The first-graders at Willard Elementary have many ways to show what the number five looks like.

You can have three circles, plus two more circles. You can have three girls and two boys. You can even have two fingers, one nose, and two more fingers.

It all adds up to five.

"They have to come up with their own strategies," said teacher Kim Benton. "It really encourages them to use higher-level thinking."

Just 58 percent of Willard's third-graders scored proficient or advanced on the 2006 Proficiency Assessment for Wyoming Students. More than 95 percent of third-graders met the same benchmark in 2008.

Willard uses Everyday Math, a standards-based curriculum focused on conceptual understanding and reasoning. Students are encouraged to solve problems however they want, which can include counting a nose, drawing pictures or using numbers.

"We play a lot of learning games," Benton said. "They're interacting and talking with their friends. They're really engaged with it."

Principal Leslie Madden said the curriculum challenges students and holds them accountable for their learning. And students are learning they can solve a math problem in more than one way.

Willard used Saxon Math until last year, when the school made the switch to Everyday Math, Madden said.

"What we liked was the high level of student accountability, and the major push for problem solving and creative problem solving," Madden said.

Willard is not alone in its increasing success with math scores. The number of students who met proficient and advanced benchmarks on the math portion of the 2008 PAWS increased at several Natrona County elementary schools.

At Pineview Elementary, Principal Chris Carruth attributed the improved scores to a combination of curriculum application by the teachers, goal-setting by the students and communication with parents about assessments.

The school uses Bridges Math, another standards-based curriculum that encourages a variety of ways to solve math problems. Having a full-time math tutor has also helped identify students in danger of falling behind.

Only 37 percent of Pineview third-graders scored proficient or advanced on the 2006 PAWS. The number jumped to 72 percent in 2008.

"This is a community effort to get these kids to do well," Carruth said.

In 1989, the National Council for Teachers of Mathematics released the first of four reports focusing on development of standards-based mathematics curricula.

Many states and school districts have since moved toward math curricula focused on conceptual learning and creativity in problem solving.

Since the first report, research done by the council indicates math scores on the National Assessment of Education Progress, or NAEP, have steadily and significantly improved for white, Hispanic and African-American students.

Natrona County School District adopted a variety of standards-based math curriculums back in 2006, said Mike Bond, executive director of curriculum and instruction.

The decision to move away from traditional math instruction was done in part because of the teacher support new curricula offer, as well as research showing how to effectively teach math, he said.

"There's more than one way of helping students to learn math," Bond said. "It doesn't always have to be a numerical equation."

The shift in math education is something Tom Rodabaugh, a former math teacher and the principal of Mountain View Elementary, is excited about.

"In the past, we would have used more computation and skills," Rodabaugh said. "Now it's much broader. We'll look at problem solving, data analysis, geometry, number sentences …"

Just 17 percent of fifth-graders at Mountain View tested proficient or advanced on the 2006 PAWS. In 2008, 52 percent of students met the same benchmark.

Standards-based curricula require students to learn how and why they come to answers on math problems, Rodabaugh said. Mountain View uses a standards-based curriculum called Math Trailblazers, which combines math, science and language arts.

"As a secondary teacher, I would just be saying, 'Holy cow, this is so much better,'" Rodabaugh said. "It's a move away from saying seven times six is 42. They have to understand why seven times six is 42."

Reach education reporter Jasa Santos at (307) 266-0593 or at Jasa.Santos@trib.com.