Reprinted here with the permission of the Council for Basic Education. No further republication or redistribution is permitted without the written permission of the editor.
Evaluating Mathematics Textbooks
by Gerald Kulm
For many middle grades mathematics teachers, the textbook is their primary guide to implementing the curriculum. Project 2061 of the American Association for the Advancement of Science recently completed an in-depth evaluation of thirteen middle grades mathematics textbook series. These books are likely to be on adoption lists or already in use in many middle school classrooms.
Data on poor student performance from the Third International Mathematics and Science Study and other research indicate that the middle school mathematics curriculum requires urgent attention. It is in middle school that many students find themselves in mathematics programs that are repetitious and non-challenging. As a result, their achievement and interest in mathematics stall, and they are unable to take advantage of the full range of future academic and career options.
Meaningful, long-lasting improvements in student learning will require changes in many areas of the nation’s complex and highly decentralized education system. At the center of this system is the curriculum itself, which is defined largely by the textbooks students use. A careful analysis of both the content depth and instructional strategies used in these textbooks is required to judge whether there is potential for students to actually learn important mathematics.
Three mathematical strands -- number, geometry, and algebra -- were the focus of the content analysis. These are the core content areas expected to be covered in any middle grades textbook series. Specifically, the content includes fractions and operations, equivalent forms of numbers, properties of shapes, computations of circumference, area, and volume, and using graphs and equations to understand algebraic concepts.
Most middle grades textbooks do a credible job addressing number benchmarks. However, only the best ones develop meanings for fractions, for example, by having students measure, build models, use number lines, and compare fractions to acquire a full understanding. Almost all textbooks present the formulas in geometry. But even some of the best ones fail to relate geometry skills to real-life ideas, such as the triangular structures used in bridges or the relationship between the distance around a city park and the area enclosed.
Too many textbooks start almost immediately with procedures for manipulating algebraic symbols and solving abstract equations. Few textbooks do a good job teaching how graphs show relationships, and instead focus on simple, linear graphs. The best series involve students with data collection in situations like a bicycle tour, giving them first-hand experience connecting concepts, such as time and distance, with tables and graphs. With this solid foundation, variables and equations are used naturally and with understanding.
After judging the textbooks on their coverage of mathematics content, analysts trained in Project 2061’s procedure, who were experienced mathematics teachers and college faculty, determined how well the texts addressed instructional criteria. Arranged in seven broad categories (marked in bold lettering), these criteria reflect principles and strategies that are supported by solid research evidence on best teaching practices.
Few textbooks do a good job identifying a sense of purpose by connecting the introductory activity with the learning goal. The best textbooks use questions such as, "How does a surveillance camera help determine a suspect’s height?" to make the purpose of lessons, in this case studying similar triangles, explicit and meaningful to students and the teacher.
The best way to separate good from poor textbooks is to observe how they build on students’ ideas about mathematics. This requires the text to offer ways to identify students’ prior knowledge and to deal with misconceptions. Poor books are not helpful, providing only general hints such as having students describe times when they have been "bogged down" in doing a problem.
Most middle grades textbooks do a good job of engaging students in mathematical ideas by providing students with first-hand experiences. In lower-rated books, the contexts are sometimes too contrived to be meaningful to students. Many textbooks satisfactorily demonstrate skills and provide practice with them in varied contexts. However, few books develop mathematical ideas, often giving the definition of a term before students have any experience with the idea.
Only a few top-rated textbooks succeed in promoting student thinking in mathematics. These books ask students to explain concepts such as distance = rate x time using words, symbols, and graphs; estimate and predict from tables and graphs; and explain why their answers are reasonable. Many textbooks do not assess student progress in mathematics in a way that is well aligned with specific mathematics benchmarks, and few books use students’ responses to test items to guide and adapt instruction. Most textbooks enhance the mathematics learning environment by including pictures of students of diverse backgrounds and ethnicities doing mathematics, but few contain activities that can interest and challenge all students.
The evaluation revealed stark contrasts in the adequacy of instruction among the textbooks. The good news is that a few effective middle-grades mathematics textbook series are available. Four of the thirteen were rated satisfactory; that is, high enough to be confident that students would learn the content of the selected benchmarks. These books are, ranked in order, Connected Mathematics (Dale Seymour Publications), Mathematics in Context (Encyclopedia Britannica Educational Corporation), MathScape (Creative Publications), and Middle Grades Math Thematics (McDougal Littell).
The top two series contain both in-depth mathematics content and excellent instructional support. For example, Connected Mathematics challenges students to plan a bicycle touring business. Students develop bar graphs and charts predicting the costs involved, depending on the number of cyclists and the distance of the tour. They write equations that can predict travel times and profits under varying conditions. Students develop and work with their own data, so they can explain how one thing increases when something else increases.
The bad news is that no popular commercial textbooks were rated satisfactory. Those rated as unsatisfactory, also ranked in order, include Mathematics Plus (Harcourt Brace & Company), Middle School Math (ScottForesman-Addison Wesley), Math Advantage (Harcourt Brace & Company), Heath Passport (McDougal Littell), Heath Mathematics Connections (D.C. Heath and Co.), Transition Mathematics (ScottForesman), Mathematics: Applications and Connections (Glencoe/McGraw-Hill), Middle Grades Math (Prentice Hall), and Math 65, 76, 87 (Saxon Publishers). These textbooks were lacking in their coverage of important mathematics, weak in their instructional support for teachers, and provided little development in sophistication from grades 6 to 8. They were particularly unsatisfactory in offering a purpose for learning mathematics, taking account of student ideas, and promoting student thinking.
Dr. Gerald Kulm was the director of Project 2061’s mathematics textbook evaluation. The full report is available online at: http://project2061.aaas.org.
Kulm, G. 1999. Evaluating Mathematics Textbooks. Basic Education, 43 (9).