The text is written in the spirit and style of *Active Calculus*. Each section begins with a short introduction followed by a preview activity designed for students to complete prior to class, and proceeds with a mix of text and 3-4 activities that are designed for students to complete cooperatively during class. The number of worked examples is small, as students are expected to actively engage with the material in order to develop conceptual understanding.

I’ve written in a backward-looking fashion: from the perspective of someone who regularly teaches calculus, what are the most important ideas that I want my calculus students to know? What are the prerequisite concepts they often struggle with? Throughout, I kept in mind the fact that the audience for this text is students who will have seen related ideas in previous courses, so I endeavored to introduce new perspectives and approaches that will challenge students to think differently and develop new understanding. For example, linear functions are formally defined as functions whose average rate of change is constant.

The result is not a traditional “precalculus” book. When I read precalculus or college algebra books, I often find a considerable portion of the content devoted to topics that aren’t used much in calculus, as well as limited emphasis on central calculus-related ideas. In *Active Preparation for Calculus*, I chose to focus on helping students understand **functions as processes **(shaped considerably by the work of Marilyn Carlson et al — hat tip: Dave Kung), gain insight into a **library of the most important basic functions **(including how these lead to** families of functions that depend on parameters**), use **average rate of change** to interpret trends in function behavior, see how familiar functions **model important phenomena** in the world around us, and begin to comprehend the use of **limits to describe key aspects of function behavior**. Throughout, we work with functions from **numerical, graphical, and algebraic perspectives**, with an emphasis on the prominent role of **inverse functions**. The text includes a modest amount of trigonometry, with the primary focus being on the **sine and cosine as circular functions, **plus some key **right triangle trigonometry**. Further, through such problems as investigating water entering or leaving a tank with a certain shape or how constrained surface area of select containers enables us to write their volume as a function of a single variable, students encounter **fundamental ideas they’ll see again in calculus in the settings of related rates and optimization problems**, and themselves develop the functions that represent the quantities of interest. We also consistently make the distinction between** exact and approximate values**. I describe my overall goals and approach in more detail in the preface.

I hope that the text will not only serve as the basis for other calculus-prep courses, but also as a useful review resource for students currently in calculus who need to refresh select fundamental concepts and ideas.

Like the original version of *Active Calculus: Single Variable*, this first draft has 3-4 challenging exercises per section. For more routine exercises, instructors will need to supplement with WeBWorK or some other source of free, open problems. You might find Edfinity an option as well. I will be adding anonymous WeBWorK exercises to the text in the near future, and expect to have these (like the ones in *Active Calculus*) in place by August 2019. For now, I have some WeBWorK .def files that correspond loosely to the text that I’d be glad to share upon request.

At the upcoming Joint Math Meetings in Baltimore, I’ll be giving a talk on the text in the OER session. The talk will occur in Room 301 of the Convention Center on Wednesday, January 16.

I’m grateful to Grand Valley State University for the time provided by a sabbatical leave; to Rob Beezer for developing PreTeXt, the publishing language that allows the beautiful HTML output; to the American Institute of Mathematics for their support of free and open texts; to Mitch Keller for feedback, suggestions, technical support, and his usual production genius in creating the PDF; to David Austin for his help with graphics generally and fantastic interactives like Figure 1.8.10 specifically; and to each of you who wrote me back in May and June with ideas and requests.

As ever, I welcome hearing from you with your comments on errors, better approaches, and suggestions for additional topics and exercises.

]]>I promised the participants that I’d follow up by reading through the chat stream from Zoom, responding to any issues that I didn’t get to in the seminar and sharing resources that others suggested. First, here are a two lists that I think others will find interesting and useful, most of which come from the many participants:

**Phrases that people suggested to describe active learning:**

+ inquiry based learning

+ making thinking visible

+ student centered

+ students drive the mathematical agenda: the discovery of the mathematics

+ actively engaging students in the classroom in authentic mathematical problem solving

+ the instructor inquires into student thinking as students inquire into mathematical content

+ productive struggle

**Examples of free or open-source materials the participants use:**

+ Desmos classroom activities – https://www.desmos.com/

+ We use OpenIntro’s statistics textbook – https://www.openintro.org/stat/textbook.php?stat_book=os

+ “find the error” by doug shaw – http://uni.dougshaw.com/findtheerror/index.html

+ I get lots of ideas from http://www.iblcalculus.com/, whether or not I implement them as an IBL activity or not

+ Poll Everywhere – https://www.polleverywhere.com/

+ http://mathlets.org/

+ Also Active Calculus multivariable – https://activecalculus.org/multi/

+ This is K-12 but has great tasks. Some of the higher grade level tasks can be used with college students: https://www.illustrativemathematics.org/content-standards

+ I am planning to use this next semester for an Abstract Algebra Course for Secondary Pre-service Teachers https://taafu.org/ioaa/index.php

+ Wolfram Demonstrations Project – https://demonstrations.wolfram.com/

+ Siefken’s linear algebra notes (I think the following link is right) – http://iola.math.vt.edu/

+ Good Questions Project at Cornell for “clicker” questions – http://pi.math.cornell.edu/~GoodQuestions/

+ wolframalpha.com for quick calculations and checks between pairs/groups

+ https://www.artofmathematics.org

+ CalcPlot3D – https://www.monroecc.edu/faculty/paulseeburger/calcnsf/CalcPlot3D/

+ geogebra – https://www.geogebra.org/

+ http://math.colorado.edu/activecalc1/index.html

+ pretextbook.org (this is Rob Beezer’s new publishing language that Active Calculus is written in)

+ MIT Opencourseware https://ocw.mit.edu/courses/mathematics/18-01sc-single-variable-calculus-fall-2010/

+ These Desmos Activities have some additional questions that are not in the Preview Activities in the book https://github.com/sergeballif/sergeballif.github.io/blob/master/Desmos/DesmosActivities.md

+ Mathquest at Carroll College: http://mathquest.carroll.edu/

+ David Austin’s Understanding Linear Algebra:

http://merganser.math.gvsu.edu/david/linear.algebra/ula/ula/ula.html

**Questions. **Participants asked a host of great questions. I’ve listed below all of the ones that came through by chat. If memory serves, I responded to all of them but one. I will refer people to the seminar recording for almost all of these, and here I want to respond to the one that I didn’t get to, which is noted in red below.

> I’d be really interested to hear more about how you went about developing the activities — this would be really helpful for me in thinking about other classes where something as great as AC doesn’t yet exist.

*I started small. Early in my time at GVSU, I wanted my students to engage in more active learning. So I started writing individual activities. Usually I tried to think of these using the following criteria:*

* + provide a rich and meaningful context that is accessible to students*

* + ask a sequence of questions that is clear and focused*

* + plan for each activity to be do-able in 15-20 minutes by students who are engaged*

* + challenge students to reason in multiple ways and from different perspectives*

*After I’d taught calculus 4-5 times, I had a collection of maybe 20 such activities, adding to the list each time I taught the course. Then I learned that several of my colleagues were doing the same kinds of things and asked them to share. After some light editing and additional writing, my collection of activities for calculus 1 grew to 50 or more; when I printed it as a coursepack and had students buy it for $6, it was about 100 pages (activity statements with room to work). That pack of activities for calculus 1 was pretty fully developed over a 10-year window of time. I used that as the basis for the textbook, for which I was granted a 1-semester GVSU sabbatical to write the first four of the eight chapters.*

*My advice for developing your own activities for courses where you can’t find good resources is: play a long game. It’s completely fine to start small and build on your work over an extended time. While the status quo might not be what you aspire to, the status quo is still ok. Just work to make the course better every time you teach it. Over a long career, it’s amazing (still almost astonishing to me) how these resources accumulate over time and can end up producing something that others find useful. And: share your work with others. We have a lot of power to develop rich materials when we share with one another since it lowers the duplication of effort and improves the ideas that we often develop in isolation.*

The rest of the questions people asked that are addressed in the seminar recording follow. I’m very grateful to everyone who participated and contributed, and again to Haynes Miller and MIT for the invitation to speak and hosting this ongoing seminar.

]]>> why is workbook by request?

> Do your students bring their own computers to class?

> How do you grade writing assignments?

> Are these webwork problems available to be added to other problem sets (not linked to the text)? do students need to create an account?

> How large is your class?

> What do your meeting times look like? (That is, how many times per week and for how long?)

> Can this work with 50-minute lectures?

> in class are students all working on a set of shared problems, or is it more individualized for each student

> How many students actually complete the pre-class activities?

> What is discussed during the ‘daily debrief’?

> I notice there is no “wrap up” at the end of class. Is that on purpose?

> Would you be comfortable using the same structure in a class of size 200?

> Are all students comfortable with working in groups? Is individual work welcomed? I am also wondering what a student would do if they finish the exercises quicker than others

> could you talk a little more about structures to provide for different learning pathways for students with varying prior experiences with mathematics and confidence in their abilities

> deskwork vs groups at a blackboard?

> How did you handle the “coverage” issue? Did you have to give up content?

> Do you collect pre-class activities? How do you handle all the paper?

Robert also mentions that, “The truly difficult part of e-text production is getting something that looks really good.” True statement. Which is why aspiring authors should also use Rob Beezer’s PreTeXt, which leads to spectacular HTML output.

While certainly there are advantages to working with a publishing house for marketing and more, the new reality is that with Twitter, the web, and Amazon, good work has the potential to get known widely without having to have its cost ridiculously marked up by one of the big corporations. Seriously, if you’re working on a book, you should try out what Robert suggests.

]]>The seminar will emphasize ways to use active learning, but there will definitely be a pitch for using and sharing free and open source materials.

The seminar is held on Zoom and is open to anyone interested in attending. Presentations are recorded and available after the fact from the website. I’m hoping that many users of *Active Calculus* will participate so that they can actively participate and share ways that they are engaging their own students.

The ancillary supporting materials that I discuss will be available to others upon request.

I hope to see you at the seminar; you’ll be able to join it a few minutes prior to noon EST at this link: https://zoom.us/j/8803591328.

]]>I’m excited to share that there are now online versions of these assignments that include embedded videos. Thanks to Charles Fortin and Gabriel Indurskis of Champlain St. Lambert College, there’s now the option of using these assignments in HTML format. Many of the assignments use existing videos from the GVSU YouTube channel, but others are newly created. The full collection of assignments is housed at http://math.mychamplain.ca/ on an easily searchable and fully indexed site. Click on “Calculus 1” or “Calculus 2” in the upper right to see the full list of daily preparation assignments for differential or integral calculus.

This is a wonderful example of the benefits of open-access course materials. I’d shared our daily prep assignments with Charles and Gabriel some time ago. They took them and made them even better, and now they’re available in an easy-to-use format for everyone. If you have similar developments related to *Active Calculus* (or calculus in general), I’d love to hear about them and be able to post them here.

Don’t forget that the preview activities are also available as a collection of Desmos activities, thanks to Marcia Frobish and Taylor Short of GVSU.

]]>By creating an instructor account in *Desmos*, anyone can use these versions of the previews and assign them in this format to their students and use the wonderful features of *Desmos* to have students explore and respond while also being able to track students’ progress electronically.

Taylor and Marcia: thank you for providing this great resource for others to use as a complement to Active Calculus.

]]>Each workbook is 8.5×11″ in size with a soft-bound cover. The activities are printed on the faces of the odd pages with the even pages left blank for additional room to work. The pages are not perforated nor three-hole punched, so they are not designed to be removed to hand in. But I think the format is a really nice one for student to take notes in: all the activity statements are provided, graphs are large and easy to mark up (including blank axes where appropriate), and all of the activities are in a single location for students.

The workbooks share the same table of contents and a single page-numbering scheme, but are separated into two books so that they are lighter and each appropriate to a single course. They each sell for $7.95.

University bookstores are still welcome to print the PDFs as coursepacks and sell them to students if that route is preferred. The PDF versions of the workbook are available upon request at boelkinm at gvsu dot edu.

Special thanks to production editor Mitch Keller of Morningside College for his efforts that have made these activity workbooks possible.

]]>- Active Calculus – Single Variable PDF version
- Active Calculus – Single Variable print version
- Active Calculus – Multivariable PDF version
- Active Calculus – Multivariable print version

Please take care in directing students to the 2018 or 2017 editions as needed. All should be clearly marked, regardless of HTML, PDF, or print.

More info at https://activecalculus.org.

]]>I’m excited to share several updates to *Active Calculus*:

**1. New 2018 edition of Active Calculus – single variable**

The 2018 HTML version is now live at https://activecalculus.org/single/. The PDF will be posted in the near future on a new page at GVSU’s ScholarWorks site. And the 2018 edition will be available for purchase on Amazon soon as well. I will post here on the blog when each of these versions in other media are publicly available.

The major differences in the 2018 edition are:

+ improved, more concise prose. Kathy Yoshiwara of the AIM Editorial Board read and marked up the entire book. Her changes have made the text less verbose, more consistent, and easier to read. I’m deeply grateful for her work.

+ appendices with answers to all activities and non-WeBWorK exercises. See, for instance, https://activecalculus.org/single/solutions-1.html. These appendices are in the HTML edition and will appear in the electronic PDF, but will not be included in the print edition in order to keep the cost of bound copies as low as possible. Huge thanks to Rob Beezer (University of Puget Sound) for the added features in PreTeXt and production editor Mitch Keller (Morningside College) for helping make these features a reality.

+ minor errors reconciled. Thanks to everyone who has sent me an email or filled out the online feedback form to provide corrections and suggestions. Feedback on errors or ambiguities is always welcome.

+ updated Creative Commons license: CC-BY-SA. The prior license had “NC” included. If you are interested in the differences, see https://creativecommons.org/licenses/by-sa/4.0/ for details.

**2. New 2018 edition of Active Calculus – multivariable — now in HTML**

My colleague Steve Schlicker has been hard at work converting the multivariable text to PreTeXt so that it could be published in HTML. He has concluded that project and you can see the result at https://activecalculus.org/multi/. Like the single variable text, the PDF and print versions are expected to be public within the next couple of weeks. I will post announcements here when they are available.

**3. Updated landing page for activecalculus.org, with archive of past editions**

At https://activecalculus.org/, you will find links to both the 2018 single and multivariable texts in HTML. When we have the PDF and print versions available, those respective links will appear there as well.

In addition, at the bottom of https://activecalculus.org/ you’ll find an archive of past editions (currently just the 2017 editions). Note particularly that the 2017 single variable text in HTML is available at https://activecalculus.org/single/2017/.

We will keep the earlier editions accessible for a minimum of several years. Faculty, be careful to direct your students to the version you’re using: if you used the single variable 2017 text for calculus 1 in the winter/spring semester of 2018, you may wish to continue using that for calculus 2 in the fall semester of 2018. Other than modest updates to the prose (which change pagination in the PDF & print versions) and the presence of the appendices of answers, there are no significant changes. If you are starting calculus 1 this fall, I recommend using the 2018 edition.

In the near future, I’ll post additional updates at this site regarding the PDF and print versions as they become public. I also have some new ancillary materials to share.

Please check out https://activecalculus.org/ and don’t hesitate to contact me at boelkinm at gvsu dot edu if you have questions.

]]>MTH 124 has run for three semesters at Grand Valley, and I taught sections of it in both fall 2017 and winter 2018. The audience is students who have passed or placed out of Intermediate Algebra, but who otherwise would take 3-credit courses in both college algebra and trigonometry. Because college algebra (MTH 122 at GVSU) and trigonometry (MTH 123 at GVSU) are stand-alone courses that serve large numbers of students as terminal courses, and we found that many aspiring math, statistics, computer science, engineering, and physics majors — whose ultimate goal was to complete part or all of our calculus sequence — were taking MTH 122 and 123, we decided to create MTH 124 to focus on ideas that are most important for calculus to strive to prepare them as much as possible.

This aspiration begs an important question: what prerequisite ideas are most important for calculus? In the 2015-16 academic year, a group of us at GVSU thought about this carefully, and developed a syllabus of record for the course. As colleagues and I have taught the course, we’ve gotten a better sense of what should be included. Indeed, as I’ve worked with my students, I’ve written a fairly extensive set of activities; if you read the table of contents, you’ll get a good idea of how the course is organized.

**So, my ultimate question is to potential users out there, before I start writing in earnest:** what topics and ideas would you most like to see? From my existing table of contents and activities, what is missing? Are there things you see in the existing materials that don’t belong?

Another question I have is: what would you like to see process-wise? I expect to write in a style very similar to Active Calculus, with a preview activity followed by 3-4 activities per section, along with a handful of challenging writing exercises. I also plan to include WeBWorK exercises in each section. There are emerging possibilities with interactive graphics and more, so if you have thoughts, please share them. The goal will be a very student-driven, active-learning text.

Finally, a relatively minor question – but still one that is important to me – is: what should the title of the book be? The working title is “Active Precalculus”, as the text will very much be written in the style of Active Calculus. But the word “precalculus” is often misused in our community, so I’m inclined to try not to use it. I’ve thought of “Prelude to Active Calculus” or “Getting Ready for Active Calculus” … neither seems quite right. If you have a good idea, I’d love to hear it.

I would welcome hearing from you in the comments, on Twitter, or directly via email at boelkinm at gvsu dot edu. Your feedback will be most helpful if I receive it by June 15.

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