Textbook Analysis

Current l ist of textbooks for undergraduate mathematics courses for future elementary teachers, September, 2009

Textbooks are an important source of content in classes that use them. A textbook can be used to define the boundaries of content as well as the specific topics, the order in which they are taught, and most importantly, how they are presented. In mathematics classes, a textbook can be a source for problems, explanations, and examples. For several reasons, it seems likely that textbooks have a large influence on the content and emphasis of the class in mathematics classes for elementary teachers:

First, we hypothesized that these classes are often taught by graduate students with little experience or by reluctant faculty members. If this were true, the textbook might be used to "get through" the semester.

Second, unless they are taught by mathematics educators (in or out of mathematics departments), these classes are unlikely to be related to the research agenda of the faculty member teaching the class. That is, if the instructor is a mathematics professor or graduate student, his/her research interest is most likely in mathematics, not in math education. Again, this suggests that a textbook might be relied on for the content in contrast to the case when faculty are teaching in their own subject area and use their own materials or selections from the work of others.

Third, we reason that the very existence of well-known long-lived textbooks implies the existence of a market that would not be there if the books were not being used. Some textbooks have been in print for many years with multiple editions and new authors taking over from previous authors.

Finally, in recent years several mathematicians have become interested in teaching classes for elementary students. They have developed books for their own use and in some cases have published them. In interviews, these mathematician-authors suggested that the available books made it difficult for them to teach the classes in a way they felt was appropriate.

All of these arguments suggest that textbooks may be important in these classes.

We began an analysis of textbooks as a first step in understanding what mathematics is being taught to prospective elementary teachers. We think of the textbook content as presenting an opportunity to learn (OTL) the ideas, topics, and procedures it includes (see the opportunity to learn page for more on that construct).

Our textbook analysis has been conducted at two levels: overall contents of the books and in-depth analysis of three focal topics. In the content analysis, we note what topics are included and whether they are entire chapters or topics within chapters. We include various page counts to look at relative emphasis, and we have created maps of each book that show the order and relative size by topic. Second, we analyze in depth the topics of multiplication, fractions, and reasoning & proof. Each of these is an important part of elementary mathematics, and each plays a different role in the curriculum. These analysis have been presented at several conferences, including a mini-conference at the CPTM summer institute, a session at the MSRI wokshop on teacher education in 2005, and the NCTM Research Presession in 2004. Another analysis has been completed looking at problems and exercises.

Two papers are available about the textbook analysis. Download by clicking on the title.

McCrory, R., Siedel, H., & Stylianides, A. (in revision). Mathematics textbooks for elementary teachers: What's in the books? (Please do not quote or cite without permission).

McCrory, R. (2006). Mathematicians and mathematics textbooks for prospective elementary teachers. Notices of the AMS, 53(1), 20-29.

Updated 09/12/2009