Teaching math has suddenly become harder in Arizona.
Drills, formulas and rote memorization don't cut it in an age when all high-school students in the state are required to pass four years of math to graduate -- and soon will be required to explain answers essay-style on a new math assessment test.
On a recent morning at Dobson High School in Mesa, math department Chairwoman Kelly Berg taught pre-calculus students how to find the maximum area of a rectangular field. But she didn't just stand at the board scribbling equations.
Instead, Berg brought in foam boards and small colored tiles to represent "fencing" and asked students to create "play areas" for children out of it.
"I have the students create several different play pens, find the areas and then write equations," said Berg, who has been teaching math for 18 years.
In other classes this year, Berg brought in stackable plastic cups to help students better understand concepts like slope and rate of change.
It's harder to teach this way, and the pre-class preparation often requires extra hours at night and on weekends.
But Berg and other high-school educators hope their new teaching strategies will help their students get through the four years of math now required by the Arizona State Board of Education -- and, a few years from now, pass a more difficult state assessment that will replace Arizona's Instrument to Measure Standards, known as the AIMS test.
The Class of 2013 is the first to have to get through Algebra I, geometry, Algebra II and a fourth class such as calculus, pre-calculus, or business math and statistics.
"It's not enough anymore to do rote calculations and learn formulas," said Suzan DePrez, assistant superintendent for curriculum and instruction at Mesa Public Schools.
Mesa, Phoenix Union, Chandler Unified, Scottsdale Unified, Dysart Unified and J.O. Combs Unified are among the school districts turning to consultants to help teachers develop more creative ways to help students understand the more abstract concepts in classes like Algebra II.
Mesa's Red Mountain High School, for instance, has partnered with Marilyn Carlson, an Arizona State University mathematics professor and director of ASU's Research Innovations in Mathematics and Science Education program.
Carlson's program has received a five-year, $12.5 million grant from the National Science Foundation to research and develop improved high-school pre-calculus instruction.
Carlson, who also works with schools in Chandler, Scottsdale and southern Arizona's Vail Unified School District, believes that all high-school students -- even those not headed for a college or university -- can understand and pass high-school calculus. The challenge, she said, is to get the students to clearly understand concepts like proportion, slope and constant rate of change in earlier algebra classes.
Such concepts are important not just for future doctors or engineers but also for students who need a clear understanding of measurements when they work as roofers and nursing assistants, Carlson noted.
"What does it mean to be going 60 miles per hour?" Carlson asked five Red Mountain Algebra II teachers at a recent morning-long workshop aimed at making their teaching more hands-on and practical. "Or if I walk 3 feet in two seconds, how many seconds will it take me to walk 6 feet?"
The teachers then worked on lesson plans that would help them teach their students how to write and graph equations to show the rate of change for Carlson's walk.
Later in the day, Ron Skinner, a Red Mountain Algebra II and Honors Geometry teacher with 20 years of experience, further applied the new teaching method in a class where he had students size photographs, chart the photos' new dimensions on a graph and explain their methods to the class.
Skinner acknowledged that teaching in this manner is far more difficult for him and his students. Even some of his top performers get frustrated at times and ask him to just give them formulas to memorize.
"My most advanced students were the ones that struggled the most at the beginning," he said. "They had a lot of resistance to not just memorizing procedures."
He and other teachers hope their efforts will yield results as current algebra students make it through all four years of math, including calculus.
Starting in the 2014-15 school year, Arizona's statewide math assessment also will become more difficult. In some sections of the test, students will be asked to explain answers to math questions essay-style.
PARCC -- for Partnership for Assessment of Readiness for College and Careers -- will replace the current AIMS test.
No multiple-choice answers to the final section are offered.
"Students are going to have to have a much deeper understanding of math to pass this assessment," said DePrez, the Mesa assistant superintendent.
Some educators believe that the best way to get all high-school students to pass four years of math is to make sure elementary-school math students do more than just memorize arithmetic facts and formulas.
"People who do really well in math tend to be people who memorize very well," said Susan Larson, a senior lecturer at ASU's Mary Lou Fulton Teachers College.
"The problem is your brain tends to dump things that you have memorized that aren't all that useful to you."
Arizona has a shortage of math teachers with the skills to help students navigate the state's tough new academic requirements.
A check with school districts of varying sizes around the state -- from the remote Yuma Union High School District to large districts in Phoenix and Mesa -- showed that many districts are struggling to find teachers who are qualified to teach upper-level math classes like Algebra II and calculus.
Data from the Arizona Department of Education shows that 1.5 percent of high-school math classes and 3 percent of junior high math classes are taught by teachers who are "non-highly qualified," or who lack formal certificates to teach math in junior or senior highs or at the college level.
The Phoenix Union High School District scrambled to find applicants for more than 30 math openings before the start of the school year, said district spokesman Craig Pletenik.
It signed on 24 with perks like an additional eight years of experience on the district salary schedule, but is still seeking to fill seven positions that are temporarily filled by substitutes or teachers who take on extra classes, Pletenik said.
Mesa Public Schools, meanwhile, had to fill 52 math openings in junior and senior highs and is still looking for four additional teachers, said Pete Lesar, Mesa's assistant superintendent for human resources.
"We emphasize to them that we offer a competitive salary and benefits package and a support system that will enhance their professional development," Lesar said.
Jaron Hopkins (left) and Jared Wheaton work on solving a problem in their pre-calculus class at Dobson High School in Mesa.
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