Reviewed by Milos Savic, Assistant Professor, University of Oklahoma, on 1/13/2015.
I thought that the book was thorough in the subjects that were listed, including limits, derivatives, integrals, differential equations, and … read more
Comprehensiveness rating: 5 read less
I thought that the book was thorough in the subjects that were listed, including limits, derivatives, integrals, differential equations, and sequences and series. I would have liked a few chapters on multi-variable calculus, but that wish should not degrade the comprehensiveness of the book. The book is hyperlinked throughout, so if on the PDF you look up a terming the index, clicking on the link will bring you right to the page that the term is introduced.
Accuracy rating: 5
The book builds upon 400 years of calculus understanding, so most of the book is accurate and unbiased in terms of the content.
Relevance/Longevity rating: 5
The text will not be obsolete for a long period of time. The topics covered, and the problems presented are relevant. I conjecture that if an application problem is ever out-of-date, it could be easily replaced.
Clarity rating: 5
This book is written contrary to many mathematics textbooks in a fresh, active, and accessible manner. The layout of each section of the text has a summary of what will be discussed, preview activities to get the reader situated, activities throughout the prose, and a summary of what was discussed prior to exercises. It seemed as though the activities and the mathematics had purpose and understanding built in, which I cannot say the same for some other textbooks. I was excited to move to the next section when reading.
Consistency rating: 5
The consistency of the textbook is fine. Every section has the same layout, and problems at the end of the section are probing no matter which section is discussed.
Modularity rating: 4
I think that it is slightly difficult to be modular with a mathematics textbook. With that being said, I thought that the authors had a different approach than other textbooks in terms of what they wanted to introduce first. For example, I have always learned to prove the fundamental theorem, I would need the interplay between derivatives and integrals. The authors prefer to conjecture the fundamental theorem from observations of velocity and position, and in the next chapter approach the proof.
Organization/Structure/Flow rating: 4
I have already commented on the flow in the modularity section. I think that many parts flow in this textbook, but there were some parts that I had trouble with initially.
Interface rating: 5
I was so pleased with the interface of this textbook. There are links to javascript modules where students can interact with the exact topics they are reading about. If there is any textbook that shows us the slight capabilities of the 21st century, it is this textbook.
Grammatical Errors rating: 5
I found little to no grammatical errors in this textbook.
Cultural Relevance rating: 5
I did not see any portion of this text that referred to any ethnicity or race, so technically it is inclusive of all races and ethnicities.
Comments
If you adopt this textbook in your classrooms, please adhere to the active learning modules in the text. They are written in a way that tries to empower the student mathematically. I really enjoyed the previews, recaps, and activities throughout each section. I enjoyed the references back to certain activities. Most of all, I enjoyed the javascript applets that accompanied this text, thus making it a textbook that takes advantage of the 21st century. I would highly recommend this textbook to any educator that wants their students to thoroughly understand the calculus material.
Reviewed by Carrie Kyser, Master Instructor, Clackamas Community College, on 1/8/2016.
This book is thorough and up-to-date in all areas of a single-variable differential and integral calculus course. I have been using it in my courses … read more
Comprehensiveness rating: 5 read less
This book is thorough and up-to-date in all areas of a single-variable differential and integral calculus course. I have been using it in my courses for over a year now, and I haven't found it to be lacking any topic, theorem, or technique.
It is current in its reduced emphasis on algebraic technique and greater attention to the underlying concepts and engineering-based applications. For example, integration techniques have been reduced in coverage and in emphasis in most calculus textbooks and this book is no exception. Substitution and Integration by Parts are featured, Partial Fractions gets a nod, and then students are introduced to the idea of a CAS (Computer Algebra System). This is in keeping with the reduced treatment of "by hand" integration techniques in most modern calculus textbooks.
Accuracy rating: 5
There are no issues with the book's mathematical accuracy.
Another kind of accuracy, though, is how well an individual activity "hits its mark" in taking the student through an illuminating example of a topic. Generally, I think the text succeeds here, but there are some edits I might suggest.
For example, in Activity 1.15, after working through this activity in class with students, I altered the graph a bit to create more variation so the resulting discussion about displacement, velocity, and acceleration would be a bit more fleshed out. Teaching with this new version of this activity has had better results in terms of student understanding.
Relevance/Longevity rating: 4
The content is not only up-to-date, but I think very forward-looking in its approach to the subject matter. The book has an almost conversational tone that I find very appealing.
However, to remain relevant going forward, I would like to see the "book" revised to take advantage of its medium. It's presented and used (especially by students, who are perhaps more open to using electronic resources than their older, more traditional instructors) as an *online* resource. To remain relevant, I hope that future editions will take advantage of the power of the computing devices on which this book is often read, and feature more video, applets, maybe some Desmos-type graphs with movable parts. When students want to learn how to do something, they are searching YouTube, not looking for a page of text that describes how they might do a thing. They want to try it on, see it in action, engage with it. We should encourage and provide more opportunities for students to do that.
Clarity rating: 4
My students did not much care for the text. I am teaching this course using a flipped model, so there is reading and also instructional videos that students are asked to do outside of class. Not surprisingly, most students prefer the videos. Some student comments (from an anonymous end-of-course survey) about the assigned reading in the text:
--I didn't find the textbook explanations very user-friendly, as they were much more difficult to comprehend than the videos. I don't know if there are textbooks with clearer explanations? About mid-way through the course, I also didn't find the reading to be necessary for most modules, as the videos and class explanations were clearer teachings of the same book concepts.
--The book tends to be confusing, as student that learns from examples, I find this book to be hard to understand.
--I liked that the textbook wasn't expensive, but I don't think the examples given were very helpful. I think they were a bit distracting from the point of the section at times.
--more videos less reading
I am not surprised that students prefer videos, but I don't think this is the fault of the text, but rather that they would prefer video explanations over ANY text. Nor am I surprised that they wanted more "example problems" from the text. Students have been taught that math is mostly manipulating expressions and equations. This book takes a very different approach. One student expressed his discomfort:
--...also there aren't very good examples and explanations in the text. For instance; A section has about a paragraph and then the preview activity.....there's no explanation or good examples of problems. We are kind of just thrown into a pit of fire.
...which is exactly the point of the text, that you learn this content by interacting with it.
The text is interspersed with Activities (as the book's title implies). I used most of the activities (either as-is or modified a bit) as group work in my Calc I and II classes. Students resoundingly preferred this "active" approach to learning calculus to the traditional lecture-based approach, and I think the quality of these activities was a big factor in students' satisfaction.
Consistency rating: 4
The book is consistent in terminology and framework, absolutely.
There is a bit of variation in the consistency of the relative difficulty of the activities, however.
For example, in the section on Implicit Differentiation--a topic that students often find challenging--Activity 2.20 features an expression that is algebraically quite complicated for students. I used this once in class. Students just laughed out loud, most refused to try it! I removed it from the set of activities I use.
At other times, there are questions that seem to confuse students because they are "too easy", like (d) in Preview Activity 1.3:
"Write a meaningful sentence that explains how the average rate of change of the function on a given interval and the slope of a related line are connected."
Students ask "Do they just want me to say that they are the same? Is that all?"
Modularity rating: 5
The text is easy to pull apart and put back together. It is suitably modular.
Organization/Structure/Flow rating: 4
The text gets full points for organization/structure/flow.
I would like to suggest perhaps an alternate version of the text where it is organized more like a workbook, with more room left between the questions/problems where students might write their responses. I don't like asking students to copy down the text of a problem when they are working; their resistance to doing so is firm and vocal! But a bunch of answers on a piece of paper with no context is not good work product, nor very helpful as a study device.
A version of this text that invited that kind of "active" participation from the reader would be a marked improvement, I think.
Interface rating: 5
The interface is fine; I've encountered no issues.
Grammatical Errors rating: 5
I think the book is not only grammatically correct, but very well-written. Not always the case with math textbooks!
Cultural Relevance rating: 5
I have encountered nothing even remotely insensitive or offensive in this text.
Comments
This book helped me to understand how I might teach calculus in a more learner-centered way, and for that I sing its praises! I recognize, though, that the "active" approach is a bit different from what most students are used to/expect, and they will need instructor support to make the most of this book and what it has to offer.
Reviewed by M. Paul Latiolais, Professor, Portland State University, on 1/8/2016.
PLEASE BEGIN BY READING THE "OTHER COMMENTS" SECTION AT THE BOTTOM FIRST.
It seems to cover all of what we need for the first two quarters of … read more
Comprehensiveness rating: 4 read less
PLEASE BEGIN BY READING THE "OTHER COMMENTS" SECTION AT THE BOTTOM FIRST.
It seems to cover all of what we need for the first two quarters of calculus except surface integrals, which we could add or move to the third term.
Accuracy rating: 5
i found no errors
Relevance/Longevity rating: 5
It is the most up-to-date book on Introductory Calculus that I have seen so far.
Clarity rating: 5
This is a book designed to teach. As such, it will not be a good resource for student who have already studied calculus. That would be a very different book.
Consistency rating: 5
consistent
Modularity rating: 4
not appropriate question for this subject.
Organization/Structure/Flow rating: 5
Excellenet. See "other comments" for more details.
Interface rating: 5
Very clear
Grammatical Errors rating: 5
I found no grammatical errors.
Cultural Relevance rating: 1
While that would be a great idea, no one has yet attempted to write a calculus textbook which was "inclusive". The closest thing was an environmental calculus book, but that included only covered the applied calculus material.
Comments
It is hard to get a good sense of how well a book will work before one has taught a class using it. Nonetheless, the approach articulated in the preface follows the the best of what is known about student learning as it relates to calculus. The approach would be challenging for graduate teaching assistants to accomplish, but possible with sufficient support and worth the effort toward the improvement of student learning.
I would do a "Dan Meyer" ( https://www.ted.com/talks/dan_meyer_math_curriculum_makeover?language=en ) on the activities and the initial questions. However, the formatting of questions and then activities seems a sound one. For example, I would not foreshadow the answer to the questions by using terminology too soon.
For example, I would change the question "How does the notion of limit allow us to move from average velocity to instantaneous velocity?" to "How do we manipulate average velocity to compute instantaneous velocity?"
Example 2: Instead of "What is sigma notation and how does this enable us to write Riemann sums in an
abbreviated form?", say "How can we write Riemann sums in an abbreviated form?"
I should have more examples, after testing this book in a class.
Our challenge is that this book would cover only 2 quarters, not the 3 quarters that we teach. We would be required to use a more traditional book (presumably open source) for the third term. Likely do-able, but challenging.
Reviewed by Bethany Downs, Mathematics Instructor, Portland Community College, on 6/21/2017.
The book covers all major topics of differential and integral calculus. However, the emphasis is on "big-picture" understanding of the topics and … read more
Comprehensiveness rating: 4 read less
The book covers all major topics of differential and integral calculus. However, the emphasis is on "big-picture" understanding of the topics and has relatively few (in comparison to other texts) formally stated theorems and even fewer proofs. This could be seen as an asset, if the goal is introducing students to the overall ideas of calculus.
Accuracy rating: 5
The text is accurate.
Relevance/Longevity rating: 5
This is as up-to-date of a calculus textbook as I've seen. The examples and activities are interesting and draw from a number of disciplines (physical and social sciences, etc.) which gives the reader a sense that calculus has many applications. While specific, the examples will not feel dated in a decade or two and could be replaced with new examples or new data as the need arises.
Clarity rating: 5
This is a really well written book. The style is clear and easy to understand. The tone is conversational and uses appropriate vocabulary and description of the mathematics - it doesn't "dumb down" the topics, but also doesn't rely too heavily on "mathy" words when an explanation using regular language would suffice.
However, there is a lot of text between and explaining the very few examples and it is hard to say, having never taught with this text, whether or not students would enjoy reading it as much as I did.
The authors choose not to state many formal theorems or show detailed proofs. The emphasis is on overall understanding of the topics, not the underlying theory that makes the mathematics possible. This approach is successful for this textbook. If, however, you prefer a formal step-by-step build-up of theory and theorems, this is not the textbook for you. Also, the flow of this book and paucity of detailed examples and homework problems would make it difficult to use as a reference book.
Consistency rating: 5
Very consistent in layout and use or terms/vocabulary.
Modularity rating: 5
The chapters and sections of the book are of the appropriate length for breaking over class periods throughout the term.
Organization/Structure/Flow rating: 5
The organization of each section is nicely done: "Motivating Questions", text with examples, activities for students, and the a "Summary" at the end followed by a homework set.
Interface rating: 5
The interface is fine.
Grammatical Errors rating: 5
No errors found.
Cultural Relevance rating: 5
I have yet to see a culturally relevant calculus textbook! This particular text is in no way insensitive or offensive.
Comments
To take full advantage of the unique approach of this textbook would need a lot of instructor planning/preparation before class. The text has very few examples and the instructor would need to provide many of his or her own examples during lecture. This is especially true for the more algebra-intensive topics.
In class, students would need a lot of involvement from the instructor. It would be very important for the instructor to make sure that the students were completing and drawing the correct conclusions from the Activities within the text before moving on. With the right preparation and implementation by the instructor, this "lab"-style approach could be very successful and enjoyable for the students.
There are only a few homework problems listed for each section. Additional problems from elsewhere (either another textbook or something like WebWork) would be helpful.