Math student works the angles
For decades, generations of Americans took the same basic high school math track. Algebra. Geometry. Algebra 2.
Now, school districts across the country are overhauling their approach, combining geometry, algebra, statistics and other math concepts into a catch-all subject called integrated math.
Experts say the change is supposed to help students understand math on a deeper level and improve their ability to apply math concepts in the real world. While the switch is not required, many local school districts have adopted the changes as part of their transition to Common Core State Standards.
“The kind of arithmetic skills that were valued when I was a boy, the ability to add numbers quickly in your head, are not as valued any more,” said Tom Sallee, a UC Davis math professor emeritus. “The skills that are needed are understanding core issues so you can program a computer or (create) a spreadsheet.”
San Juan and Elk Grove unified school districts began phasing in Integrated Math 1 in high schools last fall. Folsom Cordova and Sacramento City unified school districts started a year earlier.
This year, most freshmen in the San Juan Unified School District enrolled in Integrated Math 1, a blend of algebra, geometry, data and statistics. In the next two years, sophomores and juniors can opt for Integrated Math 2 and 3. Each will offer progressively deeper dives into many of those same topics, and, combined, those courses will help satisfy the entry requirements for the University of California.
At Sacramento City Unified, interim Chief Academic Officer Iris Taylor gives the example of a student who one day will tackle a building construction project and must calculate costs based on design, architecture, scope, labor and materials. The geometry may come into the design and the algebra will play into the costs, she said.
But some parents say it’s been a big headache and fear their kids are being used as guinea pigs.
“My son loves math,” said Laurel Dalton, the mother of a freshman at Rio Americano High School in Sacramento County. “He always has. He can’t stand math now. He’s very frustrated.”
Dalton thinks this cohort of high school students wasn’t prepared to handle the switch.
“I’m not opposed to looking for new curriculum for our schools and 21st-century thinking, because I know the world is evolving,” she said. “I’m not against integrated math. It sounds good. But why did we decide to throw this freshman class into the change when they have been doing math the same way through eighth grade?”
She said her son excelled at math in the eighth grade and helped tutor classmates. But his transition to Integrated Math 1 was tougher than expected. He passed in the first semester last fall, she said, “and we’re hopeful he’ll get a C or better this semester. But it’s been difficult.” In all other classes, she said, he is receiving A’s and B’s.
She said some parents are hiring tutors, but that’s not a solution for those who can’t afford it.
She said even some of the good teachers are struggling to figure out how to teach the blended subjects when they have a track record in algebra or geometry but not both.
San Juan spokesman Trent Allen said district officials agree with Dalton on that point. “Our teachers are also going through a transition period and we’re working to support them,” he said.
District officials are offering an eight-day program in early August to help the next group of incoming freshmen. Those who failed integrated math can take courses this summer to help them get passing grades.
Students, if they choose, also can take support classes for each year of integrated math to boost performance.
“I think for some students, the data shows, yeah, it was tougher,” said Rick Messer, assistant superintendent of secondary education for San Juan. The recognition that some students were struggling out of the gate in their freshman year made it imperative to help incoming students stay on track for graduation, he said.
“I think we learned from this year,” Messer said. “But we’re continuing to adjust to make sure we’re providing resources for students.”
My son loves math. He always has. He can’t stand math now. He’s very frustrated.
Laurel Dalton, mother of freshman at Rio Americano High School
At San Juan Unified, about 40 percent of the freshmen recorded D’s or F’s in Integrated Math 1 in the latest fall semester. That was only slightly worse than the 39 percent fail rate in fall 2014, when the majority of freshmen students took some level of Algebra 1, according to district data.
Sallee, the UC Davis professor, said he supports the shift to a more effective approach to math problem-solving, which integrated math is designed to accomplish.
The question is whether students can use what they know to solve a kind of problem they’ve never seen before, said Sallee, paraphrasing the author of “The Psychology of Learning Mathematics,” Richard Skemp. Sallee said that’s what integrated programs are trying to foster.
The United States is about the only country in the world, that I know of, that divides math understanding into these silos.
Tom Sallee, professor emeritus of math at UC Davis
“The United States is about the only country in the world, that I know of, that divides math understanding into these silos,” Sallee said. “Integrated is trying to break those silos.”
At Mesa Verde High School in Citrus Heights, students in Leslie Peoples’ Integrated Math 1 class last month worked on a problem that required them to use algebra and geometry skills to calculate angles.
Problem solving didn’t finish the task. Students then had to explain the logic behind their solutions in keeping with Common Core State Standards, which pushes students away from rote learning and toward a deeper understanding of the subject.
Christian Matutis, a 15-year-old freshman, said he likes the challenge. “We actually have to think. We have to get together and solve equations and problems that aren’t really simple. We’ve got to use our brains much more.”
But freshman Hayley Weber, also 15, said after two semesters of integrated math, she preferred her eighth-grade math class, which focused on algebra and was easier to understand. There are some easy elements in integrated math problems, she said. And there were times when problem solving was hard to explain.
“All I knew was the answer, and I knew how to do it in my head. I just couldn’t explain it very well,” Weber said.
Math problem answer
Angle 1 is 70 degrees, Angle 2 is 110 degrees and Angle 3 is 50 degrees