Mathematics

The Internet is full of math problems, but many of them are pointless, says EDC’s Paul Goldenberg. They exist solely to practice what a student already knows, without leading to or developing larger concepts or questions. In such cases, he says, “the individual problems don’t matter, and neither do the answers.”

According to researchers in EDC’s Center for Mathematics Education, traditional mathematics curricula have neglected visual mathematics in favor of verbal and logical approaches that may not work as well for many students.

In her years of research and collaboration with teachers, Deborah Schifter knows how difficult it is to change the way you teach. It’s particularly hard in mathematics, where prescriptive textbooks have provided a welcome crutch for many teachers.

Once taught primarily to college-bound students, algebra is now recognized as a critical “gateway” course for all students. “It’s considered the entrée into higher math, the hard sciences, even into university study itself,” explains Peter Braunfeld, professor emeritus of mathematics at the University of Illinois at Urbana-Champaign. “It’s become the difference between getting in and being left out.”

In our introduction to this issue of Mosaic, we referred to Paulo Freire’s description of literacy as “reading the word and world.” That same phrase-with its dual emphasis on the concrete and the abstract—can be used to characterize EDC’s definition of mathematical literacy.

One of the first principles of universal design is that it is better to build flexible options into a curriculum at the outset rather than trying to retrofit the program after it is published. A corollary might be that even when you’ve built in flexibility, you never stop retrofitting to meet the needs of an ever-expanding universe of users.

Elegance. Culture. Habits of mind. Such phrases are usually reserved for literature, philosophy, or fine arts. But in the case of EDC’s newest curriculum, they describe geometry. While covering the basics of high school geometry, Connected Geometry discusses ways to build elegant bridges among mathematical ideas, create a lively culture of mathematical investigation, and develop students’ abilities to inquire and think.

The staff of EDC’s K-12 Mathematics Curriculum Center at EDC likes to think of their new book, Choosing a Standards-Based Mathematics Curriculum, as the “eyes, yardsticks, and noses” schools will use to evaluate and select a mathematics program that fits their needs.

Al Cuoco, director of EDC’s Mathematics Initiative, and EDC Vice President Wayne Harvey, a mathematics education researcher, emphasize that improving mathematics education goes beyond a simple choice between traditional mathematics and mathematics based on the NCTM standards.

Al Cuoco might have added that there are things kids need to understand about mathematics that do not show up on the traditional mathematics tests. And that touches on a particularly difficult issue for mathematics educators today: How can we evaluate students’ understanding of mathematical methods and concepts as well as their command of specific skills? What new tools and strategies do we need? And what roles should teachers play in employing these tools and strategies?