Add It Up: Math Matters

Monday, September 1, 2008

How Is Math Taught?

From arithmetic to algebra and beyond, mathematics absorbs a huge amount of class time. Students are pushed to learn more math than ever, and sooner. Today, staff writer Daniel de Vise gives an overview of math education issues. Look for more on math in coming weeks from Washington Post education reporters.

Parents who walk into an elementary classroom might not recognize a mathematics lesson. Children are likely out of their seats, clustered in boisterous groups, flipping coins or arranging colored tiles. The exercise could be part science experiment, part history lesson, part story time.

Nowadays, hands-on learning is popular. Why ask kids to multiply 6 by 3 with pencil and paper at their desks, teachers ask, when you can use three plates of six doughnuts each?

Math programs in Maryland, the District and Virginia run the gamut from more structured, textbook-driven lessons that stress computation to relatively open-ended, exploratory curricula that urge students to solve problems in their own way. School officials contend that all the programs eventually teach the "right" ways to add, subtract, multiply and divide, although some mathematicians say otherwise.

But many teachers consider computation skills the end, not the beginning, of the lesson. Problems are culled from the everyday: If Courtney had 10 brownies, gave 2 to Allison and swiped 5 from Eva, how many does she have now?

"Math is something you can have a lot of fun with," said Heather Wilhelm Menon, an award-winning second-grade teacher at Westgate Elementary School in Falls Church. "The kids are engaged almost all of the time throughout the math period. I don't even want to say period, because I teach math all day."

Math instruction in middle and high school has become a race toward calculus. Algebra is now increasingly taken in the eighth grade. Practical courses, like consumer math, have made way for the time-honored sequence of "pure" math: algebra, geometry, Algebra II, pre-calculus and calculus. Students often go further in math today than their parents did, although some mathematicians say even high-level math courses are watered down.

How Much Math Is Taught?

Arguably, too much. It's a common complaint that math lessons are a mile wide and an inch deep. State and local math "standards" are swollen with dozens of skills to be mastered each year under the federal No Child Left Behind law, which put math instruction into overdrive six years ago. Textbooks have ballooned to 700 and 800 pages, striving to include every last standard from every major state.

A recent Washington Post analysis found that Virginia listed 41 "learning expectations" for fourth-graders in its Standards of Learning; Maryland listed 67 in its tests; the District, 45.

Much of the math community thinks that the lack of order and priority in standards is part of the reason U.S. students trail those in Singapore and other nations on global math tests. The National Council of Teachers of Mathematics tried to set things right in 2006 with Curriculum Focal Points, which spells out three concepts for each grade and a few key subjects, such as the base-10 number system, fractions and algebra, at the core of lessons in math-savvy nations. In fourth grade, Focal Points lists these skills: multiplying and dividing, working with decimals and analyzing two-dimensional shapes.

A key audience is elementary teachers, who tend to be the least experienced in math and might not know which of the 50 "standards" are really important. "Now, it doesn't mean you only do three things in the year," said Henry "Hank" Kepner, president of the national council. "We're saying: 'Here are three things that should occupy a huge chunk of time. By the time they leave here, they should really nail down whatever it is.' "

Virginia and Maryland leaders said they would incorporate the document into their standards, up for revision in both states over the next year. D.C. officials said they would try to provide greater clarity to teachers about what to teach and when.

What's the Fuss Over Math?

For decades, educators have debated mathematicians over the primacy of content (what gets taught) vs. pedagogy (how math gets taught). Mathematicians tend to believe content should drive instruction: Decide what concepts should be taught and in what order, and then build a curriculum. Many educators believe pedagogical concerns should come first: Build a lesson plan that teaches concepts in ways students are most likely to understand them.

Mathematicians contend that some programs are too light on content and too heavy on fun and games. Parents occasionally join in the criticism. Teach Math Right in Prince William County is a group opposed to the progressive "Investigations" textbook used in public schools there.

"Everybody who knows math says these programs aren't worth much," said W. Stephen Wilson, a math professor at Johns Hopkins University. "And then these school districts pick them and use them."

Some educators say that math purists shouldn't lose sight of the ultimate goal -- student learning. Mathematicians generally aren't third-grade teachers. Children don't necessarily gain much by memorizing the times table and solving number problems if they cannot relate the skills to everyday life, these educators contend, a concept reflected in the "Everyday Mathematics" textbook.

The purists may be gaining influence, through a report this year from a presidential advisory panel and other developments. But mathematicians and educators agree on many key matters, including the need for more specialized math teachers and the importance of simplifying and prioritizing what is taught.

When Should Kids Learn Algebra?

Introductory algebra has emerged as a beacon of math education. Crucial to advanced study, Algebra I is coming to be viewed as the most important math class a student will take.

So why wait until high school? School systems nationwide are pushing more students into Algebra I by eighth grade, if not sooner, to open opportunities in high school and college.

California and Minnesota will soon require all students to take the course in the eighth grade. Montgomery County schools want 80 percent of students to take Algebra I in middle school by 2010. In Fairfax County, 29 percent of elementary students are on pace to take Algebra I in the seventh grade.

Math acceleration begins as early as kindergarten in some D.C. suburbs. The goal is to reach Algebra I, considered a gateway to success on the SAT and in the Advanced Placement courses. Algebraic concepts such as the polynomial -- an expression built from numbers and variables -- form the basis for more advanced study in math and science.

There is a downside. Some parents think children are being pushed too far, too fast. Casualties of math acceleration are keeping tutors in business across the Washington region. And some algebra teachers inevitably water down the course to ensure that students pass. That is one risk of quotas and mandates, such as the one California Gov. Arnold Schwarzenegger (R) championed.

"What this means is that, in the end, no kid will take algebra," said Stanford mathematician R. James Milgram, who has written algebra texts. "They will take a course that is only called 'alge bra.' "

Math Books: A Sampling

The elementary math program a school system chooses influences classroom lessons. Some texts are identified with the progressive education movement; others have a more traditional approach. Many systems use both types of books, varying by grade level or school.

"Everyday Mathematics" -- in the District, Montgomery and Fairfax counties and Alexandria. It links math and life experience.

"Investigations in Number, Data, and Space"-- in Prince William, Loudoun, Arlington, Charles and St. Mary's counties. It uses games and activities to convey concepts.

"Harcourt Math" and "Think Math!"-- in Montgomery, Howard and Calvert counties. These comparatively traditional texts focus on mastery and retention of key skills.

"Scott Foresman-Addison Wesley Mathematics"-- in Fairfax, Prince George's, Loudoun and Charles counties. It focuses on key ideas and step-by-step instruction.