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Inclusiveness and Understanding: Twin Commitments

Lappan_Glenda-100x140by Glenda Lappan, NCTM President 1998-2000
NCTM News Bulletin, May/June 1998

What is the reform of mathematics teaching and learning guided by NCTM’s Standards all about? My answer is that we are about the following three things: upgrading the curriculum, improving classroom instruction, and assessing students’ progress to support the ongoing mathematics learning of each student.

This message is simple but compelling. It says that in the classroom, where students and mathematics come together, the mathematics must be worthwhile, the instructional strategies must be effective in promoting the students’ learning, and assessment must be a means to help teachers build and strengthen follow-up activities.

The emphasis in reform is on mathematics. Reform is about building mathematics programs that are challenging, age appropriate, and substantive for every child. Reform is not about manipulatives, group work, calculators, or writing in the classroom—all of which are important means but not ends in themselves. We must clarify this message in order to win community support for teachers making changes that strengthen mathematics programs.

Some will say that mathematics education is at fault for our 12th graders’ poor showing in the 1995 Third International Mathematics and Science Study (TIMSS). But we must remember that reform was a response to the poor mathematics achievement on the first (1964–65) and second (1981–82) international mathematics studies. The second study helped lead to the development of the NCTM Standards, the influence of which is only beginning to be reflected in more and more curricula across the country.

TIMSS, like the first and second studies, focused on achievement and the curriculum. In addition, it focused on the instructional practices that lead to high-quality mathematics lessons. It shows that we have a long way to go. But I believe NCTM’s Standards for curriculum, teaching, and assessment enable us to examine mathematics instruction for completeness, coherence, alignment, and quality across all grade levels. If we take nothing more from TIMSS than the need for such reflection, the study will have served the country well. But TIMSS also offers us the opportunity to take stock of our own commitments to mathematics education.

Behind the message of the Standards are two underlying commitments. First, NCTM is committed to inclusiveness. We believe that effective mathematics teaching and learning should be experienced by every student, not just a privileged few. Second, we believe that a primary goal of mathematics instruction is for students to develop a deep understanding of important mathematics. Thomas Romberg, who chaired the development of the NCTM Curriculum and Evaluation Standards for School Mathematics, speaks of five forms of mental activity from which mathematical understanding emerges. They are constructing relationships, extending and applying mathematical knowledge, reflecting on mathematical experiences, articulating what one knows, and making mathematical knowledge one’s own.

If we put together these two commitments, inclusiveness and developing deep understanding, we immediately confront the issue of how to create programs that have the potential to meet each of these goals.

What makes us think that we can make better mathematics accessible to more students? Changes in the mathematics curriculum itself provide one avenue for both excellence and access. TIMSS shows that other, more successful countries structure mathematical content so that in each year, even the high school years, students study multiple strands of mathematics. Newer curricula in North America are giving more balanced attention to the development of number, geometry, measurement, probability, statistics, discrete mathematics, and algebra as K–12 strands. This approach nurtures the different strengths and talents of students over their entire mathematics program.

Another tool for giving more students access in the middle and high school grades is graphing calculators. These tools, used to achieve specific mathematical reasoning goals set by the teacher, allow students to tackle problems that simply cannot be done without such aid. Often such problems provide great motivation for students. Realistic data can be handled with ease. Totally different reasoning strategies can lead to creative solutions to challenging problems. Not only is reasoning supported, but the ability to do complicated paper-and-pencil calculation by hand is no longer the huge filter that it has been in the past.

Many factors, of course, affect access. The way we teach can either support or undermine all students’ developing deep understanding of important mathematics. But probably the most important component of access is our own belief that all students both deserve and can take advantage of excellent, challenging mathematics programs.

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