As economic, environmental and health challenges mount, the ability to solve problems is an increasingly valuable commodity. Where does our educational system build capacity to solve problems? How can proposed solutions be compared? How is progress on those problems determined? All involve understanding mathematics.

Unfortunately, from recent events, it is clear that few have that understanding.

If mathematics were understood, would the credit crisis have as readily occurred? How many Americans can do the math to understand that paying on credit often entails spending two or three times the original price?

If investors understood mathematics, would they have so readily believed that the returns on investments offered by Bernard Madoff and other con men were possible?

If citizens understood mathematics, would there be a Pennsylvania budget crisis? When a proposed tax increase was described as huge, a lot of people were adding 16 (the percentage increase) to the existing rate of less than 3 percent -- and concluding they would be taxed at close to 20 percent of their income! Understanding math means knowing that 16 percent of 3 percent is less than 1/2 percent, meaning the proposed tax would be 3 1/2 percent.

For too many of us, mathematics in school was something that only a few "got." And the misperception that "getting" math is genetic has been perpetuated in American classrooms by widespread grouping or tracking practices. Those perceived to have the gene (usually on the basis of one test or past success) get to advance to learning more mathematics, usually Algebra.

Some school districts group students as early as first grade. Whether earlier or later, those not in the "privileged" group come to believe that they cannot learn math, even as they are condemned to continue to "drill and kill," which does little to build understanding of mathematics.

A recent book by Jo Boaler, "What's Math Got to Do With It?" reports studies conducted in the United States and England that follow secondary students into further education or work. She compared students from schools with tracked traditional mathematics instruction to students from schools without tracking. In the nontracked schools, all students work together to solve problems that apply mathematics in the many ways it is actually used in our world. Regardless of income level, ethnicity or previous achievement levels, the students from the school with the broadened vision of mathematics had dramatically better outcomes in education and employment than those confined to traditional tracked mathematics instruction.

If all students benefit from broader math experiences, why does the "shopping mall" high school offer different mathematics courses for different groups of students? Ms. Boaler's research shows students at the top and the bottom of the learning curve both benefit from learning mathematics together, using the broadened vision of mathematics.

Our misunderstanding of math has more to do with how mathematics is taught than the ability to learn it.

Unfortunately, it is true that much of the mathematics encountered in many schools is not connected to anything that matters in real life. Most class and homework time involves pages of problems featuring numbers taken out of any context. These numbers are repeatedly manipulated according to the one procedure featured in class that day -- with little reference to what the numbers actually represent. An international video study of U.S. classrooms revealed the familiar teacher refrain in eighth grade, "When you get to No. 23, you'll have to think ... " One wonders why the first 22 problems were assigned.

"Word problems" are traditionally the dreaded part of the unit -- and are often seen as a topic separate from mathematics because for many, math involves only "naked numbers." The content of typical word problems is too often irrelevant. Who really cares when the train leaving Chicago will pass the train leaving Cleveland?

Jo Boaler compares traditional mathematics instruction to spending years learning to write musical notes on paper without ever getting to hear the music actually played. Very few Americans ever get to the point in studying mathematics where they "hear the music." Most never develop understanding of the many ways math is applied in the world.

Mathematics instruction must move beyond the rigid, narrow approach that has not produced understanding. "How People Learn" research makes clear what works: building on prior knowledge, making explicit connections among ideas and encouraging multiple solution strategies. Brain research has proven that visualizing mathematical relationships as networks, drawings or graphs helps create understanding.

In 2003, the Math & Science Collaborative, based at the Allegheny Intermediate Unit, successfully competed to bring $21 million of federal Math Science Partnership funding to southwestern Pennsylvania to strengthen the teaching and learning of mathematics and science. Over the past six years, more than 700 teacher leaders have been prepared to share these research-based strategies with their colleagues in 53 districts. External evaluators are finding evidence that the necessary changes in instruction are emerging.

It is clear that one of the greatest challenges is "to teach differently than you were taught." Teachers need time to learn new approaches and to work together to continually refine their practices. "Teacher leaders" need to participate in regional professional learning communities that enable them to share the latest tools and resources with district colleagues. One-day, one-time experiences are not enough. The need for on-going, focused learning is not a "fad" that will run its course.

Over the past six years, 60 percent of the district and building-level leaders of those districts involved in the Math Science Partnership has changed. As personnel changes or budget concerns arise, recognition of the key value added by sustained professional learning is too often lost.

It is important for southwestern Pennsylvania to insist on support for the ongoing teacher learning that effective teaching of mathematics requires. Teacher leaders in all regional districts can access such learning in their local intermediate units in the 2009-2010 school year.

Are teachers in your school district learning how to help all students "get" math? If your teachers are not learning how to teach mathematics effectively, it is highly unlikely that their students are learning the mathematics that the region will need to navigate the 21st century.

Understanding mathematics matters!