By Michael Alison Chandler
Washington Post Staff Writer
Thursday, November 6, 2008
It might be difficult to remember a time when this question would give you pause: Which number is greater, 43 or 23? But a first-grade class at McNair Elementary School in Herndon one fall morning was batting about .500.
Behind the missed answers lay confusion about what "greater than" means and what the 4 in 43 is worth compared with the 3. Students struggled to justify their responses. So teacher Danielle Cimino called in a math coach, armed with two dozen baggies of counting blocks, to help.
As pressure mounts to prepare elementary students for high-stakes tests and for algebra in middle school, the focus on instilling math's most basic skills is intensifying. Many elementary schools are turning to math specialists or coaches to add expertise to a teaching workforce dominated by generalists who, studies show, are vastly under-prepared in math.
Elementary teachers often relish their reading lessons but lack the same confidence when it comes to math, experts say. Specialists attempt to fill the knowledge or enthusiasm gap by working with classroom teachers to improve skills. In some schools, they take over math instruction.
Incoming teachers typically don't think high-level math will add much to lessons on counting or shapes, said Beth Rodriguez, the McNair Elementary math coach. But once they start fielding questions about place value or fractions, she said, "they see they need to know it at a deeper level."
There are far fewer math specialists than reading specialists, but their ranks have grown over the past decade.
Arlington County and Alexandria have at least one part-time math specialist in every elementary school, and Fairfax County has more than 70 in elementary or middle schools. Montgomery County has "math content coaches" in about 50 elementary schools; Prince George's County has 20 coaches; and traditional D.C. public schools have 50. Many math specialists in the area work in high-poverty schools and are funded by the federal government. Other positions are paid for locally and subject to budget pressures.
Slim math requirements for new teachers add to the challenge. A study this year from the National Council on Teacher Quality found that entrance exams for teacher preparation programs typically test elementary or middle-grade math and set low pass rates. Elementary candidates are expected to take zero to six math courses, depending on the program.
Many teachers-in-training harbor bad math memories, said Jennifer Suh, an assistant professor of math education at George Mason University. Suh begins her classes "almost like a therapy session," she said, where she asks the aspiring teachers to talk about their math education. Some recalled suffering through work sheets or getting stuck in lower-level classes.
Math anxieties or dislikes "transcend when they are teaching," Suh said, so she tries to encourage a positive disposition before she reteaches early math lessons, emphasizing comprehension over memorization.
Mastery of calculus is not necessary to teach multiplication, but elementary teachers must understand enough algebra, geometry and probability to see how beginning skills link to more complex ones, educators say. To tackle abstract math in middle school -- a major goal for educators nationwide -- students should be comfortable with whole numbers and fractions. Many adults have trouble with the latter.
Deborah Loewenberg Ball, dean of the University of Michigan School of Education, said teachers need to understand math in a way it is rarely taught: going beyond rules and formulas and explaining why they work.
"People think that subtraction is simple," she said. But teaching it requires complex understanding. For example, students learn to "borrow" a 1 in some double-digit subtraction problems, but they might not know why or what the 1 represents. "A lot of kids are really confused," she said. "They think it's magic."
The challenge is finding the right word problem, diagram or explanation to help them understand.
Beefing up the math skills of 2 million elementary school teachers presents a "problem of huge scale," according to a recent report from the presidential National Mathematics Advisory Panel. A more practical solution, panelists suggested, could be to turn to math specialists.
Critics point to a lack of proven results in major studies. They cite the high cost of employing math specialists in addition to classroom teachers, as well as the practical challenges of finding enough qualified applicants.
Still, some school districts and states are taking an interest. In Virginia, the Board of Education recommended last year that one math specialist be required at elementary and middle schools for every 1,000 students. But the legislature rejected the proposal, which would have cost more than $20 million a year to implement.
The state is also among the first to develop a graduate program for math specialists, which is now offered at six state universities.
Rodriguez was one of the first to go through the program.
The 25-year teacher said that math was a "weakness" growing up and that she worried early in her career when she saw her students stumbling.
"I decided to take the leap and become a better math educator," she said. She enrolled in extra math courses at night and learned new teaching approaches through the Fairfax County school system. Eventually, she "wanted to teach math all day," she said.
When Rodriguez came to McNair this year as a fully certified math specialist, Cimino jumped at the chance to work with her. Math is not a weakness for Cimino -- she made it through calculus in high school -- but working with a specialist has helped her students go into more depth in lessons, she said.
Rodriguez and Cimino meet weekly to plan lessons and analyze student work. Twice a week, they co-teach. Cimino, a second-year teacher, said her students have made "huge gains" in the way they think and talk about math.
In one lesson on fractions, Rodriguez asked the students to take a paper and fold it in half. Some folded it vertically, some horizontally. She asked if there were other ways to make a half, and one student suggested making a half with triangles -- a step that impressed Cimino.
She credits the coach for pushing her students to go beyond "the standard, basic" responses. "If you don't ask, you won't see" what they can do, she said.
Staff writer Michael Alison Chandler is retaking second-year algebra at Fairfax High School to learn how schools are preparing more students for higher math. To follow her experience, visithttp://voices.washingtonpost.com/x-equals-why.