Klaus Witz has produced an intriguing, informative, and perhaps useful account of an interview project that explores the nature of students’ deeper engagement in and motivation for learning higher mathematics.
Witz is a Ph.D. mathematician who left mathematics after 10 years at a large university to work in the College of Education at the University of Illinois. While spending time working to understand cognition, philosophy of science, and religion and spirituality, Witz never lost his taste for mathematics. This book is well-written (although the editor missed a fair number of typos and grammatical issues) and entertaining at times. One complaint is that Witz does seem to assume the reader knows more about mathematical philosophy, metaphysics and educational theories than one might expect, but by and large, this does not detract from the reader being able to pick up the “big picture” of Witz’s research.
On venturing into this book, the reader is confronted with what this reviewer felt was an excessive 18 pages of foreword (from three different colleagues) but then emerges to delve into Witz’s Introduction, entitled “The Mystery of Mathematics as Seen in the Experiences of Undergraduates.” In his introduction, Witz outlines the motivation for his research, the types of students he interviewed, and his research methodology. Witz’s presentation of his interviews (in subsequent chapters) truly forms the heart of this book and is the most enjoyable and valuable part. But one must first understand a bit more about the lens(es) through which Witz is understanding students’ deeper and potentially fulfilling involvement with mathematics.
The first chapter of the book provides a glimpse of the aforementioned lenses. Witz walks (well, jogs) the reader through his description of the metaphysical and spiritual elements of mathematics and also the Bildung theory of deeper student involvement in a discipline such as mathematics. At one point, Witz describes his desired audience for this book and this list includes educators (college mathematics teachers), academic advisors, philosophers, theologians, psychologists, spiritual people and also social scientists. This is plainly too long of a list, which is confirmed by reading Chapter 1. I found myself drawn to the overall goal of Witz’s project and wanting to learn of his results, but his account of the underpinnings of his research quickly stretched beyond my understanding, which is that of a college mathematics teacher. Thus, I could not fully appreciate this chapter (and the foundations of Witz’s work) because of my lack of understanding of things metaphysical and spiritual.
The chapters presenting the interviews are the most engaging portions of this book, and so perhaps my inability to follow the context for the research is a personal failing. It did not stop me from enjoying the remainder of the book.
Witz spends chapter two describing his research project more precisely and then devotes the subsequent five chapters to sharing the details of and insights gleaned from his interviews. Witz interviewed two types of mathematics students: teacher education students and “Ph.D.-bound” students. Witz introduces us to Amber and Brian, the two teacher education students. We learn of their quest for fulfillment in their chosen discipline and the route they are taking (or have taken) to get there. Witz does an effective job of bringing the reader into the worlds of Amber and Brian. Both students come across as very “human” and devoted to their career paths (for notably different reasons), rather than as guinea pigs in a research experiment. One grows to understand their backgrounds and appreciate the decisions they have made in choosing to learn mathematics and eventually to teach it.
Witz then gives us four chapters on his interviews with the Ph.D.-bound mathematics students: Elizabeth, Frederick, Janos and Jack. The most interesting part of this book is to read through these four individuals’ interviews and to learn how they have attachments to mathematics that are as strong (and “spiritual”?) as they are unique. Witz tells us he is trying to present portraits (of all six students) that “communicate the [students’] inspiration, deeper aesthetic metaphysical etc. commitments in connection with mathematics, and how these things were part of a larger understanding of themselves and their [lives].” No slight intended to the teacher education students, but Witz comes the closest to achieving his goals in these four chapters.
One learns how Janos, in 8th grade, found “mathematics [to be] tapping him on the shoulder, telling him where he was supposed to be.” Thus, an emotional and personal bond with the discipline seems to have developed in him. And despite spending several years away from college (working at a pizza place!), Janos came to the realization that “math and spirituality [were] unified with [the] philosophy of intense living.”
On the other hand, one hears about how Frederick’s journey to mathematics took him through Christian theology, fractals, dynamical systems, and heavy drug use (LSD and mushrooms). And yet one learns of his eventual epiphany, his personal spiritual realization that to him mathematics is a “sacred activity.”
Witz does a fine job of letting the reader into the worlds of all of these four students, along with the two teacher education students. He clearly has done a skillful job of interviewing the students over an extended period of time. And he does an even better job of communicating to the reader what he heard. While many of Witz’s transcripts need no interpretation, Witz interjects his voice to help the reader keep an eye on the big picture as his exposition proceeds.
Witz concludes his book with a set of reflections putting all of his interview results into context. He tries to make the reader, presumably a mathematics aficionado, aware of the larger and more subtle and powerful dimensions of their own experiences in mathematics. But he also encourages any mathematics teacher reader to look upon his own students with fresh eyes. Perhaps such a reader can recognize indications of this “inner relationship with mathematics” in his own students and potentially help them to unfold it with them. This final chapter is summative and reflective and effectively reiterates the main contextual issues Witz discusses throughout the book. Moreover, Witz asserts that his research supports the hypothesis that a major interest in and commitment to a discipline like mathematics inherently has spiritual aspects.
Russell E. Goodman is an Associate Professor of Mathematics at Central College in Pella, Iowa. His mathematical/pedagogical interests are commutative algebra, teaching with technology and helping students learn to write (better) proofs. His non-mathematical interests are coaching and watching lots of soccer, running, reading books by Jules Verne and Michael Chabon and spending time with his family.