks by offering administrators and faculty a constant stream of data about how students are doing.”

The cynic in me looks at the url for CourseSmart (http://www.coursesmart.com/), and doesn’t read “Course Smart”, but rather “Courses Mart”, and thinks that the e-publishers are mainly interested in this as a way to increase their revenue stream.  I’m skeptical that having electronic eyes on our students will do much in the way of encouraging students to learn.

At any rate, rest assured that Active Calculus remains free.  And without tracking software.  Students can read it or not read it.  No database will report either way.

BTW, if you do read the NYT article at the link above, don’t miss the last two sentences.  Classic.

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What is the purpose of calculus?

Posted on June 19, 2013 by Matt Boelkins

One of my springtime habits this year has been to stop by Robert Talbert‘s office at 3:35 pm as I make my way back from teaching a linear algebra course (that runs in 6 weeks’ time, incidentally!).  He’s been teaching calculus I over the same period, using Active Calculus, and we’ve had frequent conversations about the teaching of calculus and linear algebra.  Our chat yesterday inspires today’s post.

In talking about the goals and purpose of calculus, we both expressed a desire to introduce students to mathematics different from calculus that is more modern and, in many ways, more important.  We were in agreement: if it was curricularly possible, we’d both make radical changes to the three-semester calculus sequence.  Instead, we’d follow the West Point curriculum for the first two years; or teach linear algebra, discrete math, and statistics; or … something.  It reminded me that I’ve always liked what Gil Strang says:  “Too much calculus!”

But, with so many client disciplines relying on calculus in their programs, it’s probably not curricularly possible to make a radical departure from calculus.  (Whew, says the textbook author in me …)  So, what should be the goals and purpose of calculus?  Robert had a great phrase:  “calculus should be an introduction to doing mathematics in the style of a professional.”

Now, as Robert points out, that begs a question:  “what does it mean to do mathematics in the style of a professional?”  That question merits further thought, thought that I hope to flesh out through additional posts and the comments.  But for now, here are some basic thoughts we have on “doing mathematics like a professional.”  For instance, students should have to think critically about hard problems, to write well and technically, and to use technology in a meaningful and responsible way.  In thinking about further goals or purposes for calculus, I would add this: knowing calculus is part of being liberally educated in mathematics.

To expand a bit:

  • Calculus students should have to think critically about hard problems.With the computing technology of today, the main point of calculus cannot be solving small, isolated, algorithmic problems.  WolframAlpha (The Wolf!) exists.  Deal with it.  Students need to develop the skills to handle problems a computer cannot:  ones with ambiguity, with multiple questions to approach, and that require critical thinking.  If all we are expecting of students is that they can replicate tasks that WolframAlpha can do in milliseconds, we are failing them.
  • Calculus students should write well, and technically.  In addition to being good problem-solvers, students should be strong communicators.  Here, too, calculus offers a great opportunity:  to improve their written prose, to write technically about difficult content matter, and to learn to use notation, syntax, and mathematical language in ways that explain deep ideas in their own words.  In a world of fast-changing and complicated ideas, clear written (and oral) communication skills are incredibly valuable.
  • Calculus students should use technology in meaningful ways.  One of the beautiful and powerful things about mathematics is the fact that viewing the same concept from multiple perspectives often illuminates the idea.  Using technology in a way that generates additional perspective and insight is another valuable skill that students should acquire.  In addition, any student who needs to actually do mathematics as part of her professional life will need to understand how to apply and make sense of results that come from using computational technology:  spreadsheets, Geogebra, the Wolf, Maple, Mathematica, and more.
  • Students who are liberally educated in mathematics should know calculus.  Calculus is one of the great intellectual achievements of humankind, and it explains the behavior of moving and changing quantities in our physical world.  It’s worth the time to learn, even if sometimes it seems like we spend too much time on calculus and its ilk.

As I reflect on some of the struggles I see students encounter when they transition from the more algorithm-based subject of calculus to more abstract and advanced mathematics, I think that calculus should also be an opportunity for students to see more of what mathematics is really like:  beautiful, challenging, open-ended, interesting, technical, and more.  We can use that perspective to make calculus a course where students can really strive to develop some of the most valuable skills of a liberal education, including being a creative and independent problem solver, being a strong communicator, and absolutely knowing how to work hard.

What am I missing?  What do you think is the purpose of calculus?

PS: if you aren’t reading Robert’s blog over on the Chronicle’s site, you should.

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A great text, newly free

Posted on June 6, 2013 by Matt Boelkins

[Sheepish apologies for my too-long absence from blogging.  Life!]

My friend and GVSU colleague Ted Sundstrom has recently made his wonderful text, Mathematical Reasoning, free to the public.  After being originally published by Prentice Hall in two separate editions and widely adopted, Ted has gotten the copyright given back to him and generously chosen to make the text available for free in .pdf format.  See https://sites.google.com/site/mathematicalreasoning3ed/ for a link to download.

At GVSU, we have a very good “bridge/transition” course titled “Communicating in Mathematics,” which serves as our formal introduction to proof-writing, along with giving students some exposure to logic, proof techniques, congruence arithmetic, set theory, induction, and functions and equivalence relations.  The class is a prerequisite to all of our upper-level proof-based courses.  Along with our colleague Karen Novotny, Ted was instrumental in the  development of Communicating in Mathematics, and he wrote this book originally to serve as a textbook for our particular course.  Prentice Hall published two editions, many folks at other institutions found his exposition valuable, and the book has been a great success.  Personally, I have used the text for more than a decade, and I recommend it most highly.  Great exposition, activity-driven, good problems … it’s the whole package.

I’m thrilled that Ted has chosen to move to a Creative Commons license and make the book available for free.

If you wish, you can still purchase the for-profit published version from Amazon.  But why would you?

 

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Using Geogebra in Calculus

Posted on April 2, 2013 by Matt Boelkins

Last week Thursday I gave a colloquium talk at a local college on some of my favorite results in the area of mathematics known as “the geometry of polynomials.”  During the talk, I used a couple of demonstrations built in Geogebra.  When I did so, I asked my audience of approximately 50 students (almost all math majors) and 10 faculty:  “who here is a Geogebra user?”  Not one student hand went up, and just one faculty hand did.

It therefore occurs to me that it’s still worth advertising this fantastic free software.  So here goes.  While comparable in capabilities to Geometer’s Sketchpad, it can be downloaded freely for local use, or even just run through a browser.  See http://www.geogebra.org/cms/ for details.  There is also an incredible community of active users, with a giant repository organized on GeogebraTube at http://www.geogebratube.org/.  You can even follow Geogebra on Twitter: @Geogebra.

In an earlier post, I wrote about how I’ve used Marc Renault’s outstanding collection of Geogebra applets for calculus in my textbook.  But in my own calculus classroom, I also have my students work with Geogebra directly themselves.  I especially like having students learn to use the slider bars and spreadsheet mode.  The former enables them to easily build their own applets, and the latter gives an easy-to-use way to investigate numerical patterns.  It’s also incredibly simple to work with functions in Geogebra:  if you want to define a rule by g(x), you type “g(x) = …”  If you then want to work with the derivative, all you do is refer to g'(x).  I’m delighted that it looks like my own department is moving in the direction of using Geogebra as the primary software for calculus 1 and 2 instead of the proprietary and [insert your own criticism here] Maple.

I’ve posted a couple of sample files that show how I use Geogebra with my calc I students:  an introduction to GGB that involves ideas with limits and continuity, and a more advanced use of GGB to instantiate Newton’s Method.  Students find the program intuitive and easy to use, and its graphics are fantastic and easy to export.  For the introductory lab, you can find the file in or , as well as the supporting ; for the Newton’s Method lab, the file students receive is posted in or .

If you’d like to use any of these files, please feel free to use and modify as you see fit.  I’d appreciate you acknowledging my role in their development in some way.  But they, like Geogebra, are completely free, even if I did a double-take when I saw .

Finally, a disclaimer:  I am a relatively novice Geogebra user.  You’d do well to check out my colleague John Golden’s work, which is often featured on his excellent blog.

Again, if you’ve not used Geogebra, please try it.  It’s free, and it’s awesome.

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What Leads to the High Prices of Textbooks?

Posted on March 23, 2013 by Matt Boelkins

Lots of hard work goes into the writing of any textbook.  No question about that.  But few textbook companies front that money to the author(s).  Further, while textbook companies regularly cite the high costs of developing and producing texts, those seem overstated to me.  For example, after our for-profit differential equations with linear algebra text was finished, one of my co-authors (who has substantial experience in for-profit self-publishing) told me that he could get our book printed in small volume runs for as little as $5 per text.  The text sells for a not-outrageous $89.95 (at least in comparison to other differential equations texts), but still with a huge markup.  With royalties shared 3 ways (and some other pricing complexities), I make well under $3 per text that sells.

In my particular experience, I don’t understand where the publisher generated major up front costs, as my editor seemed to invest a limited amount of time, energy, and resources in the project.  So, as I watch textbook prices rise, I often wonder about the real source, which I have typically suspected is something like “it’s what the consumer will bear.”  A recent case heard by the supreme court has brought to light an interesting perspective on where these high prices may really come from, and seems to confirm my suspicions.

Perhaps first made famous on the Colbert Report, Cornell student Supap Kirtsaeng came to the U.S. from Thailand, and he found our textbook costs ridiculous.  So ridiculous that he started having his family buy texts back home, ship them to him in the US, and he sold them for far less than college bookstores, making over $1 million in a short time!  Wiley sued Kirtsaeng, and the case went all the way to the Supreme Court.  The high court ruled this week, exhonerating Kirtsaeng.

Now, this issue in textbook copyright law has long been a problem.  It’s what leads to a strange used textbook market, as well as the neverending publisher’s game that leads to popular books being printed in their 13th edition.  This has always struck me as unfair to authors:  if authors could get a small royalty on used text sales (and publishers, too), that would seem to be the fairest use of this type of intellectual property.

That said, there’s an interesting take on how publishing houses are acting in their pricing model in a worldwide market, which is again what I suspected: it’s what consumers will bear.  As Jerry Brito notes, “In order to maximize profits, Wiley charges different prices to different consumers according to their willingness to pay.”  (Emphasis mine.)  So, basically they can produce the text so cheaply that they can sell it in Thailand for a few dollars, while in the U.S. they sell it for $150.

Here’s hoping that many of the factors discussed on this blog are contributing to college students the world over collectively being far less willing to pay $150 for a textbook.

Hat tip: The Dish.

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It’s Text Selection Time of Year

Posted on March 14, 2013 by Matt Boelkins

If your school is like mine, the university bookstore is clamoring for textbook selections to be announced for the coming year.  To that end, I want to add my voice to the many who are urging faculty to consider free or other low-cost options for students.  While this has been a consistent theme here on my blog (even if I’ve been posting infrequently of late), it never hurts to be reminded in stark terms.

For instance, on Andrew Sullivan’s blog, he recently posted this chart:

GrowthTextCosts

Insane, right?  I mean, one can almost understand the inflationary costs of medical services.  But textbooks?  See more detail on this in Jordan Weissman’s article on textbook costs, which includes the chart above, which was created by Marc Perry.

If you’re looking for various options for free mathematics textbooks, Prof. George Cain at Georgia Tech has a nice list of math texts.

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Going Free

Posted on February 8, 2013 by Matt Boelkins

I’m starting to get more and more email traffic that puts me in contact with people or organizations who are taking concrete steps to implement an overall strategy for the adoption of free and/or open source textbooks.  This post is focused on two such exciting examples.

1.  The State of California.  Go big or go home, eh?  This past fall, the governor “signed into law a proposal to create a website that will allow students to download digital versions of popular textbooks for free”.  As I understand it, the state is underwriting the development of 50 new texts for introductory college courses, as well as providing a site to host them.

Interesting.  I’ve heard that the California state system is one of the most coveted book contracts for publishing companies.  Which makes sense:  their K12 curriculum uses standard texts, and perhaps many of their universities do, too.

2.  Scottsdale (AZ) Community College Math Department.  At Scottsdale CC, they have a major initiative underway to teach all of their introductory course from free texts.  They have a wonderfully organized site that offers easy download for students.

A professor from the department contacted me about their interest in Active Calculus, the consideration of which is ongoing.

When I think more and more about how a typical student and a typical instructor use a textbook, I am more convinced than ever that we (all of us) have been substantially overpaying for our books for a long, long time.  I hope that more and more organizations — departments, universities, and even states — think about how they can use existing resources and their own to provide high quality free resources to students.  Don’t miss the American Institute of Mathematics’ approved open textbooks as part of their Open Textbook Project.

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Chronicle Articles on Textbooks, E-Books, and More

Posted on February 1, 2013 by Matt Boelkins

My friend and colleague Robert Talbert recently pointed me to a big collection of articles over at the Chronicle that are focused on the many issues surrounding textbooks on college campuses.  Lots of worthwhile reading there.

One article asks about the feasibility of any textbook remaining truly free, noting that perhaps state governments could play a positive supporting role, as appears to be happening in California.  Another interviews a collection of students and shows a lot of insight regarding how students view “required” textbooks.  Money quotes:

“In The Chronicle’s focus groups, students praised e-books for their instant availability, searchability, and portability. They also described taking advantage of freely available online lectures and materials.

…

“But others struggle with electronic learning materials. They report getting more easily distracted, or feeling frustrated at not being able to underline the text. Using an online book for one class, Eduardo C. Albano, 18, found he had to spend twice as much time to read it.”

Many good points to ponder in these articles and more.  I’ll make one point: if you use Active Calculus, you can download the .pdf for free.  And with any .pdf editing software (Preview for Mac, Adobe Professional, or iAnnotate for the iPad), you can mark up your copy all you like.

Posted in General, Publishing, Text Files | Tagged , , , | 3 Comments