New and Noteworthy Titles on our Bookshelf

Off the Mark: How Grades, Ratings, & Rankings Undermine Learning (But Don’t Have To)

Harvard University Press, 2023, 296 pp.

By Jack Schneider and Ethan L. Hutt

Like many long-standing institutions, education has a number of inherited traditions. One of these traditions is the earning of A–F grades in courses. Grades have many advantages; they serve as a tool to communicate the accomplishments of a student to interested parties, act as a motivator to student behavior, and have the benefit of being coordinated across nearly every level of schooling. As the final grade for a course is part of a student’s permanent academic record, and due to the longevity of one’s transcript, we often see that grades are a source of anxiety. An important question that educators are asking is: how effective are grades at indicating learning? In Off the Mark, the authors explain not only the history of grades and their strengths and weaknesses, but also how alternatives to traditional grades can increase a student’s motivation to learn the material in the course.

To those of you who research mathematics education or have experience with alternative grading, this book will likely reiterate information you already know. What this book does well is explain in a straightforward way the juxtaposition of an efficient assessment tool, namely grades, with their shortcomings and how grades fail both students and educators. While the book includes opportunities to make incremental changes, I wish it contained more specifics, since an instructor who desires to adopt alternative grading mechanisms will find little in terms of a pathway forward here. However, I think this book is a great jumping-off point for someone who is open to learning about the ramifications of traditional grading.

The Mathematics of Shuffling Cards

American Mathematical Society, 2023, 346 pp.

By Persi Diaconis and Jason Fulman

Consider any specialized area of interest, and certainly there are mathematicians interested, too. So, it was only a matter of time before a publication such as this one came along. Gamblers, magicians, and card-players alike have a vested interest in not only how to shuffle (and there are many “proper” ways!) but also how the shuffle can affect the outcome of a bet, trick, hand, or game. Call me easily impressed, but I loved the full-color pictures of the types of shuffles in this book. There are more than I even knew about, including the riffle, butt, one-handed, overhand, and perfect shuffles. I’ll admit that I grabbed a deck of cards to try some that I had not done before. (Though I’ll need plenty of practice before nailing the perfect shuffle!)

To my knowledge, there is no other book like this; there are many that can teach you how to shuffle or illustrate impressive card tricks, but this one takes the topic into serious and quite technical mathematics. Some of the tools used to study shuffles include Hopf algebras, Markov chains, partitions, symmetric functions, and algebraic topology. For mathematicians, this book provides a thorough and technical approach to applications of several areas of research. The authors of this book are very passionate about this project, and they have put together a comprehensive text on the topic. I think this could serve as a great way for a graduate student to learn an application of their theoretical work, perhaps through an independent study course or a summer reading course. Of course, any mathematician could appreciate learning about the mathematics of card shuffles, especially one who loves playing card games!