by Glenda Lappan, NCTM President 1998-2000
NCTM News Bulletin, January 1999

One bonus of being president of NCTM is getting to visit classrooms in the United States and Canada. It helps keep one's eye on what is really important--the kids. It also gives one a front-row seat to the remarkable challenges and accomplishments of teaching.

Picture this--a sixth-grade classroom with students working together, each group on a different problem. The six problems have been carefully chosen to collectively show different kinds of patterns of growth, some linear and some nonlinear. The students work on the problems using mental calculation and some paper-and-pencil work until the numbers get very large. Then they go to the equipment table, get a calculator, and continue to extend the pattern of numbers in their table.

One can see that the teacher has established a classroom where the expectations are clear. Every student is engaged, working hard to generalize the patterns, testing ideas, and then moving on to another aspect of the problem until all students in the group are convinced that they have found a way to generalize the pattern. In some groups, the generalization is stated as a recursive rule. In others, the generalization is stated as a rule that depends only on the position in the sequence of terms, i.e., the 34th term, and possibly the starting number.

As I wander around this classroom asking questions, the students are receptive, eager to engage in even more challenging problems. The issue comes up of whether a pattern could be continued in more ways than one. One student extends the known information as a geometric pattern; another finds a linear pattern that fits the given information. The group is amazed. I am also amazed as I consider the challenges this teacher is facing.

In this classroom, two of the six groups include children who do not speak English. Two children speak Spanish and another Polish. The two Spanish-speaking girls are in a group with a bilingual Portuguese girl. The fourth group member speaks only English. Despite their language differences, the four have become a group that is functioning reasonably well. The two Spanish-speaking girls understand enough of their groupmates' combined Portuguese and English explanations to work the problems. The group seems to be taking responsibility for one another's understanding, as does the group with the Polish-speaking boy. However, he has less help, since the only language resource is English.

The teacher in this classroom is a second-year teacher who wants to succeed with each student in the class. He is thinking hard about the mathematics curriculum, but he also has to work to support his students so that they can succeed. It is no easy job. He does not speak Spanish or Polish and worries about whether these three students have sufficient support.

Let's take a different challenging teaching scenario--a "terminal" high school geometry class. The students do not really want to be there, but their teacher works to help them believe that they can succeed in this class. They know that she is glad to be there with them.

They have been working for several days preparing for an experiment in which they will use trigonometry to measure inaccessible heights. They have built tissue-paper, hot-air balloons and are going to fly them to see which one will go highest. The teacher goes over what is expected, and then we go outdoors to fly the balloons. But nature doesn't cooperate. A downpour begins and the flying is off. With a group of disappointed students and three wet visitors, the teacher trudges back into the classroom. She goes to the chalkboard and begins to create problems for the students to solve that use the trigonometry they have been studying.

The teacher personalizes the problems by making class members the characters in the problems. The class is quickly totally engaged in a new world that features them and mathematics problems. Trees fall, safely missing houses. The hero in another problem lands on the hot-dog stand (his favorite food) rather than in the cotton-candy machine as the Ferris wheel tumbles. In front of visitors, working with students who came to her having already given up on themselves in mathematics, she has the class eating out of her hand for more mathematics problems.

Both the sixth-grade teacher and the geometry teacher face multiple classrooms of students five days a week. Each child is different and needs special attention to learn to his or her fullest potential. Yet, guided by their knowledge of, and love for, mathematics and their unswerving belief that each child can meet high expectations, these teachers are finding ways to give their students what they need to succeed in mathematics. Such commitment to high standards and expectations is an underlying part of the NCTM Standards, and it's rewarding for me to see it in action in mathematics classrooms across the continent. We have a long way to go in our commitment to a high-quality mathematics experience for every child, but we need to stop occasionally and celebrate what excellent teachers are already accomplishing.