by Glenda Lappan, NCTM President 1998-2000
NCTM News Bulletin, July/August 1998

As the school year ends, we are often relieved that we have a chance to reflect, plan, revitalize our minds, and renew our commitment to teaching. We view summer, short as it is, as a chance to get ourselves ready for another school year, working on the curriculum and organizing our plans.

But we also need to rest, to clear our minds, to refuel our patience, and most of all to rekindle our enthusiasm. Teaching is an exhausting, demanding job.

Given the usual desire of teachers to get the school year finished, imagine my surprise during a recent conversation with a Minnesota teacher who emotionally said, “I do not want this year to end—I have so much more that I want to do with my kids!” I asked what she meant. She replied, “I have so many good mathematical ideas and problems that I want to use with my students,” and explained that she was in her second year of a new curriculum series that had given her a terrific boost in her enthusiasm for teaching.

The materials her school had selected were designed to reach the goals of the NCTM Standards and provided her with stimulating lessons for her students. She saw the new series as very challenging, both for her students and for herself. The materials engaged students in multistep problems that required reasoning, inventing, generalizing, abstracting, and applying mathematics. The lessons were carefully sequenced so that the mathematical ideas developed over time in a connected way. Students were able to see how the math they were learning this week related to math they learned a month ago, and the teacher herself knew exactly where the mathematics was leading.

She no longer had to work so hard to find or create tasks that would help her students learn important mathematics. She could spend her energy polishing the lessons so that they worked well in her classroom. She noted that even she was learning anew about the mathematics she had been teaching for years, thanks to the lessons that made one think deeply about the mathematics. She felt confident that her students were reaching levels of reasoning and understanding that they had not reached in years before. Her students’ state test scores confirmed that.

What does it take to help all of us experience the renewed joy of teaching and learning exemplified by this teacher’s comments? One thing is obvious—an excellent set of mathematics materials around which to plan our lessons. The emphasis here is on the quality of the materials. Just as we have come to value the importance of mathematical tasks to students’ learning, we have to value the importance of mathematics materials to teachers’ teaching.

For years, many teachers have been driven to create their own materials because the available textbooks were not sufficient to meet the goals of reasoning, communicating, connecting, and problem solving in mathematics. Nor were the text materials sufficient to develop an understanding of important concepts, skills, and procedures in mathematics. But in some areas, the need to overhaul the system led to excessive stances against text materials. Teachers got the message that those who used text materials—books or modules—were not doing as good a job as teachers who created their own curriculum materials.

But think of the complexity of creating coherent, complete mathematics materials from scratch that have an internal structure, a spine—materials that guide the development of mathematical understanding and skill and that support students’ learning to reason mathematically, to see connections among mathematical ideas, and to solve challenging problems. Given the work life of teachers, the time to create rich mathematical activities is seldom found. Choosing an excellent mathematics series that meets the goals of the NCTM Standards can be the first step toward revitalizing our mathematics classes.

But materials alone do not make the mathematics program. Another key to success is a teacher’s willingness to increase the effectiveness of the materials by spending considerable time planning the lessons, listening carefully to what students are saying in the classroom, analyzing what students are learning, and consequently adjusting the mathematical tasks and the questions asked. In other words, teaching matters. Good mathematics content and committed teachers—the combination can be a powerful boost to students’ learning. But this is true only if the materials are coherent, connected, challenging, and mathematically on target and if the teacher is a professional who is committed to helping every student reach a high level of excellence in mathematics.