Review: Robert Stein: Math for teachers. An Exploratory Approach.
Robert Stein: Math for teachers. An Exploratory Approach.
Bob Stein’s textbook for prospective K-8 (kids age 5-14) mathematics teachers, which appeared in its second edition in 2009, is interesting to the HPM community because it includes the historical dimension. In this review, I will therefore almost entirely be interested in the way it includes history.
In this book, history of mathematics is included in four ways. First, there are about 70 historical footnotes giving additional information on the topics treated in the text. They range from a sentence on who first used the equality sign to mini-biographies on mathematicians such as Blaise Pascal. The second way of including history of mathematics is to include it in the main text. For instance, the text on multiplication includes some historical algorithms. The third way is to give exercises explicitly based on the history. For instance, there are exercises on historical proofs of Pythagoras’ theorem. The fourth way is to base the treatment of the mathematical topic on the historical background in an implicit way, such as giving a geometrical way of solving quadratic equations without noting the history of such methods. The combination of these four strategies means that the historical dimension becomes an important part of the book, without competing with “an exploratory approach” as the main approach.
Students reading this book will have access to a significant amount of historical information, and may well be inspired to look for more elsewhere (for instance in the books noted in “Selected References with Annotations” in the back of the book). However, they are not given any help as to how they could themselves include history of mathematics in their own teaching. There is no discussion of different ways of including history of mathematics, drawing on the discussions in the ICMI Study (Fauvel & Van Maanen, 2000) and discussions in HPM conferences, for instance. Thus, the students are mostly left to figure these things out on their own or to ask their professor for help, or to look at the Historical Modules (Katz & Michalowicz, 2005) which are mentioned in the references. It could be said, of course, that the book sets an example on how history of mathematics can be included in teaching. It would be helpful, though, if this was explicitly commented upon to make students aware of this.
Moreover, because the author tends to give information about who did what first, the readers will mostly be shown how mathematics has developed through history, not how it has been used in different cultures. They will see that mathematics is a field of knowledge developed by human beings, but the role that mathematics has played in different societies and cultures throughout history will not be so visible.
Continuing in a critical vein, I will note that the history of mathematics is unevenly distributed. For instance, the part on “counting and probability” has few historical components. In my experience, the history of probability is highly suitable for work with students.
The history of mathematics is such a rich resource that every person can have his own favorites, and not everything fits into a textbook of less than 800 pages, covering so many subjects. This is a textbook which gives the students a taste of what history of mathematics can be and a possibility for understanding a little about how mathematics has evolved. That is in itself valuable for prospective mathematics teachers.
Bjørn Smestad, Norway
Fauvel, J., & Van Maanen, J. (2000). History in mathematics education: An ICMI Study. Dordrecht: Kluwer Academic Publishers.
Katz, V. J., & Michalowicz, K. D. (Eds.). (2005). Historical Modules for the Teaching and Learning of Mathematics: Mathematical Association of America.