Math with all the feels

The following is a guest post from David Austin. David is Professor of Mathematics at Grand Valley State University, author of the free OER text Understanding Linear Algebra, chair of the American Institute of Mathematics’ Open Textbook Initiative Editorial Board, and much more. He is also one of my closest friends and colleagues, and I’m delighted to share this post about the exciting work he and others are engaging to make braille versions of mathematics textbooks for unsighted users, especially regarding David’s work that creates tactile graphics. You can contact David at austind at gvsu dot edu.


If you’re reading Matt’s blog, chances are you already embrace a fundamental principle that motivates the open textbook community:  students should have access to everything they need to be successful on the first day of class.  This also means that mathematics textbooks should be accessible to our students regardless of their abilities.

In fact, accessibility is a key design feature of PreTeXt, the authoring system that Matt uses to create his great books.  For example, a visually-impaired reader can easily navigate the web versions of the Active books using a screen reader, and Rob Beezer, the founder of PreTeXt, recently made a braille version of Active Prelude directly from Matt’s PreTeXt source.  What’s missing, however, are the many figures that enrich a reader’s intuitive understanding of key concepts.

Your first thought may be, how can one communicate visual information to a visually-impaired reader?  In fact, the relatively new field of tactile graphic design intends to do just that. As described in a recent MIT Technology Review, tactile graphics communicate visual information by touch rather than by sight, similar to how braille’s raised dots express written language.  While tactile diagrams may be created using a variety of technologies, you could think of a collection of dots, raised by an embosser, that represents graphical information.  

Over the past year, I’ve been developing software to help authors create accessible mathematical diagrams following the PreTeXt paradigm.  In particular, an author produces a diagram by creating a textual description of the diagram’s components and how they relate to one another.  For instance, you could say that you want a diagram with a set of axes, the graph of a function, and the tangent line at a point.  Software will then convert this description into a requested format, such as an SVG file for inclusion in a web document or a tactile version suitable for embossing.

Here are two versions of a calculus diagram that were created from the same description.  The one on the left could be placed in a print version of a document or in an online version.  Besides the graphical description, an author can provide annotations that help a reader navigate the diagram using a screen reader and the graphs can be sonified to provide an aural description of the visual information, thanks to contributions from Volker Sorge.  These capabilities are demonstrated in our submission to the Accessibility Challenge at the Web4All conference last May.

A tactile diagram can be created from the image on the right when it is sent to an embosser.  The image has been resized to fit on a standard 11” x 11.5” embossed page, and the labels have been converted to Nemeth braille, a version of braille that communicates mathematical expressions.  Here’s a photograph of a similar embossed image:

Photo credit: Alexei Kolesnikov

The key point is that the author only concerns themself with the description of the diagram while the software handles all the details of producing the graphical output, whether tactile or not.

Last year, the disability resources office at Grand Valley State inquired to our department about accommodations for a blind student taking intermediate algebra because the course’s textbook publisher wanted $40,000 to produce a braille edition.  While a better option quickly appeared, we knew that this student would be using Active Prelude this fall and Active Calculus in the near future.  As a result, Rob got to work making a braille edition of Active Prelude, and I created tactile versions of almost all the diagrams in the book.  Our student has now begun the semester with a braille textbook, complete with tactile diagrams, produced at no cost.  

It’s sometimes said that attention to accessibility benefits everyone.  For example, SMS text messaging was originally developed as a means for the deaf to communicate, and most of us have probably been glad to use a wheelchair ramp at one time or another.  How does that principle apply here?

First, since they are meant to be read by touch, tactile graphics have a much lower resolution and braille labels typically require more characters.  As a result, space feels like it’s at a premium, even though the diagrams are embossed on 11” x 11.5” paper.  As I’ve started to create tactile diagrams, I’ve been reconsidering design principles I’ve used in diagrams for sighted readers, and I feel the urge to reduce visual clutter and communicate information more efficiently.  I’ve been thinking more carefully about diagrams and how a wider range of readers might interact with them, and my hope is that the new diagrams in Active Prelude, once they are included in the next edition of the text, are an improvement for all readers.  

Another issue arose when a blind mathematician was reading one of my tactile diagrams that illustrated a graph and its tangent line at a point.  He told me that his sense of touch had a hard time distinguishing between the graph and the tangent line.  In some sense, that’s the point the diagram is trying to convey, that a tangent line gives an excellent approximation to the graph on a small scale.  In this case, the very idea that I wanted to communicate made it difficult for a tactile diagram to express.  A solution is for the author to carefully ensure that the text and the diagrams are tightly integrated with one another.  In other words, we shouldn’t assume the point we’re trying to make is obvious to every reader, but instead we should strive to be explicit and to reinforce crucial ideas.  While this sounds like a simple principle in expository writing, expanding our understanding of how we can be misinterpreted is extremely powerful and a real gift.

In the introductory article to the recent accessibility edition of the MIT Technology Review, The future is disabled, Ashley Shew considers some of the problems we face as a society, including climate change and environmental racism, and concludes with:

We need more ways to be. Part of that involves looking to alternative ways of sensing, processing, moving, understanding, and communicating, and seeing those ways as good and worthwhile. Opening ourselves up to all-access thinking and disabled expertise will mean a more livable world—one that we all can inhabit. 

This work is part of a larger effort organized by the Raised Mathematics group.  Feel free to reach out to me with thoughts and questions: austind at gvsu dot edu.

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Three notes about updated HTML for APC and ACS

For all Active Calculus texts, users should always view the HTML version of each as the definitive version: the HTML is easiest and fastest to update. You can always see the last date the HTML was updated by going to the book’s front matter page (for example, ACS).

For 2023, the vast majority of updates to Active Calculus Single Variable are minor; most of them are minor typos that shouldn’t cause any confusion between the PDF or print version (each of which are now several years old) and the HTML itself. There is primarily one section of the text where the changes are a bit more substantial: Section 3.1. In response to feedback from several different users, I’ve updated the First Derivative Text and a bit of the surrounding text. If you regularly work from the PDF or print version, I urge you to look at the HTML in advance when it’s time to consider that section with students.

Additionally, this year I’ve made public the alternate version of Chapter 8 at the landing page Three key things about that version: (1) Chapter 8 is entirely different, taking a path through infinite series with the main emphasis being Taylor polynomials and Taylor series with limited emphasis on formal convergence issues; (2) Chapters 1-7 match completely with the original and standard version of the text, with the exception that all of the preview activities in the alternate version are rendered as interactive WeBWorK exercises, which in some cases means that a few of the questions are slightly different (primarily to make formerly open-ended questions more suited to WeBWorK feedback); and (3) the alternate version is only available in HTML at this time. One of the reasons for (2) is that the alternate version of the text is the one that we’ve chosen for the Runestone version that’s available this fall and discussed in this earlier post.

Finally, for Active Prelude: like for the standard version of Active Single, the HTML has been recently updated, and nearly all of the changes are to correct minor typos. There shouldn’t be anything confusing between the print or PDF versions and what’s present in the HTML, though again the HTML will have the fewest errors.

There is certainly more work ahead and in the coming year I hope to make considerable progress on other issues that have been raised. As my favorite example so far, a couple of users have pointed out a fact I didn’t realize: the long-term temperature of a potato in an oven approaches 212 degrees Fahrenheit, not the temperature of the oven itself. This fact means that several activities and discussions need to be updated, and that will occur in the next official version of the text; I chose not to make those changes this year since it would lead to differences in the Activities Workbooks and I feared this would mean greater potential for short-term confusion.

As ever, I am immensely grateful to users who submit errors and suggestions. Please keep sending them to me, ideally via email at boelkinm at gvsu dot edu.

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More on Active Calculus in Runestone

As noted in an earlier post, at Mathfest in Tampa, Chrissy Safranski and I led a minicourse on teaching Active Calculus and using Runestone. We had a great time doing that and here I want to share a few updates and reflections along with some resources we developed.

We had more than 30 people attend the workshop; it was delightful meeting so many new people who are interested in using Active Calculus in some way and who are considering using Runestone as the learning platform on which to deliver the textbook.

Briefly, Runestone is a Learning Engineering Analytics Platform (LEAP) that allows us to render the HTML version of Active Calculus in a way that all of the WeBWorK interactives are “trackable” by allowing students to log in to the textbook. Runestone started out as a platform for free, open, online interactive computer science texts. In the past couple of years, Runestone and PreTeXt have combined forces, and that has led to new opportunities for math textbooks, especially those with embedded WeBWorK exercises.

You can now find a version of Active Calculus (single variable*) in the Runestone library (scroll to “Mathematics”) that features every Preview Activity in WeBWorK and even more WeBWorK exercises at the end of each section. (* the Runestone version of AC is for the one with the new alternate Chapter 8 focused on Taylor series – a good way to get a sense of how this text looks is to look at the online version of AC-alternate.)

If you are interested in learning more about how to get started, Chrissy and I are glad to share with you some resources we developed: a Google doc of instructions for getting started as a student, and another on getting started as an instructor. Of course, you can also read the Guide to Getting Started on PreTeXt Books in Runestone.

The WeBWorK features in Runestone are still in beta — functioning well and getting better all the time; Chrissy was the first person to teach Active Calculus from Runestone in Winter 2023, and she and I and several other people will be doing so in our classes this fall. Some folks from the minicourse are also interested in using Runestone, so I am going to organize a small Google group just for Runestone users (or folks who are curious to learn more). If you are interested in participating, please email me at your earliest convenience.

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Active Calculus – Multivariable

In case you hadn’t heard already, Steve Schlicker is retiring soon (Congrats!) and we have taken over managing and editing Active Calculus – Multivariable (ACM). A few years ago, we started writing material for a chapter on vector calculus topics which many of you have tried and tested. We have incorporated a lot of the feedback and made significant revisions to the materials on vector calculus which will now be included as Chapter 12 of ACM. While the previous versions of this material were rough in spots and sometimes were not parsed into pieces that were right for in class activities, our new presentation has been simplified and activities are more consistent in length and effort levels. Chapter 12 also includes the frequent use of Sage interactive elements when displaying graphics of math elements in 3D. In the summer 2023 edits, we have added WeBWorK and pencil and paper exercises to each of the twelve sections in Chapter 12.

The motivation and presentation of topics in Chapter 12 has been approached from the perspective of trying to measure a particular quantity, like the amount of vector field that flows through a surface or work done by a vector field while moving along a path. Many of these are rooted in physical measurements but the descriptions do not assume any physics background. Since vector calculus is a set of topics that has quite a variety coverage levels at institutions, we tried to make it possible to do surface level coverage or deeper discovery-based activities. In order to aid faculty in planning how they will use Chapter 12, we also have given a flow chart of dependencies for the twelve sections in vector calculus. We selected notations for vector calculus that emphasize the nature of what we are measuring and make notes or comments about other notations that students will see in other sources. For instance, line integrals of vector fields use the notation \(\int_C\vec{F}\cdot d\vec{r}\) to emphasize that we are looking at the accumulation (integral) of the dot product of our vector field with displacement.

ACM (as well as ACS) is now available on Runestone as well. As Matt included in his update post, you should check out all of the amazing features that come with hosting materials on Runestone. (ACM’s Preview Activities are not yet implemented using WeBWorK, but the WeBWorK exercises at the ends of sections can be assigned in Runestone.)

Over the next couple of years, Mitch and I will be working on edits to other parts of ACM including creating a solutions manual and updating other elements across ACM for consistency and easy of use (for students and faculty). Please join us in the ACM users Google Group to make any suggestions for corrections or improvements, as well as get updates on other elements of our work.


Mitch Keller and Nick Long

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Two free, open calculus texts for specialized audiences

If you are teaching a class titled something like “Business Calculus” or “Calculus for the Biological Sciences” anytime soon, this post is for you.

Mike May and Anneke Bart of Saint Louis University have an excellent text for business calculus, Business Calculus with Excel. Endorsed by the AIM Open Textbook Initiative, the text follows MAA recommendations for such courses, the text offers resources that include a collection of Excel worksheets. Learn more at the book’s landing page.

Jeff Shriner of Colorado State University has developed a new textbook titled Calculus for Biological Sciences that builds upon the source code for Active Calculus. The book focuses on dynamical systems in a one-semester course serving life science majors. In addition to adding considerable new material, Jeff’s work includes embedded Desmos interactives, including a full suite for instructors in the “Instructors: Read This” section that he uses as in-class group activities throughout the semester. There are also WeBWorK .def files that align with the text that are available upon request (Jeffrey.Shriner at colostate dot edu).

These books are two great examples of the growing collection of excellent resources available for calculus instructors, ones that leverage the PreTeXt environment and provide interactive activities for students.

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Active Calculus news and updates for Fall 2023

The summer of 2023 has been an exciting time of new developments and opportunities related to Active Calculus. In this post I’ll offer a short overview of the biggest items, and then offer more details in subsequent posts. View this post as a preview of more information to come throughout the month of August.

New website, new blog location: like a fish in water, you’re swimming in it! Thanks for finding the new blog site here on I’m excited to have all of the information about the books and this blog in a single location. Also, some pretty amazing technological developments with PreTeXt have made it possible to build the HTML version of each text right on the hosting server where the books live, so that will make minor updates (for fixing small errors, say) much easier than it was before.

Runestone: a LEAP into the future: “LEAP” stands for “Learning Engineering Analytics Platform”. Imagine having students log in to their book and be able to complete exercises such as Preview Activities and WeBWorK sets right in their HTML with their results saved for them and shared with their instructor. Runestone (which is free and open source) makes this all possible, and we are piloting a Runestone version of Active Calculus (Single Variable) this fall. As noted in a recent post, more info on this to follow after the Mathfest minicourse.

Chapter 8 alternate: Using feedback from instructors who piloted the new version of Chapter 8 last academic year, we now have an alternate version of the text posted here on the website that offers this possibility. More information to come for folks interested in using that version, especially regarding a custom workbook for students for chapters 5-8. Also, I’ll try to make it extremely clear the differences between the two versions and have things organized in a way that makes it easy for people to know which they’re using and where to go for resources.

DoenetML: DoenetML is a new markup language for creating interactive activities for students that is exactly what I’ve been waiting for. I spent a week at the University of Minnesota with about 40 others learning more about the language and its spectacular possibilities. Imagine being able to easily write activities for students that involve moveable graphs and interactive response cells that provide students with immediate feedback … it’s awesome, and you can see some of what a group of folks accomplished at the workshop for preview activities in Active Calculus. Here’s one of my favorites. Like Runestone, DoenetML is free and open source.

Two grant proposals: I’m excited to be part of two large grant proposals — one to extend the types of questions textbooks ask and study how students and instructors use them, and another to establish and grow an open-source ecosystem to support students, teachers, and more. Hopefully there will be good news to share in the future about the being funded and the resulting work and progress they will drive.

Active Prelude in Braille: One of the amazing outcomes of PreTeXt is that the same source that generates the HTML and PDF versions of the text can be used to create a Braille version. Rob Beezer has produced a Braille version of APC that one of my GVSU colleagues will use to work with a blind student this semester. At least as exciting is the work David Austin is doing to generate tactile Braille figures for the Braille version of the text. I look forward to sharing more details soon.

Active Multi – soon with the vector calculus chapter included: Mitch Keller and Nick Long have been hard at work on their additional chapter on vector calculus, and we will soon release that as part of the standard HTML for Active Multi. Watch for a post here on the blog from Mitch and Nick that shares more detail.

Updated ancillaries: by August 21, I expect to post on the Google group for instructors an updated collection of ancillary materials for each of APC, ACS, and ACM. Instructors on the list can see the post from September 6, 2022, for what was available last year; some of that will persist, but I will also be able to add and update.

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Getting ready for Mathfest

At Mathfest, Chrissy Safranski and I will be leading a minicourse titled “Teaching Active Calculus using Runestone” that will introduce participants to the Runestone platform. Runestone is a Learning Engineering Analytics Platform that allows students to log in to their book, to save their work in it, and to have their instructor be able to see and record their progress. Specifically, we have a Runestone version of Active Calculus Single Variable that has all of the Preview Activities instantiated in WeBWorK, along with a larger collection of WeBWorK exercises in each section; all of these can then be “assigned” within Runestone, and the students can do all of that work right inside the HTML version of their text. Once we’ve delivered the minicourse, I’ll post more information here along with some links to resources.

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Welcome to the updated

Welcome to the redesigned, including this new location for the blog that was formerly hosted at

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Fall 2022 reminders and updates

A list of things you might find helpful if you are teaching or learning from APC, ACS, or ACM:

+ Updated HTML

There have been minor updates to the HTML for APC and ACS. These are almost all tiny and fix small typographical issues. The PDF and print versions have not been updated because of the extensive work involved in generating those formats. The HTML version is always the most up-to-date and definitive.

+ Read This!

In both APC and ACS, there are sections in the preface titled “Students! Read This!” and “Instructors! Read This!” If you are new to using APC or ACS, these are strongly recommended.

+ unique URLs for specific items in the text

If you are in the HTML version and hover in the left margin next to any prominent feature of the text, you can get a permanent URL for that feature. For example,

if you click the lavender “link” symbol above, you’ll get a permalink for that particular example. This is a nice way to direct students to a very specific location in the text.

+ Google group for instructors

If you are an instructor using APC, ACS, or ACM and are not part of our Google group, you are welcome and encouraged to join. There I will post more information about ancillaries and supporting materials for instructors.

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A Calc 2 Teachalong

My wife is a professional knitter. She designs patterns, teaches classes and techniques, works at major events like Rhinebeck (think “yarn conferences”) and manages the social media for a yarn company and a yarn shop. Yarn folks often engage in a “knitalong” where a group of knitters gather regularly — sometimes in person, sometimes by Zoom — to work through a pattern together, occasionally led by the pattern designer themselves. This gave me the idea for a “teachalong”.

This fall, one of my classes at GVSU is Math 202, Calculus 2. I haven’t taught this class in 10 years, and already in planning my syllabus and the first week of classes, I have relied on shared materials and advice from several GVSU colleagues.

For anyone who wants to join me, I’m offering a teachalong. First I’ll give a quick overview of the course, and then I’ll sketch out what I think the teachalong will look like (with the disclaimer that I’ve never done this before :-)).

A few things about Math 202 and my section of it:

  • MTH 202 is a 14-week, 4-credit course. My section meets MW 4-5:50 Eastern from Monday 8/29 through Wednesday 12/7 with the final exam on 12/14. We have the usual holidays: Labor Day, Fall Break, Thanksgiving.
  • My class will use Chapters 5-8 of Active Calculus, but Chapter 8 will be the new alternate version I recently drafted. There will be considerable edits to that chapter before November 1, based on feedback I’ve already received.
  • Class meetings are structured to be active. The majority of class time is devoted to students working in small groups on activities in the text.
  • I use an alternate grading system that is designed to promote growth, persistence, and success. There are no midterm exams, but instead weekly Checkpoints (like quizzes) that are based on 15 Learning Targets, along with a consistent workload involving daily prep assignments, WeBWorK sets, written homework, and lab activities. Almost everything is marked on binary scale (“Y” or “NY” – “yes” or “not yet”) with opportunities for revision/re-attempt. Full details in the syllabus.

If you want to join me for the teachalong, here’s what I’m thinking:

  • I will expect no additional work or commitment from you; you can observe, engage, correspond as much or as little as you want. You don’t have to teach the course in any way similar to me. And if it turns out that what we’re doing isn’t of interest to you or you don’t have time for it, you can drop out with no questions asked and no hard feelings from me.
  • With everyone who signs up, I’ll share a large portion of my teaching materials/files: semester schedule, daily “script” (my notes to myself), daily prep assignments for students, WeBWorK sets, Homework exercises (that I’m basically writing from scratch as we go), Labs, and Checkpoints. These will be in a shared drive that folks who sign up can access as the files in it grow and change.
  • I will host a standing 30-minute Zoom drop-in at least every-other-week. This is subject to scheduling constraints, but based on my own calendar, I expect such meetings will be late on Thursday afternoons or sometime on Fridays between 12 and 2:30. There is no agenda for these meetings other than to discuss how our classes are going and any questions you’d like to ask of me. This is also an opportunity for me to learn from you how you use Active Calculus and ways I can be of additional support.

If you are interested in participating, email me at boelkinm at gvsu dot edu by 4 pm on Sunday, August 28, and put the word “teachalong” in the subject line. By early next week I will correspond with the people who have expressed interest, invite them to the shared drive where I post my materials, and send out a poll to find a possible meeting time.

As always, if you have questions about particular resources for any of the Active Calculus courses, I welcome hearing from you.

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