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

Posted on September 4, 2013 by Matt Boelkins

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)

Posted on August 30, 2013 by Matt Boelkins

[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

Posted on August 28, 2013 by Matt Boelkins

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

Posted on August 22, 2013 by Matt Boelkins

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

Posted on August 19, 2013 by Matt Boelkins

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

Posted on August 12, 2013 by Matt Boelkins

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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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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