by Glenda Lappan, NCTM President 1998-2000
NCTM News Bulletin, May/June 1999

Not long ago, the selection of a mathematics textbook was such a sleepy event that no one but the teachers noticed. The school board agreed with teachers' recommendations in a fairly routine manner. As long as the change from one textbook to another was so slight that parents were able to understand the problems assigned for homework, all was well.

In recent years, textbooks have begun to change to reflect emerging thinking about content and methods. Consequently, mathematics textbook selection is now a big event in many states, especially those like Texas and California that have a centralized textbook adoption process. Now the stakes are very high for all concerned. More and more teachers want textbooks that engage students with mathematics in ways that require deeper thinking on the part of the students. Yet, to stay viable, textbook companies need to sell textbooks that meet a variety of needs. And others outside the education community are demanding to have a say in textbook adoptions--even in communities in which they are not residents.

The widespread interest in mathematics education is important--teachers cannot improve mathematics teaching and learning alone. Some debates over textbooks have been healthy; however, more and more often, the discussions are disintegrating into divisive battles. These conflicts are signs of more-fundamental disagreements over the changes in mathematics curricula. Unfortunately, when people are fighting over content and methods, they are often not asking the most important questions about materials, such as "What are the mathematical goals for the students?"

The divisiveness is hurting our progress. We need to stop and remember why fundamental changes are being proposed in mathematics textbooks and instructional strategies in the first place. In the past three international comparative studies of mathematics performance (covering more than three decades), the U.S. results have been consistently disappointing--signaling to us that the old curriculum and textbooks have not been competitive in the international arena. The most recent study, the Third International Mathematics and Science Study (TIMSS) conducted in 1994–95, brought some good news (our fourth graders are above the international average), but mostly bad news (our eighth graders are below average, and our twelfth graders are well below average among the countries that were a part of the study).

Consider these results in historical context. In the two earlier international studies, the first in 1964 and the second in 1981–82, the results at grades 8 and 12 were similarly disappointing. For instance, in the second study, eighth-grade students were slightly above the international average in computational arithmetic and well below the international average in noncomputational arithmetic, for example, problem solving. Despite a few bright spots, these results showed a decline in achievement between the first two studies. The declines were somewhat greater for the more demanding comprehension and application items than for the computation items. Low performance at the international level is not a new finding.

The U.S. curriculum, which for the most part had not changed much from 1964 to 1995, received consistent criticism. The second international study's report on curricula says it all in its title--The Underachieving Curriculum. Ten years later, TIMSS researchers described the U.S. curriculum as "a mile wide and an inch deep."

Another sign of the ongoing weakness of mathematics curricula is the lack of preparedness of college students. Consider my own university as an example. For the past 25 years, 25 to 30 percent of entering freshmen at Michigan State University place into remedial mathematics courses even though the number of years that students have studied mathematics has increased.

Although I've pointed to signs of trouble, we have not failed all students. We have always produced some students that are as good as the best in the world. Recent results from the National Assessment of Educational Progress show that although mathematics performance declined between the first two international studies, it has been improving over the past decade.

But that's not enough. Our modern society requires greater knowledge of mathematics for a much greater segment of the population. We can and must do better. Better than we have done in the past. Better than we are doing now. That is what the Standards--which grew out of concerns raised by the second international study--aim to help us do. Positive curricular changes as a result of the Standards are just now beginning to bear fruit.

Despite the signs that we must make focused changes in the curriculum and select textbooks that are proved to work, we've been bogged down by a polarizing war of words over curriculum and teaching. The participants in this effort sometimes forget that none of us should be about "winning." Our only concern should be for the children in our mathematics classes and for the teachers who are with them on a daily basis. Unless we put aside our passions and hear one another, consider where we agree, and carefully articulate our differences, our students--the very ones we seek to help--will be caught in the middle of a destructive tug-of-war.

We'd be well served to follow the example of the National Council of Supervisors of Mathematics. It asserts that our students will be best served by mathematics programs that balance the best of the past with the best emerging content, methods, materials, and technology of the future. Extreme positions--such as a return to the books of the past or a rejection of computational proficiency and basic facts--resign us only to more bitter fights over textbooks and curriculum. And our children and teachers will be the losers. Maintaining the status quo is unacceptable. We must find ways to come together to better educate our students in mathematics.

Look for Part II in the July/August News Bulletin.