• This web page describes an activity within the Department of Mathematics at Ohio University, but is not an official university web page.
• If you have difficulty accessing these materials due to visual impairment, please email me at mohlenka@ohio.edu; an alternative format may be available.

Calculus Textbook Consideration

Considerations

• We need to follow the TAG/OTM guidelines for what is in each course. Note that this might not include everything we currently teach in the course.
  • MATH 2301 Calculus I: TMM005
  • MATH 2302 Calculus II: TMM006
  • MATH 3300 Calculus III: TMM018/OMT018
• MATH 2301 and MATH 3300 serve different populations. Although using the same book for the whole sequence is convenient, it could cause an inferior choice for some of the courses. There are 4 to 5 times as many students taking 2301 than 3300. Usage of online homework by instructors declines from 2301 to 2302 to 3300.

Assessment of Active Calculus

Kelly Bubp, who used the book in Spring 2018 and Fall 2018, says "... I endorse the book 100%. This does not mean that I do everything exactly as the book does it, but that overall, I believe the book supports an optimal, research-based, learning environment for students."

The more detailed assesment below is by Martin Mohlenkamp, based on his usage in Fall 2018 (syllabus).

Format

The primary access is an online html version. (There is a pdf version and printed version but few students use them.)

• Free
• Mobile friendly. Works well even on phones.
• Accessible (anytime, anywhere (with internet))
• Accessible (compatible with screen readers for the visually impaired)
• Some interactive content: live WeBWork exercises (scores not recorded), links to applet demos. (More is possible within the format.)

General comment: Whether we switch to this book or not, these format features are "The Future" for lower-level textbooks.

Online Homework

• Not attached to a particular system.
• Kelly used WeBWork, hosted by the MAA
• I used Edfinity, which puts a modern front-end on WebWork.

General comment: The ecosystem for online homework systems is in great flux. Not being attached to a particular system would allow us to try options and switch more easily.

Pedagogy

• See the authors' statement of goals and text features.
• Provides an out-of-the-box way to do active learning. Instructors do not have to design their own activities.
  • Preview Activities encourage students to come to class prepared. (I collected and graded them using a simple scale. Kelly assigned them in WeBWork.)
  • Many in-class Activities. Some are routine and some are "rich".
• Emphasizes rates of change (especially velocity and acceleration of an object) and consistently motivates the calculus by them. (For example, starts with average velocity without first doing a chapter on limits.)
• Has better connectivity between sections and more repetition. Concepts are anticipated in earlier sections and revisited in later sections. (For example, the concept of increasing is anticipated in section 1.1 and keeps being used, while not officially covered until section 3.1 on extreme values. In Stewart increasing does not get mentioned until section 4.1 on extreme values.)
• More graphical and conceptual. There are many activities where students deduce things from graphs.
• Less sadistic. While many activities use "hard" concepts, few have gratuitous calculations. (I remember a problem in Stewart that required taking a derivative using the product and chain rules, applying a trigonometric identity to convert all sines to cosines, factoring the result polynomial in cosines, figuring out the angles that made each factor zero, ...)

Content

• More graphical and conceptual. Successful students may have a better understanding.
• Less computational. Will not be as effective at filtering out students who cannot handle messy calculations. (Filtering could be good or bad.)
• Less comprehensive and so not as good as a reference. (For example, has the derivatives of \(\arcsin(x)\) and \(\arctan(x)\) but not the other inverse trigonometric functions.)
• Misses some TAGS/OTM topics (IVT, Squeeze, MVT,...).
  • I made a (basic) supplement to cover those topics. The library might be able to fund a graduate student to improve it.
  • This gets worse in 3300, since the multivariable book stops before 3300 does.
• There are fewer homework problems for the students to (not) do. (The authors suggest using the WeBWork library for additional routine problems.)
• See my syllabus for the section names, order of topics, supplemental topics, etc..

Results

• One the final exam, my section did okay. As there is much variation in the populations in each section, I only conclude that using this book did not cause a disaster.
• My DFW rate was 35%, which is about 15% lower than last year. I gave a lot of C grades. Since my students were different and my tests were different, I only conclude that using this book did not cause a disaster. The Freshman DFW rate was only 18%, indicating that the student population in each section largely affects DFWs.
• My student evaluations were poor, with some students quite angry. For a good wince, read them. It could be that my implementation was poor, but I gave it a good effort, so this suggests many instructors would have unhappy students if this book is adopted.

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Last modified: Fri Feb 1 18:35:44 UTC 2019