Apex Calculus
OER Reviewed: Active Calculus by Matthew Boelkins
Reviewer: Trefor Bazett, Assistant Teaching Professor, Department of Mathematics and Statistics, University of Victoria
OER has been shared as an optional resource and some activities in the OER previously used for teaching by the reviewer.
Note from the reviewer
To contextualize the rest of this review, I should briefly explain the core idea of Active Calculus. As the name suggests, this is meant to support a course in calculus taught from the perspective of active learning. Whether this is a good text or not for a course probably largely depends on whether the instructor intends to similarly engage in active learning. For instance, the text includes “Preview Activities”, intended to be done before class, and “Activities”, intended to be done during class. My review below primarily is assigning ratings ON THE ASSUMPTION that the instructor intends to use these active learning components to some degree, and I will occasionally note how the ratings might differ if one is aiming for more traditional lecture during class.
Rating
Each criterion asks the reviewer to rate it on a scale of 1 to 5 (1 = very poor and 5 = excellent).
Comprehensiveness – Rating: 3-4
The OER covers all areas and ideas of the subject appropriately and provides an effective index and/or glossary.
The OER covers all areas and ideas of the subject appropriately and provides an effective index and/or glossary. Every standard Calculus I/II topic is covered, with the exception of Complex Numbers which some courses may adopt. There is a well-functioning index and table of contents that is particularly useful in the html version of the text as students can follow the hyperlinks.
The text is not intended to be a reference text, instead it aims to facilitate active learning. Thus the comprehensiveness of many sections is quite a bit shorter than one would expect in other texts, because large portion of the development is intended to be done in Preview Activities before class or Activities after the class (the latter only has answers, not solutions, for instance). While the major topics are comprehensive in their exposition, more minor topics are often done very briefly. For instance, partial fractions (whatever one thinks about the value of this topic) is extremely brief and focuses on using computer tools to execute the algebraic manipulations.
Similarly, there is a decent sized set of questions (many use WebWork to let students input answers) that are generally appropriate, but nonetheless still less total practice problems than a traditional reference non-OER text in Calculus.
Also a note that while the text is standard calculus fare, it does not include much in the way of connecting to applied problems in the world.
Rating: 3/5 as a reference text, 4/5 as a text to support active learning in class.
Content Accuracy – Rating: 5
Content, including diagrams and other supplementary material, is accurate, error-free, and unbiased.
I saw no inaccuracies nor biases.
Relevance/Longevity – Rating: 5
Content is up-to-date, but not in a way that will quickly make the OER obsolete within a short period of time. The OER is written and/or arranged in such a way that necessary updates will be relatively easy and straightforward to implement.
Calculus from a content perspective has been consistent and unlikely to change. This book establishes all the normal topis and I can’t think of a topic likely to be included in the future that it doesn’t cover now. From a pedagogy perspective, this book represents a shift in emphasis to using active learning in the way it presents that content, so if tides shift from this particularly view of active learning or an instructor doesn’t wish to buy in now, then the book won’t be of much use. For instance, an instructor not wishing to use the Preview Activities intended to be assigned before class will find these to be extraneous.
Rating: From a content perspective it is a 5/5, but from a pedagogy perspective I’ll give it at 3/5.
Clarity – Rating: 4
The OER is written in lucid, accessible prose, and provides adequate context for any jargon/technical terminology used.
I find the textbook generally to be well written. Calculus has a lot of technical jargon and these are developed appropriately and written in clear, simple-to-understand prose. My only main objection was in the ‘Motivating Questions’ section at the top of each topic, which sometimes includes jargon that won’t be introduced until much later in the page. While I think the goal here is to scaffold students perspective of the module, I’d appreciate more attempts to phrase these motivating questions purely in terms of terminology the students already know.
Consistency – Rating: 5
The OER is internally consistent in terms of terminology and framework.
Yes, this book makes consistent notational and stylistic choices that provide a coherent text.
Modularity – Rating: 3
The OER is easily and readily divisible into smaller reading sections that can be assigned at different points within the course (i.e., enormous blocks of text without subheadings should be avoided). The OER should not be overly self-referential, and should be easily reorganized, and realigned with various subunits of a course without presenting much disruption to the reader.
To the degree that this is possible given the logical dependencies within the standard path through calculus, yes this is modular. The typical flexible topics (i.e when/if you cover an introduce to ODEs) can be easily moved around. However, there are occasionally attempts to re-order the calculus sequence in a way that changed the logical dependencies and this text would fail to be modular in that sense similar to most texts that focus on the standard path.
Organization/Structure/Flow – Rating: 5
The topics in the OER are presented in a logical, clear fashion.
Yes. The structure is fairly standard and organized all very effectively. The html version makes the structure particularly clear and obvious.
Interface – Rating: 5
The OER is free of significant interface issues, including navigation problems, distortion of images/charts, and any other display features that may distract or confuse the reader.
The text has an interactive html website, a pdf and a printed version on Amazon. The pdf is similar to any normal textbook in terms of chapters and section and table of contents etc, which is all fine. The html version really excels as it makes it very easy to jump around and go find things from the past you are interested in. It is a big improvement over physical or pdf books in general.
Grammatical/Spelling Errors – Rating: 5
The OER contains no grammatical or spelling errors.
None that I have found.
Diversity and Inclusion – Rating: 1
The OER reflects diversity and inclusion regarding culture, gender, ethnicity, national origin, age, disability, sexual orientation, education, religion. It does not include insensitive or offensive language in these areas.
The text does very little or perhaps nothing in this direction. Partly this is because the text in general focuses on the standard development of calculus with little attempt to include applied examples or contextualize the results. So structurally this decision eliminates many natural places to include EDI issues in this structure, but nonetheless I think this should be more directly added.
Recommendation
- Do you recommend this resource for the specific course taught in the first-year engineering common curriculum (in place of a commercially available resource)?
For instructors planning to use some elements of active learning, then yes I recommend this. I definitely think it can be a stand alone resource, it just depends on how the instructor wants to use it. For instructors planning to use the text as a reference text that compliments primarily traditional lecture, I think there are better options. - If yes, please briefly summarize the reasons for recommending this resource
The book is very well thought out in its approach to facilitating active learning and has a lot of well-designed preview and class activities that instructors needly only lightly modify or use verbatim, while providing a sufficient resource for everything else in a fully online format that is easy to use. If you are bought in to the basic active learning model, then this book might be among the best resources available. Even if not assigned, it can be a great supplemental text or even a source of problems and motivation for instructors. - If not, why? What improvements, if any, could be made?
Its largest flaws are that the focus on active learning could detract from someone teaching in traditional lecture format who wants to use the book as a comprehensive reference. If you aren’t bought into that, challenges like the extraneous activities that don’t have solutions will be a distraction at best. - What gaps in content have you identified?
Only potentially missing section is on complex numbers. The main challenge here is that many canonical examples you would expect to be written out in a normal textbook are done as ‘Activities’, meant for before or during class, and thus don’t have worked solutions. So if an instructor’s primary goal of the textbook is to have it as a sort of backup reference where students can always go look up every single possible thing, then the book covers a lot but not everything because it has these holes in the exposition where the activities are. If an instructor wants to have the text to be very integrated into the course where these holes are assigned to be worked on and flushed out in class, then the textbook is great. A third possibility is an instructor chooses to use Active Calculus, integrated into the course, but then also share a second OER that was more traditional and comprehensive just as a backup reference, and that would be fine too.