by Johnny W. Lott, NCTM President 2002-2004
NCTM News Bulletin, March 2004

During my two years as NCTM President, I have had many opportunities to visit schools, teach classes, and talk with local teachers and principals. In one large city school system, a wonderful teacher named Jacqueline Smith summed up what was happening in her district in this way: "Teachers are teaching. Students are learning." These remarkably simple statements provide a wonderful description of what I have witnessed in schools across the United States and Canada. As my term is ending, I'm prompted to share experiences from our mathematics classrooms and convey the wisdom they have imparted to me.

• Don't underestimate students' knowledge and abilities.

Third-grade class in Montana—In the beginning months of 2001 when I was talking to students about the largest numbers that they knew, a child wondered out loud, "I heard that you can compare infinities. Is that true?"

• Don't assume that students don't have access to technology.

Third- and fourth-grade combination class in a middle-class school in Alberta—When I asked who in the class had an e-mail address and used it, all but three students raised their hands. That night I received a wonderful e-mail message from a third-grade "idmieer" (admirer).

• Don't be afraid to build lessons around students' extra-curricular interests

High school junior class in Mississippi—To demonstrate the production of a sine or cosine curve, I borrowed an idea from a Denver professor. In preparation for the lesson, I asked the teacher to have a student bring a skateboard to class. When the time arrived, I stood on the skateboard and had a student push me across the room in front of the whiteboard. Before the student began pushing me, I started drawing continuously up and down in a consistent manner, trying to keep the segments that I was drawing the same length. While being pushed along, I continued to draw in the same manner. A reasonable facsimile of a trigonometric curve resulted and gave us an opportunity to talk about the line's components and how they might be altered by changing pieces of the production process. Try it.

• Extend the mathematics that you are teaching beyond the here and now.

Fifth-grade class in South Carolina—In a creative arts school, students played a traditional mathematics game called nim on their calculators. Using only the buttons for 1, 2, +, and =, the students were encouraged to find a winning strategy for reaching a selected target number of 21. By changing the buttons and target number, students were also led to explore divisibility and remainders and their uses in strategy games.

• Look for everyday applications of mathematics and use them for teaching.

High school sophomore class in Utah—In a geometry class, students who spoke many different native languages were discussing angles, angle measures, and their uses. Students talked about "natural body angles" that added comfort to the design of recliners and car seats, and they also discussed headings, directions, and the numbering of airport runways.

• Teach even though students are being tested beyond reasonable limits.

Fourth-grade class in Alabama—In what may not be an unusual situation, students in this school are assessed with standardized tests five times a year. The teacher, an isle of sanity in severely tested waters, continues to teach the basics of computation through problem-solving techniques and manipulatives.

• Use your students' families as resources.

Sixth-grade class in Quebec—Family members whom I met at a school meeting were fascinated by the possibilities of working in small groups with their children and others, and they also sought help in finding sources of mathematics problems and readings for themselves and their children. Be sure to use these resources to support your students and reinforce the lessons you are teaching.

• Don't forget where the mathematics comes from and where it is going.

Twelfth-grade class in Alberta—In an international baccalaureate calculus class, questions about infinity that are known to have intrigued ancient mathematicians also captured the interest of very bright senior high school mathematics students who had become very comfortable with some "infinite processes" in their calculus classes.

I can assure you that in all the classes mentioned here, whether they were geared toward very bright students or toward students who were mathematically challenged, the teachers were teaching and the students were learning. The public should know this. I believe that it is our responsibility as mathematics educators to go to the reporters, go to the public-service clubs, and go to any other outlet that can help us enlighten the public about what is actually going on in our classrooms. At the same time, we should also get out the message that it is important for teachers to have opportunities to leave the classroom for professional development so we can address our classes with teaching skills and methods that are up-to-date and effective.