They train in classrooms with pencils and calculators.

And all their preparation paid off.

Three of the public charter school's students will represent Arizona at the Lockheed Martin MathCounts National Competition in Denver in May.

At the state MathCounts competition, held March 1 at Vail's Cienega High School, eighth-grader Richard Spence finished in second place, followed by classmates Langston Harris, who finished third, and Joshua Sloane, who secured the final qualifying spot by finishing in fourth place.

Sixth-grader Peter Bian also competed for Sonoran Science Academy.

Richard, eighth-grader Langston and seventh-grader Joshua — along with the first-place winner, who is from the Phoenix area — will be among the 228 students competing in the national event.

"Our success is not an accident," said Kadir Bahar, the school's high school math teacher and the MathCounts coach. "We have studied for this competition for seven months. I meet with these smart kids every day and on the weekend. We studied really hard."

"They don't do anything past eighth-grade level (math), but they make it confusing," Richard said about the MathCounts competitions.

Sonoran Science Academy's training regimen leading up to the competition involved after-school practice three times a week and practice on Saturdays.

In addition to Bahar, professors from the California Institute of Technology and Arizona State University also help the students.

Then there's the students' sheer talent.

Richard, 14, and Joshua, 12, both said their parents have something to do with their natural aptitude for math.

"My parents pushed me to higher-level math classes, so when I was in fourth grade, I was doing sixth-grade (math)," Richard said. "When I was in fifth grade, I was doing eighth-grade (math)."

All the students have reasons for their attraction to math.

"Math is so bizarre and mystical, but at least math is almost always 100 percent definable," Langston said. "Well, more like 99.99 percent definable, because there are some things that you can't really do. Like, for example, division by zero. But other than that, unless there is something wrong with the problem or question, then you can always find (the answer) out."

All three say that for them, the subject is not confined to the classroom, and there is always something more to learn.

"Whatever math you are at, there is always something else to go see," Joshua said.

Richard and Langston won't be able to compete in MathCounts in the next school year because the contest is only for middle school students, but they will continue to train for the American Mathematics Competitions, and if they perform well enough, the American Invitational Mathematics Examination.

Richard competed in last year's national MathCounts contest and finished in 120th place.

"This year I should be top 60 or 70," he said.

This year's competition will fall on the same day as the National School Scrabble Championship, but Richard opted for math problems, not wooden squares.

He participates in the school's Scrabble Club and plays on the Internet.

"I'm good with words," he said. "And Scrabble has some math in it. Just arithmetic."

Joshua and Langston also are avid video-game players.

But when it comes down to it, their activity of choice is math.