As the authors state early on, this book is intended in part as a response to the 2001 report from the Conference Board of the Mathematical Sciences on the mathematical education of future teachers.
There is a very definite need for books like this one. While courses and textbooks on mathematics for elementary teachers are common across America, few schools offer a course for which this book would be a good fit, and that’s probably regrettable. There is a good argument to be made for offering prospective secondary teachers the same kind of course — in which they consider the math they expect to teach from an advanced perspective and with some attention to how to teach it — that we routinely require of prospective elementary teachers.
I have taught such a course, as an independent study, to about ten students over the years. I have used two likely competitors of this book, and the three all take slightly different approaches to the challenge. Mathematics Methods and Modeling for Today’s Mathematics Classroom, by Dossey et al., is a COMAP project with a focus, as the title suggests, on mathematical modeling using middle and high school math. By contract, Mathematics for High School Teachers: An Advanced Perspective, by Usiskin et al., follows a path similar to what we see in textbooks for the standard mathematics for elementary teachers course: an examination of topics that the students will someday teach, in somewhat more depth than in a high school textbook.
Mathematics for Secondary School Teachers is more traditional in its content than the first of these predecessors and more ambitious than the second. The topics are drawn from high school mathematics, but there’s a depth of content that outstrips the Usiskin text. The authors note (p. 143), in introducing a chapter on hyperbolic trigonometry, that “Most of us first encounter the hyperbolic trigonometric functions in a calculus course” — which is surely accurate. They then go on to take students through a development of those functions starting with hyperbolas, and that is an excellent coverage of precalculus topics at an appropriately challenging level.
There is additional thoughtful and deep content in the chapters on the algebraic properties of number systems, which may well give a prospective teacher coming out of an abstract algebra course some important insight into how that material might connect to his or her future career. Due to these and other examples, the suggestion of the CBMS report that “Prospective mathematics teachers need mathematics courses that develop a deep understanding of the mathematics they will teach” will be well-realized by a course based on this textbook.
Mark Bollman (firstname.lastname@example.org) is associate professor of mathematics at Albion College in Michigan. His mathematical interests include number theory, probability, and geometry. His claim to be the only Project NExT fellow (Forest dot, 2002) who has taught both English composition and organic chemistry to college students has not, to his knowledge, been successfully contradicted. If it ever is, he is sure that his experience teaching introductory geology will break the deadlock.