Here’s an interesting article regarding the effect of electronic vs print textbooks on student learning when reading for understanding: https://www.businessinsider.com/students-learning-education-print-textbooks-screens-study-2017-10.
“Our work has revealed a significant discrepancy. Students said they preferred and performed better when reading on screens. But their actual performance tended to suffer.”
The article has lots of interesting observations on things like the scrolling effect, how the purpose of a person’s reading matters in connection to the medium, and how some students with certain reading traits are actually more effective reading electronically over print.
I’m going to use this article to start a conversation with my students about what version of the text they should use for my courses, and encourage them to consider print. While both Active Calculus and Active Prelude to Calculus are free in .html and .pdf, the print versions of each can be purchased for $21 and $17, respectively. For many students, it may well be worth the additional money to invest in a print copy.
Many instructors use online homework systems with their students. This approach provides accountability for students, immediate feedback and multiple attempts on their work, and simple grading for instructors. While I’m always glad to share WeBWorK .def files with users who have access to a WeBWorK platform, for people without such access there hasn’t been a good low-cost alternative until recently.
Edfinity is a new online homework platform that offers access to WeBWorK’s Open Problem Library through an easy-to-use modern interface. Several different schools that have adopted Active Calculus have been using Edfinity for the past year, and as a result, a full “course” of online homework exercises that correspond to Active Calculus (single variable) is now available. You can access the course from Edfinity’s course catalog; you can edit and modify as you see fit, but by using the course you’ll have a pre-selected collection of online homework problems that align directly with the text.
Edfinity is very affordable, especially when used in conjunction with a free text like Active Calculus. There are three options to pay the fee (which varies, but comes out to $2-$4 per student per month, something on the order of $12-$16 per course):
If you are already using Edfinity or choose to use it this year, I’d welcome hearing from you about your experience (either here in the comments or privately by email – boelkinm at gvsu dot edu). I’m hoping to experiment with it myself in a full course in the near future.
I added new sections to the preface of Active Calculus this year, including “Students! Read This!” and “Instructors: Read This!” My main goal in writing these was to help better ensure that users of the text are aware of some of the features of the text, especially in the HTML format. There are similar sections in Active Prelude to Calculus.
In addition to the written text, I created a 15-minute screencast on how I think students should use the text. In the video, I discuss the different formats of the text, how a typical section is structured, the importance of using an Activities Workbook, knowls and interactive graphics, WeBWorK, and how the text looks on a smart phone.
I hope anyone using AC or APC (instructors included) will take time before the semester begins to watch it.
I’m excited to share several important updates:
1. new landing page at https://activecalculus.org
2. updated versions of Active Calculus (single variable, 2018 edition) in HTML, PDF, and print (with updated activities workbooks [1-4], [5-8], too)
3. updated version of Active Prelude to Calculus, now hosted at the main page and with HTML, PDF, and (new!) print available (plus an activities workbook)
In a bit more detail:
1. At https://activecalculus.org, you’ll find information about all three texts I’ve contributed to: Active Prelude to Calculus, Active Calculus (single variable), and Active Calculus Multivariable. In addition to the landing page, there’s an individual page devoted to each text, and those pages provide additional information about the text and available ancillary materials.
2. Thanks to a large amount of helpful user feedback in the 2018-19 academic year, I’ve made numerous updates to the 2018 Edition of Active Calculus, resulting in “2018 Edition – UPDATED”. The vast majority were minor (many had to do with correcting errors in the answers to activities and exercises, which were newly included in the 2018 edition); the differences were not substantial enough to merit calling it the “2019 Edition”. The most significant changes can be found in Section 5.6 (with a much clearer discussion of the error of numerical integration techniques), Section 3.1 (some clarification on terminology with “increasing” and “decreasing”), and Section 5.2 with an added exercise on how the absolute value arises in antidifferentiating the natural logarithm. If you would like a full list/changelog of what has changed between August 2018 and July 2019, email me to ask: boelkinm at gvsu dot edu.
The main logistic issue of note: if you have students who were using the 2018 edition for calculus 1 at some point in the last year and will be taking calculus 2 in Fall 2019 or later, they should download the updated PDF and be aware that there are some minor differences between that and the version they had previously. This is especially important if they purchased a print copy of the text from Amazon before July 30, 2019. The 2018 print version is still fine to use, but just beware the changes noted above. Same for activities workbooks.
In print and PDF, you know you have the most up-to-date version if on the cover you see “UPDATED” following “2018 Edition”. The HTML at https://activecalculus.org/single/ is “2018 Edition – UPDATED”.
3. In January, I released the first public version of my new calculus-prep text, Active Prelude to Calculus. I originally titled it “Active Preparation for Calculus“, but subsequently decided that the “Prelude” title was a better fit, and that it was early enough in the book’s life to make the change.
Over the course of the coming year, I expect that my GVSU colleagues and I will develop some ancillary materials to support Active Prelude; for now, the main one available is the activities workbook, which you can acquire for free in PDF by emailing me (boelkinm at gvsu dot edu) or in print form on Amazon.
As ever, I welcome hearing from users at any time with questions, error corrections, or suggestions. Thank you for considering https://activecalculus.org as a resource for your calculus-related teaching and learning.
[August 2019 update: I re-named the text “Active Prelude to Calculus” as part of recent summer 2019 editing. I won’t change the title again :-). All else below still applies, with updated links.]
Back in May, I wrote of my pending fall 2018 sabbatical and plans to write a textbook for the calculus-prep course that we now offer at GVSU. I’m pleased to share that a complete draft of my latest free, open-source text, Active Preparation for Calculus, is now publicly available in HTML, PDF, or its original PreTeXt source. I also have an activities workbook in PDF available upon request.
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.
On Tuesday 10/2, I was honored to speak in the MIT Electronic Seminar on Mathematics Education. The recorded video from the seminar is now available to view; my slides are also posted. If you watch/listen to the recording, I apologize in advance for the fact that I struggled with my voice and a cough as I was getting over a cold.
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?
I stumbled across this great post by Robert Ghrist of the University of Pennsylvania. More people should read and follow it. I’ll add that I agree with nearly everything he says and add one additional positive that’s not explicit: by self-publishing on Amazon, you can also release your work electronically for free (if you so choose).
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.
I’m excited to share that I’ve been invited to be one of the speakers in the excellent MIT EMES seminar. My presentation on Tuesday, 10/2/18, at noon EST will be a practice-focused discussion centered on how I structure my calculus classes around active learning. I’ll share explicitly how I use Active Calculus and a collection of ancillary materials that I and others have developed. The talk will be a good update to this post that I wrote four years ago (especially since I never completed the promised following post).
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.
One of the ancillaries that we offer to support the use of Active Calculus is a collection of “daily preparation assignments”. These assignments are modeled on Robert Talbert’s “guided practice” and provide students a short list of concrete tasks to complete prior to class so that they are prepared to actively engage with new ideas during class meetings. The .tex and .pdf files for full semesters of differential and integral calculus are available upon request to any who asks by email (boelkinm at gvsu dot edu). I wrote the assignments for differential calculus; my colleague David Clark wrote the ones for integral calculus. A typical daily prep assignment has an overview, a brief summary of learning objectives, a short combination of reading and/or videos to watch, and usually the completion of a preview activity and a couple of basic exercises.
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.
