Puzzle-based learning, as described by the authors, is a way of teaching students to think critically in several different fields of study, including, foremost, mathematics, but also business, physics, and computing. Puzzle-based learning might also be used in teaching a separate course on critical thinking, as a general education or liberal arts course somewhat like rhetoric or expository writing. While this book is aimed mostly at the teaching of college undergraduates, the techniques do seem applicable within lesson units at K through 12 levels or within informal learning environments such as corporate retreats.

The book’s approach is to present many problems, and for each one, discuss how to present it to students and how to help them learn in the course of working on it. The problems are most often logical. Some involve geometric situations or combinatorial issues, and some relate to probability.

One of the first puzzles in the book requires that a farmer get his cabbage, goat, and a wolf across a river subject to some constraints. Another is the Monty Hall problem. In this problem, a master of ceremonies offers three closed doors to a participant; one door hides a new automobile while the other two hide goats. Several problems require high school mathematics. No college-level mathematics is required for the presented problems. However, sometimes the problems require only everyday knowledge (“Name ten three-letter words that represent body parts”). Most of the puzzles are clever and challenging, sometimes becoming relatively simple after a key insight is gained. One way of thinking about this book is as a cross between a Martin Gardner puzzle book and a pedagogical text on how to teach problem solving.

Probably the biggest challenge to a teacher applying the methodology described in the book is figuring out where in the curriculum to put a course on puzzle solving. If the teacher has the freedom to offer a course on critical thinking through problem solving, this is the ideal scenario. Otherwise, it may be a question of using puzzle-based learning as a style of teaching mathematical problem solving or simply incorporating small bits of puzzle-based learning as motivational or methodological lessons within courses on other subjects such as physics, business administration, automobile mechanics (think Car Talk puzzlers), or mystery novel reading and writing.

For many students, computer science (CS) education often begins with a course with a title such as “Problem solving in Java.” Such courses focus primarily on the syntax and construct semantics of programming languages, and they seldom address the kinds of critical thinking issues covered in this book. If a CS instructor really wants to teach problem solving as well as programming, I could see it being done by combining the approach covered by Meyer et al. with traditional programming language material. The book cites the work of Tim Bell on Computer Science Unplugged (http://csunplugged.org/), which already offers a variety of lessons on computing that take the form of puzzles and games. There is clearly potential to take the puzzle-based teaching methodology a lot further in CS education. The book starts to point in that direction in chapter 11, “Simulation and Optimization.”

Each puzzle in the book is presented using a standard format: (a) a concise statement of the problem; (b) some discussion of how the problem fits into an educational context; (c) typical student pitfalls and biases that make the problem challenging; (d) teacher tips, such as offering hints and how long to let students struggle; and (e) either key insights that lead to the solution or the solution itself. For example, Problem 5.8 is to find the number of distinct bracelets that can be made using only six beads, each of which is either black or white. The discussion covers how students must grapple with the definition of “distinct” or “different” as part of understanding the problem. A typical student pitfall is to believe one should simply apply a well-known formula, such as two to the power six, to get the answer. A teacher tip is to ask the students to draw all the possible bracelets and through that learn the value of a good diagram. A key insight is to recognize the inability to distinguish bracelets that include certain patterns, and these are easily enumerated with the diagram.

Perhaps the most famous book on problem solving is Pólya’s How to solve it [1], which was first published back in 1945. For a teacher who wants to teach problem solving and critical thinking in the context of logic puzzles and simple mathematical problems, this book by Meyer et al. is probably the first book to get after Pólya’s.

In summary, this book does a very nice job of bringing together an impressive collection of puzzles and presenting them to teachers in a manner that supports their use in an undergraduate classroom.