Senator Eliot Shapleigh - El Paso, Texas

Melissa Eastman really got fractions for the first time this summer -- eight years after she began teaching kindergarten.

She knew that one-half is greater than one-fourth, and that one-fourth is greater than one-eighth. But why was less clear. It didn't seem logical that fractions got smaller as the numbers got larger.

During a math workshop for Mansfield school district teachers, it finally clicked. The teachers cut paper into smaller and smaller pieces to show how fractions make up the whole.

"I remember my dad sitting down with me and trying to make it make sense, but it didn't," said Eastman, who teaches at Anderson Elementary School. "I needed it explained to me in a different way."

Experts say it's common for elementary school teachers like Eastman to struggle in math.

Trained as generalists, elementary education majors typically take one or two core math classes in college and one on how to teach math. That's in addition to classes that prepare them to teach reading, social studies, science and even art in some cases. The weakness in math has become more acute in recent years as the state and federal governments have looked harder at standardized-test scores.

"If you don't have a strong foundation, then there are going to be a lot of holes that start to form" in a young student's learning, said Kathy Smith, an assistant education professor at Texas Christian University who also trains public school teachers in math methods. "That's where the idea of whole numbers and fractions and addition and subtraction start. If you don't teach them correctly, you can turn a child's world upside down."

Math scores on the Texas Assessment of Knowledge and Skills are telling.

In 2005-06, 90 percent of Texas third-graders passed their first attempt of the reading test compared with 83 percent who passed the math portion.

Among ninth-graders, the gap was even bigger, with 88 percent passing the reading tests but only 58 percent passing math. Among 10th-graders 86 percent passed reading, and 62 percent passed math.

Problem solving

The learning gap is being attacked on two fronts: through intensive undergraduate courses and through math specialists hired to coach teachers and students in individual schools, similar to the specialists districts have hired in recent years to beef up reading scores.

For the past four years, TCU has required education majors to take two in-depth classes on teaching math rather than one. Next year, all TCU education majors will also be required to take calculus.

Amanda Owens and Betsy Lujan, both 20, worked with classmates in one of Smith's recent TCU math methods classes to multiply 13 by 16.

First, they used wooden blocks to build rows and columns on a grid illustrating the product, 208.

Then they taught each other the FOIL method, which stands for "first, outside, inside and last."

They multiplied the "first" numbers, 10 times 10. Then the "outside" numbers, 10 times six; then the "inside" numbers, three times 10; and the "last" numbers, three times six. That led to the equation 100+60+30+18, which equals 208.

"Before this class, I was extremely scared to teach math. I was so bad in math when I was younger," said Lujan, a junior. "Now, when she goes deep into it, I'm like, 'Oh, now I get it.'"

Southern Methodist University recently began offering a master math teacher program for elementary teachers who want an additional certification offered through the state. The yearlong program includes rigorous course work in mathematical reasoning, geometry and measurement and data analysis.

The certification has been available since 2001, but so far only 35 teachers statewide have earned it.

Mansfield teacher Christi Crafton said there's little incentive to seek the certification.

Crafton, an educator since 1978, received her master math teacher certificate in July. Her tuition for SMU's program was paid with a state grant; otherwise, Crafton said she probably would not have been able to come up with the almost $4,000 cost.

School districts typically do not pay extra stipends for the certification unless the teacher also obtains a master's degree.

"It's time-consuming, difficult and costly if they have to pay for the additional training themselves," she said.

Specialized help

Crafton is now a math specialist at Nash Elementary School. She works with other teachers to make sure they understand in-depth how to do problems and work with struggling students.

Indiana, Massachusetts and Virginia are leading the nation in putting such specialists to work, said Francis "Skip" Fennell, president of the National Council of Teachers of Mathematics in Reston, Va.

Texas' new four-year math requirement for advanced high school diplomas could put the state on track toward hiring more specialists soon, he said.

The Birdville school district is experimenting with math specialists this year at 10 elementary campuses. The specialists divide their time among schools and focus on specific problem areas with small groups of students and teachers.

Birdville's specialists must have at least four years' teaching experience and extensive math backgrounds, said Caren Sorrells, math consultant for the district. Some are former high school math teachers; one is a retired math coordinator from the district. They excel in interactive, research-based exercises, she said.

The district saw increases in TAKS passing rates from 2004-05 to 2005-06 in almost all grades, although the third-grade passing rate dropped to 80 percent from 85 percent.

"We tried several things and have seen some successes, but we need more," Sorrells said.

The specialists are paid on a teacher scale, but their salaries come from funds designated for struggling schools, such as federal Title I grants and state funds for poor schools. If the district expands the program to all of its 21 elementary campuses, as officials hope, extra money will be needed. Sorrells said the cost is worth it.

"I can't believe the difference we saw even in just two weeks," she said, noting that some students who struggled before working with specialists were starting to pass, and even excel on, math tests and quizzes.

Other districts, including Mansfield, are focused on retraining elementary teachers.

Those lessons have already made a huge difference, Eastman said.

Before her summer session, Eastman would ask a student to solve a problem, and once satisfied, she would move on to the next question.

Now, she said, she takes time to ask how the student got the answer and whether anyone else arrived at the same answer in a different way.

"If we're doing a counting jar, one student may use 12 tally marks to get the answer," she said. "Another one may just write 12 and another may write 10+2.

"American teachers have taught an inch thick and a mile wide," she said. "But we need to teach a mile thick and an inch wide so they develop deep understandings and critical thinking skills."