OER Reviewed: Calculus Volume I & Calculus Volume II (Openstax)

Reviewer: Peter Sinclair, Instructor, Capilano University and Douglas College

OER previously used for teaching by reviewer.

Rating

Each criterion asks the reviewer to rate it on a scale of 1 to 5 (1 = very poor and 5 = excellent).

Comprehensiveness – Rating: 4

The OER covers all areas and ideas of the subject appropriately and provides an effective index and/or glossary.

• • The OER includes all of the standard topics for Calculus I and II and has a thorough index.
  • There are a few chapters where the OER could benefit from a deeper exploration of applications, such as Applied Optimization Problems and Differential Equations. The content necessary for the course in these chapters is complete, but students may be left without a complete understanding of how the topic would be applied outside of a mathematics course.

Content Accuracy – Rating: 4

Content, including diagrams and other supplementary material, is accurate, error-free, and unbiased.

• • Review for this criterion is based on my general experience with using the OER in past courses and a thorough investigation of the following randomly chosen sections: 2.1 and 4.5 in OpenStax Calculus I; and 3.6 and 5.2 in OpenStax Calculus II.
  • The content in the main text, including diagrams, is overall very accurate, error-free, and unbiased. There are a few small typos in the main text, but nothing that would confuse a student.
  • The exercise solutions have a higher rate of errors, but exercise solutions are notoriously error-prone even in commercially available textbooks. Of the four sections I investigated closely, most had 2 or 3 mistakes in the solution set (about 5% of the solutions).
  • The supplementary materials for this OER are quite sparse:
    • There is a student solution manual which simply lists correct answers for odd-numbered exercises. It is word-for-word identical to the appendix in the main textbook with solutions, including mistakes.
    • There is an instructor solution manual which lists correct answers for all exercises (odd and even). I did not check this as thoroughly as the main text, but it presumably has mistakes at a similar or slightly higher rate, since it has been looked at by fewer end-users.
    • There are sets of lecture slides that contain diagrams from the text. They do not contain any apparent errors.

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.

• • The content presented in this OER has not changed in recent memory and is unlikely to change in the foreseeable future.

Clarity – Rating: 4

The OER is written in lucid, accessible prose, and provides adequate context for any jargon/technical terminology used.

• • The OER is written using clear language that only uses technical terminology where necessary.
  • Technical terminology is always introduced using clearly stated definitions (usually in a highlighted box) that make it easy for students to notice when a new term is introduced.
  • At times, the OER uses slight variations on certain technical terms, such as “inflection point” or “point of inflection,” without explicitly mentioning that the variations are equivalent. While this is unlikely to cause problems for most students, those who are unsure of the material or who do not speak English as a first language may worry that these terms refer to different concepts.
  • There are a few instances of long wordy paragraphs that could be broken up into more digestible pieces, but these instances are not particularly frequent.
  • The prose is interspersed with figures and examples to help students understand the written content.

Consistency – Rating: 4

The OER is internally consistent in terms of terminology and framework.

• • The OER is generally consistent with terminology and framework
  • At times, the OER uses slight variations on certain technical terms, such as “inflection point” or “point of inflection,” without explicitly mentioning that the variations are equivalent. While this is unlikely to cause problems for most students, those who are unsure of the material or who do not speak English as a first language may worry that these terms refer to different concepts.
  • Most of the OER follows the standard mathematical practice of numbering Theorems by chapter; for example, Theorem 4.18 is the 18th theorem in Chapter 4. There is at least one notable exception to this standard: in Section 4.4 of Calculus I, the text includes three corollaries to the Mean Value Theorem. It refers to these as Corollary 1, Corollary 2, and Corollary 3, even outside of Section 4.4. This could easily cause confusion to readers, who would not know where to look for Corollary 3.

Modularity – Rating: 4

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.

• • The OER is divided into sensible sections and subsections. As with any calculus textbook, most sections build on the previous sections. That said, there are a few instances where material could be skipped or presented out of order and there is nothing in this OER that would prevent that.
  • The Exercise numbering is only reset at the beginning of each chapter, not at the beginning of each section. For example, in Calculus I, Section 1.1 contains exercises 1-58, then Section 1.2 contains exercises 59-112, etc. This choice for Exercise numbering does not prevent the re-ordering of sections and chapters, but would make any re-ordering stand out unnecessarily. The numbering also makes it more challenging to add additional problems, as subsequent sections need to be re-numbered.

Organization/Structure/Flow – Rating: 5

The topics in the OER are presented in a logical, clear fashion.

• • The OER follows a very standard organization of topics that is used in many other textbooks. Some instructors may wish to follow a different ordering of topics, but that would be a case of personal preference; all of the choices made by the OER authors are logical and sensible.

Interface – Rating: 4

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.

• • I have viewed the OER in three forms: as a downloaded PDF, through its web interface (using Firefox and Chrome on Windows 10), and through the OpenStax app (on an Android phone).
  • There are no major display issues in any of the versions of the OER
  • Charts and images are clearly rendered without distortion
  • Boxes for definitions, theorems, and examples highlight those elements without distracting from the rest of the text.
  • In the online and app versions, the solutions for examples in the text can be toggled, giving students the opportunity to try the examples on their own before looking at the answer.
  • The math display in the PDF version has some imperfections; it would benefit from being created in an editor designed for mathematics like LaTeX. These imperfections do not cause any real readability issues, but do make the text look less polished than most commercially available resources.
  • When switching tabs when viewing the OER online (Firefox, Chrome, and app), it sometimes lost my place. A similar issue occurred when using the provided links to access solutions to practice problems.

Grammatical/Spelling Errors – Rating: 5

The OER contains no grammatical or spelling errors.

• • Review for this criterion is based on my general experience with using the OER in past courses and a thorough investigation of the following randomly chosen sections: 2.1 and 4.5 in OpenStax Calculus I; and 3.6 and 5.2 in OpenStax Calculus II
  • The OER contains very few grammatical or spelling errors; I only noticed two in the four sections I read closely, neither of which would have caused any confusion for students.

Diversity and Inclusion – Rating: 3

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.

• • I did not find any insensitive or offensive language in the OER
  • There is a clear effort to balance the number of male and female names used in examples and exercises, but those names are all stereotypically white-sounding (such as Andrew, Jessica, Joe, or Sandra)
  • The historical figures mentioned in Calculus I include only European men; the historical figures mentioned in Calculus II are slightly more diverse
  • OpenStax has a set of diversity and representation development guidelines. These guidelines acknowledge the need to address issues like the ones I mention above, and so the lack of diversity reflected in the OER may be improved in future revisions

Recommendation

1. Do you recommend this resource for the specific course taught in the first-year engineering common curriculum (in place of a commercially available resource)?
   • Yes, I would.
2. If yes, please briefly summarize the reasons for recommending this resource
   • This resource covers the standard material for Calculus I and II in a clear and accurate manner. The prose is aimed at the correct level and is supplemented by useful diagrams, examples, and exercises.
   • The textbook is nearly as polished as a commercially available alternative; it is consistent, organized well, and has very few errors.
3. If not, why? What improvements, if any, could be made?
4. What gaps in content have you identified?
   • The OER would benefit from more real-world examples of the concepts presented, especially in Calculus I.
   • The OER would also benefit from presenting a more diverse group of historical mathematicians.