More Fallacies, Flaws and Flimflam by Edward J. Barbeau is now available in the MAA eBooks Store. A paperback version will be available in the MAA Store soon.
Here is another collection of Fallacies, Flaws and Flimflam, mostly drawn from the column of this name in The College Mathematics Journal between 2000 and 2008. As in the first volume, there is a variety of items ranging from howlers (outlandish procedures that nonetheless lead to a correct answer) to errors that are deep or subtle often made by strong students. While some are provided for entertainment, others offer a challenge to the reader to determine exactly where things go wrong.
There are many proposals to improve the quality of mathematics education, but they seldom address the need for students to pay careful attention to what they do and to check their work. It is through an engagement with meaning that students can avoid the pitfalls that come too naturally. Accordingly, this volume should be useful to teachers at all levels by giving them examples of flawed work they can use in the classroom. Encouraging students to find where someone else went wrong may help them avoid similar errors in the future.
The items are sorted according to subject matter. Elementary teachers will not find much of use beyond Chapter 1, while middle and secondary teachers will find items in Chapters 1, 2, 3, 7, 8 that they might use. College teachers should find material in every part of the book.
The mathematical topics covered include arithmetic, algebra, trigonometry, geometry, combinatorics, probability, and calculus.