openmathbook.org

As an outgrowth of the previously-mentioned session at the Baltimore Joint Meetings on open textbooks, Albert Schueller has started a new blog, Open Mathbook, to offer “a place to promote, discuss, and develop free and open source mathematics texts.”  There’s already a bunch of great posts there, including a trove of interesting developments from a range of people deeply involved with the free and open math text movement.

Ironically, while I haven’t had time to post here recently, I was honored to have Albert ask me for a contribution, and I have a new post over at OpenMathBook, based on the talk I gave at the JMM.

Soon I’ll follow up here with some exciting news we have regarding plans for a multivariable addition to Active Calculus.

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Joint Meetings 2014: free and open textbooks session

While it was certainly a good conference overall this year, last Friday at the Joint Meetings in Baltimore was particularly fantastic.  From 8-11 and 3-5, we had about 15 different presenters share interesting and exciting work and opportunities in the world of free and open-source mathematics texts.  Here are a few highlights:

Richard Hammack of Virginia Commonwealth University gave a nice presentation on how to set up on-demand publishing.  I like Richard’s model:  give the text away for free in .pdf format, and establish a print-on-demand setup where folks can buy the book for an incredibly reasonable price (for his Book of Proof for a transitions course, a nearly 300-page book in softcover for under $15, with a modest profit to the author as well).  His book looks beautiful, too.  This spring, I plan to get Active Calculus set up for print-on-demand so that students can order a bound copy, if desired.  The .pdf (and other eventual formats — see the part on David Farmer below) will always be free.

Nicole Allen of SPARC, the Scholarly Publication and Academic Resources Coalition, provided an overview of the free and open textbook movement.  Nicole began her interest in and advocacy for free and open textbooks as an undergraduate student, and now she’s working professionally for this cause.  Among the many interesting things she shared in her presentation to us:  the US textbook publishing business is an $8.8 billion dollar per year industry — nearly comparable to the NFL, which apparently reports in at approximately $10B per year.  Think about it.

– David Farmer of the American Institute of Mathematics gave us a peek at the amazing work he and others (including Rob Beezer and Tom Judson) are doing to enable authors to have their work translated to multiple electronic platforms (including ones that haven’t been invented yet).  For some samples, see http://aimath.org/jmm/, which shows how several different papers written in standard LaTeX code can be turned into gorgeous, easy to browse web pages.  As I understand it, the basic idea is that Rob Beezer and others have created an XML to TeX translator, while David is working on one that translates TeX to XML.  And if you have “good” LaTeX code, one of these brilliant programmer can run your TeX through their machine and produce other formats with nearly no additional effort.  Be sure to take some time to browse the link above, and be certain to click on a few of the links within each web page that appear.

Suffice it to say: I wish that I had seen David’s talk 24 months ago before I started my project.  But I’m optimistic that with a little bit of time and care on my (already decent) LaTeX code, I can eventually have my book translated into not just this great web page format, but also into forms suitable for eReaders and more.

There was, of course, more good publicity for AIM’s open textbook project.  Mostly, it was fun to be in the room with a bunch of creative, interesting, relatively like minded people who were all excited about developing free and open-source texts to make the mathematics learning community a better place.  I got some great ideas and made some new friends … which is exactly what a good conference is for.

I should have at least one more post upcoming soon on some cool people I met and resources that they are developing, particularly a couple of items related directly to calculus.

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Active Calculus v.12.30.13 – updates

This fall I was glad to have a much larger number of beta testers using Active Calculus; about 10 of my GVSU colleagues used it for either our calculus I or calculus II, and at least that many other people at other institutions employed the text in some fashion.  Several of these 20+ people provided regular and consistent editorial feedback, and I’ve just recently had the time to implement their corrections and suggestions.  My deep and sincere thanks to them for every single one of their emails.

The newly updated files are now available from my download page; as always, any person interested in the original source files may request them from me directly, and I will share them via Dropbox.

As has been noted previously at this site, thanks to my colleagues Robert Talbert and Marcia Frobish there is now a full set of screencasts to go with the first four chapters of the text: see the GVSU Math 201 YouTube Channel.  My students in the fall semester of 2013 raved about the helpfulness of these videos.

I also now have full sets of .def files for WeBWorK exercises for the text, available upon request.

As winter semester begins soon, I wish everyone well in preparing for and starting their classes, especially those in calculus.  If you choose to use AC, I welcome hearing from you at anytime with corrections, suggestions, questions, or reactions.

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Three months later, …

My last post was September 4, 2013.  Oops.

In the first week of October, I got a new (additional) job at GVSU:  director of faculty advisors for freshman orientation.  Given that we welcome over 4000 new first-year students each summer, for the past two+ months I’ve had considerable work to do in learning my new job and planning for summer 2014.  With that added to my normal workload, a few things had to be put off.  Blogging and tweeting got set aside.

With apologies for being gone, I’m glad to be back.  Here’s an overview of some upcoming posts that I’m working on:

  • updates to the text:  during the fall semester, I got a bunch of great feedback from colleagues near and far who were using the text, plus from my own students.  I carefully collected all of that, and over the next couple of days, I will be implementing the needed corrections and changes.  New versions of the .pdf files will post on the text’s download page no later than December 30, 2013.
  • reflections on fall 2013:  this past term was the first time I’d gotten to use the text myself, and I’m keen to share my and my students’ reactions.  Plus I still owe the post “part 3 of 3”, tied to how my fall 2013 differential calculus class looks (looked!).
  • talk at the Joint Meetings:  there’s an exciting paper session at the Joint Math Meetings in Baltimore in early January that is devoted to free and open texts.  I’m giving a talk there, so I’ll post a short preview of the talk, plus put in some publicity for others on the schedule.

Now, back to editing …

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How my calculus class looks this fall (part 2 of 3)

In an earlier post, I thought to make my teaching more public, and then subsequently shared some reflections on how my calculus I course looks overall.  In this post I’ll give an overview of how a typical week is structured, and in the near future reflect on how a prior class day.

As of Monday, September 9, my class will have met 6 times for 50 minutes, and, inside and outside of class, students will have worked through the vast majority of the ideas and activities in Sections 1.1-1.3 of Active Calculus.  That is, we’ll have discussed average and instantaneous velocity, the notion of limit, and the definition of the derivative at a point.  This is representative of my goal for the semester:  to proceed through Active Calculus at a pace of about two sections per week, or 1 section every two class meetings.  With four meetings a week for 14 weeks, that’s 56 meetings:  4 get given to exams, and I leave 2 relatively open and unplanned for flexibility, so that leaves us 50 meetings to consider the 25 sections in Chapters 1-4.

My class meets MWF in a “regular” classroom, and once more on Tuesdays in a dedicated computer lab.  The computer lab meetings are, on balance, devoted to self-directed computer-based explorations and activities that are designed to strengthen students’ understanding of calculus.  We’ll be using Geogebra as our principal software tool, including its marvelous spreadsheet view.

Here’s what I have planned for next week — week 3 of the semester, September 9-13, which looks pretty typical.  For Monday, students will prepare by reading the start of Section 1.4, completing the Preview Activity for that section, and watching some of the great screencasts being produced by Robert Talbert and Marcia Frobish.  They are directed and assessed in these tasks in the Daily Prep Assignment for Monday, 9/9.  Having started to encounter the derivative as function, in class we will have a short debriefing time, a bit of all-class discussion, and then devote the preponderance of class to Activity 1.10, an exercise on graphing the respective derivatives of various given functions.

On Tuesday, class will be primarily devoted to a graded computer lab activity that focuses on using the limit definition of the derivative to find a formula for f ‘(x) and using a graphical perspective to check the correctness of the resulting formula.  This work will parallel Activity 1.11 and essentially complete our study of Section 1.4.

Wednesday, we’ll transition to Section 1.5 where the focus is interpreting the derivative in applied contexts.  Similar to Monday, students will complete a daily prep assignment and come prepared to debrief and discuss ideas such as the units associated with the value of the derivative.  Our class meeting will involve debriefing on the daily prep, 25-30 minutes devoted to work in small groups on Activities 1.12 and 1.13, and then some closing all-class discussion of the activities.  So far, my students are doing a very good job of working actively in class and asking good questions.  We’ll look to continue that habit in all upcoming meetings, but particularly on days like this one where the majority of class time is devoted to work in small groups with support from me.

As the week rounds out on Friday, we’ll take some time at the start of class to consider* students’ questions on assigned homework (WeBWorK) exercises or problems of the week they are working on, do a short recap of what we’ve learned so far about the derivative function, and then spend the remainder of class on Activity 1.14, which regards a problem where you really, really have to think about the units on the derivative, since the independent variable itself is a rate of change.  Friday will be a rare MWF in that there’s not a daily prep assignment to complete.

While the material will change and there will be some adjustments to the schedule around exams, Week 3 is representative of life in my calculus class this semester.  In the near future, rather than looking forward to a particular week of class, I’ll look back and reflect on a recent class meeting.

* One note about how I manage student questions on homework:  I typically only spend about 15 minutes of class time each week discussing homework exercises, and students have to make their requests in advance of class via email in response to a message I send them.  I’ve done this for the past 7 or 8 years now, and it has greatly improved my efficiency in use of class time.  (A) Students have to let me know in advance, so they ask more focused and meaningful questions; (B) I know when I enter the room what the main homework questions are, and I can respond to them more democratically — homework discussion is based on a range of voices, not just whomever is most vocal in class; (C) I’m much more efficient in how I allocate class time to the questions of students.  In particular, I’ve found that I can write all the problem statements down in advance, possibly along with a couple hints or key points, and then use the document camera in the classroom to display the problems on the board.  In 15 minutes, we can consider 5 or 6 problems; previously, where I’d take questions on the fly, I’d be lucky to consider 3 questions in 15 minutes.

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How my calculus class looks this fall (part 1 of 3)

[update: I moved some Dropbox files around and the original links were broken.  I updated these on 8.11.14.]

Well, it looks full.  31 students, 1 over the cap of 30, filling essentially all the seats in our regular classroom, and all but one of them in our computer lab.  Bless the good folks who designed our building with small classrooms and computer labs that only seat 32.  We are running at capacity here at GV … which of course is a nice problem to have.

And from my view of the room, things look great.  I’ve got 31 pleasant students who seem eager to learn and ready to contribute.  Which is a good thing, since I’ve got plenty for them to learn and contribute to.  Here’s a bit about how my course is set up.

First, my goals:  well, you can read them in my syllabus, and as I regularly say out loud to my students, “I want you to be successful.”  I imagine that an average student equates “successful” with “an A in calculus.”  I’m always careful to say that what I mean by “successful” is that you “develop deep personal understanding of calculus that you can demonstrate.”  In my book, good grades are a consequence of success, not the definition thereof.  I want what we study to make sense to my students … if that happens, lots of other good things will follow.

And while I certainly want my students to develop competence in calculus I that will serve them well in other courses that use these ideas, particularly calculus II, I definitely want much more:  for my students to become more liberally educated, to become much better independent learners and problem-solvers, to considerably strengthen their communication skills, and to have a reasonably big-picture understanding of what calculus is about.

Now, to achieve those goals, some hard work is in order.  By me and my students alike.  Here’s an overview of the activities and assessments my students will encounter.  Like the title of the book, Active Calculus, every part of the course expects students to be active learners.  Active when we meet in class, active when working on their own outside of class, and doing some active collaboration with peers in each setting.

For most days that we meet, students complete a “Daily Preparatory Assignment”, which includes an overview of what to expect in the upcoming meeting, some basic and advanced learning outcomes, resources to learn from independently (reading the text and watching some videos), and finally some questions to answer.  Here’s a recent example.  While I had almost always used reading assignments as a requirement for doing some active learning prior to class, my move to “daily prep” is modeled on my colleague Robert Talbert’s use of “guided practice assignments.”  Daily prep assignments count 6% of my students’ semester grade.  In many ways, these are daily accountability assignments, work that students should do regardless, and work that enables them to come to class well prepared and ready to engage actively in our work.

We are also using WeBWorK for some of the more routine exercises in the course.  At GV, we now have a dedicated WeBWorK server that can handle all 5000 of the students we have in our courses in fall semester.  I choose to typically assign two WeBWorK sets per week, each with about 10 problems, and to have the students keep a parallel “homework journal” in order that they have a written record of their work.  If you’re interested, you can read my WeBWorK document.  WeBWorK and the journal count 12% of the overall grade.

Students will also undertake a “problem of the week” project that asks them to choose 10 challenging exercises from the text, a subset of a list that I identify.  They have some flexibility on submitting drafts and collaborating with peers.  To avoid information overload, I think I’ll save the description of that for a later post.  This major project counts 18% of the semester grade, and some additional work on labs and in-class activities will account for 8%.  That leaves 36% for four one-hour exams, and 20% for the comprehensive final at the end of the term.

So that should give you some sense of what I’m asking my students to do this semester.  Again, the big goal:  to develop deep personal understanding of calculus, and be able to demonstrate this to others.

In closing, some demographics:  of my 31 students,

– they are majoring in at least 7 different fields, including cell & molecular biology, chemistry, computer science, engineering, geology, international relations, and mathematics.  About half the class consists of engineering or CS majors (8 of each);

– just 6 are first-year students, while the vast majority are sophomores, with a smattering of juniors and seniors;

– all but one of them owns a laptop.

That last fact is making me start to rethink the notion of a weekly “computer lab” — which we have, but for which the separate room and day/time is always something of an planning challenge.  More on that later, too.

It’s been a great first week.  Looking forward to 13 more.  Up next: related posts on what a typical week looks like, and reflections on a single particular class meeting.

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Making my teaching more public

I’ve made a promise to blog regularly this fall on my experiences in teaching calculus I at GVSU using Active Calculus.  Before starting that endeavor, here are a few overall thoughts.

Teaching is an oddly private endeavor.  While it is certainly public and open with my students, my work as an instructor can almost be done in confidence relative to my university colleagues.  I find this odd for several reasons, but a big one is how this stands in contrast to doing research.  In scholarly work, peer-review is the prized standard.  If I think I have discovered something new or done some innovative mathematics, it’s imperative that I share my work with other experts in the field for feedback, validation, and further development.  But with teaching, we professors are often content to keep much of our work to ourselves.

For me, one reason that I think I often tend to keep my teaching endeavors private — or only shared with a small number of peers — is that I’m afraid of doing stupid things in front of my colleagues.  This seems tied to one of my fundamental human instincts:  wanting to always appear like I know the answer to whatever is at hand and to look like I generally know what I’m doing.  That instinct doesn’t (a) stop me from ever doing dumb things, (b) keep me from appearing stupid in front of others, or (c) prevent me from still harboring some fears about appearing stupid.  But, being unafraid to fail is a key trait for success in life generally, and math in particular.  So, I keep working on that:  being unafraid to fail.

Writing a calculus text has forced me to face some of these fears.  Having others use a text you wrote means they are certainly going to find errors in it, certainly encounter ideas that aren’t communicated well, and certainly offer suggestions for improvement.  As more folks are using Active Calculus this fall, I find myself mostly excited to get that feedback so that the book can improve, and improve quickly.

I’m hoping that as I share some instructional materials this fall through the blog that I’ll get similar feedback.  My students will provide their own suggestions and support, as they tell me what seems to work well and what doesn’t.  Indeed, every semester for the past 10 years I have taken some time for oral course evaluations by my students.  In that 20-30 minutes with them, I learn a tremendous amount about how my instruction is perceived, what students value, and what they wish was different.  But I am hopeful that by sharing more of my work and more broadly, the professional community of my peers will provide ideas, critique, and new direction in my work.

So, a plan for my next three posts (modulo other more urgent items that might arise):  (1) an overview of the structure of my calculus class this fall — what my top goals are, what the typical student activities will be, and what the major assessments will be; (2) an overview of a typical week in calculus — what we aim to accomplish in our four hours of meeting and 8-12 hours of outside work; (3) reflection on a single meeting — what I planned in advance, what actually happened, and what I think in retrospect.  Along the way, I will post a couple of relevant documents via Dropbox links so that anyone interested can learn more.

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College textbook prices: up close and personal

In the year since starting this blog, I’ve posted frequently about the rising costs of college texts, including here, here, and here.

Recently I learned that it’s one thing to read articles about the issue or to hear students talk about costs; it’s another thing to actually be on the buying end.  My oldest son is starting his freshman year of college this fall, and the other day we went online to his university’s bookstore to look up his classes and corresponding books.

For his five classes, there were 9 required texts.  A couple were modestly priced paperbacks in the $15-25 range.  But three texts, for courses in economics, psychology, and statistics, had list prices in the $175-275 range.  Seriously.  An 8th edition of one such book was listed for $275 new, and over $200 used.  Had we purchased all the books through the university, the total – for one semester – would have been between $700 and $800.  I realized then that I had forgotten a key stat from an earlier post:  the average college student spends over $1100 per year on textbooks.  And my kid appeared to be striving to be above average.

We instead pursued some of the many online options and found much more reasonable prices.  Still steep, but not outrageous — 9 books at an average price of a bit under $50 per book.

The experience left me thinking again about textbook authors who live in $24M homes.  And their publishers.

I’m delighted that for each of my classes this fall (thanks partly to AC, and partly to Ted’s Mathematical Reasoning text), students can have the book electronically for free, or get a print copy for basically the cost of photocopying.

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Active Calculus: now endorsed by the American Institute of Mathematics

One of the goals of the American Institute of Mathematics (AIM) is “to encourage the adoption of open source and open access mathematics textbooks.”  Their editorial board maintains a list of approved texts that have been reviewed according to their evaluation criteria.  The list includes books for courses from calculus through many advanced topics, and now numbers more than 20 texts.

I’m delighted that AIM has seen fit to include Active Calculus among their approved texts.  You can see the particular page here, as well as from the main page, where you’ll find 4 other options for calculus texts, or 2 for linear algebra, or 3 for intro-to-proof courses (including my colleague Ted Sundstrom’s book, mentioned previously), and more.  It’s exciting to see such a strong, growing collection of materials for instructors and students.

In related news, Active Calculus is now featured among a list of “101 Prime Sites on Advance Math” at  http://onlinemathdegrees.org/prime-resources/.

I’m grateful to both of these organizations for their efforts to promote free and open resources for students generally, and their support for Active Calculus in particular.

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Looking ahead to fall semester

In an earlier post, I mentioned that I’m excited to have a considerable number of my colleagues at GVSU teaching from Active Calculus this fall.  One reason is that an increase in people using it will lead to suggestions and improvements that will help the text mature and be even better for others to use in the future.  In addition, several of us will be collaborating on related work for the course, and I plan to share some of that work here on the blog.

Along with piloting a new text, many of us will also be working to implement proposed changes in our department’s use of technology in the calculus sequence.  Historically, we have been a Maple platform:  our calculus classes all meet in a computer lab one day a week, we strove to introduce students to some key features of Maple in calculus I, and we used a significant portion of the computer lab meeting time for students to work on self-directed computer lab activities that various instructors develop.  Recently, however, many of us have been feeling that it’s time to move away from Maple in single variable calculus in favor of technologies that are more intuitive, more available, and perhaps more suited to learning calculus.  We’ll still meet weekly in a computer lab, and we absolutely want to continue using learner-centered activities that use technology to build and enhance understanding.

Geogebra has unquestionably been a driving force in this change in perspective.  Completely free, easy to use, most of the desired graphical features of a full CAS, plus a superb spreadsheet view and option … these features and more make the software well-suited to use in the teaching and learning of calculus.  As several of us will be refining or developing new lab activities that use Geogebra, I plan to share a couple exemplars on the blog.

We will also be entering out second academic year as a fully supported WeBWorK platform.  That is, our department now has its own server, capable of carrying the demands of 5000 students a semester, and any class we teach in the department can use WeBWorK.  This has already been a fantastic addition to our technology platform, and I look forward to using it in calculus I this fall alongside Active Calculus.  At the end of the semester, I will make publicly available the library of problems I select to go along with Active Calculus chapters 1-4.

Finally, as I work with others in my department, I expect the blog this fall to provide some more narrative on teaching differential calculus.  By sharing some thoughts while teaching the course, I hope to provide some insight and perspective on ways that AC can be used by anyone who’s interested.

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