*Hi everyone! A massive thanks to Professor Matthew Boelkins, Grand Valley State University, for taking the time to share some info about his project, Active Calculus. -SY*

*1. Please tell us about yourself.*

I've had the good fortune to serve on the math faculty at Grand Valley State University in Allendale, MI, for more than 20 years. I'm also one of the two editors-in-chief of PRIMUS (Problems, Resources, and Issues in Mathematics Undergraduate Studies), and have held that position for 5 years, following 5 years as associate editor. My interests span a wide range of undergraduate teaching and learning of mathematics, but much of my recent creative energy has been focused on developing textbooks that encourage active learning.

*2. Briefly describe “Active Calculus”? How much does it cost to the student?*

Active Calculus (there are both single and multivariable texts; I'm the lead author of the single variable one, and will focus on that in my responses) is a free, open-source textbook designed for a standard calculus sequence taught from an active learning perspective. Rather than lots of worked examples, most of the text is structured around activities for students that are designed to be completed before or during class, the latter with encouragement and feedback from peers and instructor. Interested people can learn more at https://activecalculus.org/.

*3. What are some of the reasons why you decided to write “Active Calculus?”*

There were two main reasons. First, I read an article in MAA FOCUS about the \$21M home built by the author of a popular calculus textbook. I figured that if the author had earned that much in royalties, the publisher had likely made \$210M. It was no longer tenable for me to ask my students to pay \$150 for a textbook that had ideas in it that had been well understood by humankind for decades, even centuries. I wanted to write something that would be free for them.

In addition, while at the time I began writing (around 2010) I didn't fully know the scholarship that tells us why active learning is better, I used a lot of active learning in my own teaching and had found my students to be more successful than when I used to lecture. Having developed a collection of activities for calculus to use in my own teaching, I had the idea to use those as the foundation for the textbook, and that's what led to Active Calculus. When the Freeman report came out in 2014 (https://www.pnas.org/content/111/23/8410), that provided added motivation for making the text a good one.

*4. What is a typical day like in a course using “Active Calculus” when you teach using it? Can you use it with flipped learning or with IBL methods?*

For each class meeting, I prepare a written script with estimated times. In advance of most classes, students complete a "daily prep assignment" that normally consists of a short reading, a preview activity from the text, and 1-2 additional questions; students spend 30-45 minutes completing these, and their work is graded on effort and completeness for 5\% of their semester mark. Most classes then begin with a "daily prep debrief & discuss" (6-8 minutes) where students check in with one another and see what questions they might want to discuss as a class.

From there, we usually engage in some brief (5-7 minutes) lecture & discussion to build on daily prep and set stage for an activity. Students then work in groups of 3-4 on an activity from the text for 15-20 minutes, followed by or including some discussion for closure, transition, and new ideas (adding another 5-10 minutes), and then we are on to the next activity for 15-20 minutes. Often I teach our 4-credit calculus class on a schedule with two 2-hour meetings a week, so we basically rinse and repeat this schedule for a second hour, but without a daily prep assignment to start the 2nd hour.

I've written a blog post that has some more information and detail, including references to key preface sections of the text for students and instructors, as well as a video for students on how to use the text: https://opencalculus.wordpress.com/2019/08/05/how-to-use-active-calculus/

I think the text is particularly well-suited to a flipped learning setup: when I have students complete daily prep assignments, they are doing some key basic learning on their own outside of class. The in-class activity-driven style also fits with engaging students during class in the some of the most important and demanding work of the course. Some of my GVSU colleagues have created screencasts that accompany the text, and these would work especially well for a flipped experience:

*5. What are some of the responses by faculty and students after using “Active Calculus”?*

For views of some faculty who have reviewed or used the text, see https://open.umn.edu/opentextbooks/textbooks/active-calculus-2-0. I get a lot of email traffic about the text, and many of those responses express gratitude for the text. Recently, an instructor who is a first-time user this fall sent me a very kind thank-you note: "I wanted to write to say how much I've appreciated Active Calculus. I was a bit suspect (I've been using Stewart), but I am so impressed with it. I like the problems, the students working in class, the organization ... it's really quite good. I'm excited to be teaching this class again. And thanks for saving our students some money as well."

This fall, I also surveyed Active Calculus users via my email list and Twitter, and in an open comment part of the survey, I got additional feedback such as:

"I appreciate you and your work on this so much. It's really let me teach calculus in the way I want to without having to create the material from scratch. A million thanks."

"The book is well thought out with great examples. When I teach the class, I really feel like I am actively working through the book with the students. One comment our Quantitative & Symbolic Reasoning Center director told me was that students in Active Calculus sections are asking why a concept is true and being stuck on the theory, while students not using AC are asking questions on the algebra and not thinking about the concepts of the course. "

"I really appreciate the structure and the way that the text works. It has been a game changer for my teaching of Single Variable Calculus! Our pre-calc teacher is now using Active Prelude as one of her core texts and we are excited to see how that influences students being prepared for my class."

"I've been using Active Calculus since my first year of teaching AP Calculus AB and I can't imagine using any other curriculum. I cannot thank you enough for the time and energy that you have put into your work and my hundreds of students over the years thank you as well."

As to what students say, I think that many students find the book different at first, and thus at times frustrating. They have been trained to expect a book that has lots of fully-worked examples, followed by exercises that are similar to the examples. Active Calculus is not that way.

Some of the instructors who responded to my survey commented on what students say:

"It's an excellent book. Students and I both really appreciate its clarity and accessibility. Just yesterday I was recommending to a student the very nice "Summary" bits at the end of each section, and they said, "oh, that's exactly what I was looking for.""

"I really like the text and got mostly positive comments from the students on the course evaluations last year. In the past, the comments were almost all negative or neutral."

"I asked my students and they expressed appreciation for how easy it is to read. Some students also said they wished there were more examples, which gave me an opportunity to remind them why there aren't more examples. :)"

*6. How widespread is “Active Calculus”?*

One of the challenges of having a text that's free and available online is knowing exactly where it is being used.

I'm aware of at least 17 4-year universities, 2 2-year colleges, and 5 high schools that have formally adopted Active Calculus as their required textbook. People from at least another 30 institutions have responded to my recent survey to say they are using it fully in their own course, even though the text hasn't been adopted by all of their peers.

Here's the list of adopters I have at present:

California State University, Monterey Bay

Carroll College

Doane University

Dordt University

Lane Community College

Laurentian University (@ St. Lawrence College)

Lebanon Valley College

Lenoir-Rhyne University

Nevada State College

Scottsdale Community College

Sonoma State University

St. Mary's College of Maryland

Texas Lutheran University

The College of Idaho

University of Northern Colorado

Vermont Commons School

Vernon Hills High School

Westfield State University

Westminster College (SLC)

Westmont College

Wyoming Seminary

*7. Could this book be used in high school?*

Absolutely, and several of them have publicly shared their experiences. For instance, Dave Sabol of St. Ignatius High School has used AC for several years and writes about corresponding activities he has developed on his blog, https://therationalradical.wordpress.com/calculus-resources/. Jim Pardun and Steve Korney of Vernon Hills High School recently presented on their work teaching AP Calulus using AC at the regional NCTM conference in Nashville.

*8. What are your future plans for your texts?*

The overall goal is to keep making both Active Calculus and Active Prelude to Calculus better.

For Active Calculus, the original text was written in LaTeX and later converted to PreTeXt, which allows the HTML output. I'm realizing that I haven't yet taken advantage of many of the features PreTeXt offers, such as having better cross-referencing, a better index, and more interactive features. A first goal is to make revisions to take advantage of those features. I am also considering adding Sage cells to the text to offer some embedded computation and experimentation for students; having some interactive computational opportunities is a second thing I hope to incorporate in the not distant future. And a third significant goal is to have some additional exercises, ideally with many of them focused on modeling and applications.

For Active Prelude, this is the first year the text has been public, so I'm waiting on some user feedback to see where to focus energies next.

*9. Anything else?*

People can learn more at https://activecalculus.org and https://opencalculus.wordpress.com/, and I always appreciate hearing directly from users or people interested in the text by email at boelkinm at gvsu dot edu.