Misteaks: And How to Find Them Before the Teacher Does by Barry Cipra (A K Peters, 2000) is a small book (about 72 pages in length) that appears to be intended primarily as supplemental reading for a calculus course. The purpose of the book is to illustrate common errors that calculus students make and how to catch these errors. Common errors and how to find them
This review discusses the third edition of the book; however, according to the preface, the only changes from the second edition were the addition of the preface and a short list of suggested readings, so the review could apply equally well to the second edition.
While this book focuses on calculus, many of the general principles discussed in this book, such as estimating calculations and areas, reducing to a special case, generalizing, ensuring that units and dimensions are consistent, using symmetry, looking for common errors such as missing negative signs, brackets, coefficients, exponents, etc., could be used by any student of mathematics. However, the calculus student will probably find this book the most useful, as the majority of the examples involve differentiating or integrating.
This book does an absolutely excellent job of illustrating most of the common errors that students will make. Of course, it's hard to imagine every single way in which people will fall into error, but all of the most common ways are illustrated here. This book contains several examples of such incorrect reasoning and calculating. While the author includes a few demonstrations of how to troubleshoot and fix the errors that were made, most of the examples simply illustrate errors, along with an explanation of how you might catch that error. I think that it would be helpful to include more information on how to actually troubleshoot problems, not just tell whether something's gone wrong or not. Presumably, however, as a supplement to a course textbook, the reader should have enough resources to gain experience troubleshooting on his/her own. This does slightly diminish the ability of the book to stand on its own, however.
Misteaks is written in a relatively light and humourous style, which seems to be a good fit for a book of this nature. Overall, a fun, unique, and useful book.