| 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.
Source:
Basic Education, May 1999 - Volume 43 - Number 9 |
 |
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).
