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Math education always included basics

Math education always included basics
Sunday, September 24, 2006

On Sept. 12, the National Council of Teachers of Mathematics released a document called "Curriculum Focal Points," which was written to help states decide what needs to be taught at each grade level, prekindergarten through eighth grade. The Curriculum Focal Points present three significant mathematical topics students need to understand thoroughly at each grade level to build a strong mathematics foundation.

The media coverage of the release of the document has misrepresented both the substance and the intent of the focal points. Reports have implied the math council has gone "back to the basics" in its new document. This misrepresents the fact NCTM has always supported learning the basics. Memorizing the basic facts, however, is not enough. Memorization does not suffice when students get to calculus and higher mathematics. Students must understand the math they are doing in order to use it effectively and successfully at those levels. This is one of the main reasons why for decades, long before NCTM first came out with the 1989 standards, most students dropped out of higher mathematics courses once memorization no longer served them.

Critics have called the implementation of the math council's standards "fuzzy math." They have said that teachers implementing NCTM standards ask children to be "creative" in their thinking by solving problems in ways other than just memorizing the answer. The standards do call for children to be able to solve problems in a variety of ways - ways that are logical and efficient. Knowing more than one way to get an answer to an arithmetic problem helps children become flexible in their thinking and builds the foundation for algebra.

For example, 7 + 8 = 15. Second-grade children should know this basic fact. However, they should also understand more than just the fact. In examining different ways to solve this problem, a child can prove that 7 + 8 = 15 by thinking about "doubles + 1." When a teacher records the child's thinking, a foundational property of algebra, the associative property, can be taught.

Student: "I know 7 + 8 = 15 because 7 + 7 = 14; and 7 + 8 = 1 more than 14 so 7 + 8 = 15."

Teacher: "You know that 8 = 7 + 1, so the problem can be written 7 + (7 + 1). Since you used 'doubles + 1,' the problem becomes (7 + 7) + 1 = 15."

This student is using the associative property, a + (b + c) = (a + b) + c. When the teacher points this out, applying these rules to algebra later is not a mystery because they are properties that students have used and understand. Teaching algebra, while also teaching number relationships and basic facts, is very different from the media description of a child "wandering around" looking for "creative" ways to solve a problem.

The Trends in International Math and Science Study report is an influential research study of mathematics and science instruction across 41 countries. One of the findings of that study is that in American classrooms, teachers are expected to teach up to 68 different math concepts in a school year, while in countries that outperform the United States, teachers focus on just a few big mathematics topics each year. This traditional American curriculum was identified by one of the report's researchers as "a mile wide and an inch deep." NCTM has long been an advocate for students developing a deep understanding of mathematics. This deep level of understanding is not possible when teachers are trying to cover 68 topics in a school year.

Recent newspaper articles have blamed America's declining math test scores on the effects of the implementation of NCTM standards. The TIMSS report indicates the standards are only being implemented in roughly 10 percent of American classrooms. It is not that the standards have failed; it's that they have not been widely used. The Greater Birmingham Mathematics Partnership is attempting to help teachers provide quality mathematics education for all students in the world of the 21st century.

The mathematics partnership is a consortium of nine Birmingham area school districts, the University of Alabama at Birmingham, Birmingham-Southern College and the Mathematics Education Collaborative, a nonprofit organization in Washington state dedicated to advocacy for quality mathematics education. The National Science Foundation awarded the partnership a $9.96 million grant over five years to improve the teaching and learning of mathematics in the greater Birmingham area. The partnership provides mathematics content courses and followup workshops for teachers as they work to improve their practice. The group also works with parents, university mathematicians and community and business leaders to secure quality mathematics programs in our schools.

Faye Clark, Ph.D., (e-mail: and Ann Dominick (e-mail: are project directors for the Greater Birmingham Mathematics Partnership, which has scheduled a series of community mathematics nights for the public. Call 205-934-3738 or go to