## A Test on Textbooks

- Schools typically adopt new mathematics textbooks every five to seven years.
- Before publishing and distributing new textbooks to schools, textbook developers field-test and revise new materials on the basis of evidence of effectiveness.
- Textbook authors and publishers base the content of mathematics textbooks on national curriculum standards.
- U.S. textbooks resemble textbooks used in countries where students perform well on international mathematics assessments.
- Mathematics textbooks have a direct impact on what schools teach and what students learn.

## Schools typically adopt new mathematics textbooks every five to seven years.

*True*. The five- to seven-year cycle allows for various disciplines, such as science, language arts, and social studies, to regularly select new textbooks while distributing their cost somewhat evenly from year to year. Schools replace textbooks because the textbooks deteriorate physically and because teachers revise their instructional approaches or modify the emphasis on content. In general, however, U.S. schools do not adopt new mathematics textbooks in a given month or year. This means that textbook publishers must produce continuously marketable materials for states or school districts with different adoption timelines.

## Before publishing and distributing new textbooks to schools, textbook developers field-test and revise new materials on the basis of evidence of effectiveness.

*False*. Two factors generally preclude textbook publishers from field-testing new material: the high cost of developing and publishing a new textbook series—in excess of $20 million for a complete K-6 mathematics textbook series—and the need to produce materials for varied markets under tight timelines. In addition, consumers rarely demand proof that commercially generated materials are indeed effective. Publishers sometimes test new materials with teachers, but this assessment generally relates to the physical design of the textbook rather than to content or pedagogical approach. Most publishers do not gather scientific evidence regarding the effectiveness of the textbook during its development or during its use in the classroom. The result is that textbooks, a potential change agent for improving student learning, generally undergo few, if any, major changes from one edition to the next.

## Textbook authors and publishers base the content of mathematics textbooks on national curriculum standards.

*False*. The United States, unlike most industrialized countries in the world, leaves the decision about what mathematics to teach and when to teach it to local control. At the state or local school district level, individual teachers or committees of teachers, administrators, and parents make decisions about course content. The federal government does not provide national curriculum standards to guide local decision making. The National Council of Teachers of Mathematics (NCTM), a nonprofit organization of teachers, has produced a K-12 curriculum framework for mathematics. This framework,

*Principles and Standards for School Mathematics*(2000), presents general guidelines for mathematics learning expectations in four grade bands (preK-2, 3–5, 6–8, and 9–12). Some publishers do take these guidelines into account when producing math textbooks.

## U.S. textbooks resemble textbooks used in countries where students perform well on international mathematics assessments.

*False*. U.S. textbooks are unique in their size and amount of content covered. Authors and publishers tend to add topics to U.S. mathematics textbooks to meet various local and state curriculum requirements, but they rarely delete information to make room for new topics. The textbooks grow larger with each new edition. U.S. mathematics textbooks address substantially more information at each grade level than textbooks used in countries where students perform well on international assessments, such as Japan and Singapore. Also, U.S. secondary schools have historically organized school mathematics courses into separate content strands, such as algebra, geometry, statistics, and calculus. Schools outside the United States, however, typically integrate mathematics so that students study algebra, geometry, and statistics every year.

## Mathematics textbooks have a direct impact on what schools teach and what students learn.

True. Tyson-Bernstein and Woodward (1991) note the ubiquitous nature of textbooks in U.S. schools; textbooks are a prominent, if not dominant, part of teaching and learning. This phenomenon, however, is not limited to the United States, as international studies indicate (Robitaille & Travers, 1992):Teachers of mathematics in all countries rely heavily on textbooks in their day-to-day teaching, and this is perhaps more characteristic of the teaching of mathematics than of any other subject in the curriculum. Teachers decide what to teach, how to teach it, and what sorts of exercises to assign to their students largely on the basis of what is contained in the textbook authorized for their course. (p. 706)

#### Figure 1. “Traditional” U.S. Textbook Lesson: Volume of Cylinders and Cones

The textbook method of presentation necessarily affects instruction. Stigler and Hiebert (1999) characterize the typical 8th grade mathematics lesson in the United States as “learning terms and practicing procedures” (p. 27). According to the researchers' analysis of videotaped lessons, U.S. teachers usually follow a routine that begins with short-answer review questions followed by relatively long segments of homework checking. After checking the homework, the teacher presents the students witha few sample problems and [demonstrates] how to solve them. Often the teacher engages the students in a step-by-step demonstration by asking short-answer questions along the way. (p. 80)

## A Better Alternative

#### Figure 2. “Standards-Based” Textbook Lesson: Volume of Cylinders and Cones

## Selecting a Textbook

- What key mathematical ideas in each content strand should each grade level address?
- How does the content of the textbook align with these key mathematical ideas?
- What types of activities does the textbook provide? Are students challenged to think and develop understanding, or are they simply shown how to work some exercises and then asked to practice procedures? Will these activities engage students in mathematical thinking and activity?
- Is there a focus on mathematical thinking and problem solving? Are students expected to explain “why”? Does the textbook encourage students to explore “what if” questions and to offer and test conjectures?