This is a very slim book with an interesting purpose: to use puzzles (some of them mathematical) as a way of training the reader in ‘effective thinking’ – a reflective problem-solving mindset that ‘includes the objective analysis that is typically associated with critical thinking, but also includes broader modes of creativity, originality, engagement, and empathy’ (p. 11). The book stems from a course offered by the author at Southwestern University in Texas; an outline of the course appears as an appendix to the book.
The book begins with a rallying-cry for an enquiry-based education, rather than one that is obsessed with assessment, before going on to outline the core principles of effective thinking. These include, for example, the recognition that a binary ‘yes’ or ‘no’ is not necessarily a useful answer to the question ‘do you understand?’, and pointers towards how best to learn from failure. The puzzles that follow are designed to enable the reader to practice the principles outlined.
Aside from the additional (more challenging) bonus puzzle that appears at the end, the remaining 24 puzzles are arranged in eight groups of three, with the intention that each triple be one week’s challenge. Within each triple, the problems are ordered by difficulty. One or two of the problems were familiar (for example, Alcuin’s puzzle concerning a wolf, a chicken, and a cabbage), but most were new to me, although some were of a recognisable type (arranging matchsticks into a prescribed shape, for instance). To my mind, the better (and also the most challenging) problems were the logic puzzles embedded within short stories, although the style of the stories themselves did grate on occasion.
For readers who have difficulty getting started on any given puzzle, a chapter of ‘prompts’ is included (printed upside down). These are often quite vague with respect to the puzzles, and are more about pointing the reader towards the effective thinking techniques that they ought to be trying to apply in each instance. The chapter of solutions (printed in mirror image) is similar, so the frustrated reader who has been entirely stumped by a particular puzzle may find themselves even more frustrated after consulting the ‘solutions’.
Within the book, the author uses the Greek term paideia to describe a mode of education in which students are encouraged ‘to think through the material within every course of study and connect that thinking with ideas and knowledge beyond the course itself’ (p. 6). Indeed, it seems that the notion of paideia is key to the educational philosophy at Southwestern University (www.southwestern.edu/about-southwestern/paideia/). A ‘paideia moment’ is ‘an exciting moment of meaning and deeper understanding’ (p. 6). Whilst working through the puzzles in the book, I did indeed have several very satisfying ‘paideia moments’, usually in connection with the logic problems, and usually only after having mulled them over for a long time. Moreover, in spite of (I must admit) an initial cynicism about its ‘self-help’ nature, I do find myself applying the techniques of the book in day-to-day life. Overall, the author does seem to have achieved his goal of promoting effective thinking. Thus, although the book can of course be approached simply as a traditional puzzle book, the reader might find that they learn things that they didn’t necessarily expect!