Integrated math in the mix at high schools

The shift to Common Core is still rolling in at most high schools, with teens caught midstride in the traditional algebra-geometry path allowed to finish their journey, while incoming classes start the integrated math 1, 2, 3 progression.

What changed was not so much the math as the method. Students taught with the essentially Socratic method of Common Core math appear to have more confident student discussions, and veteran teachers say they see a better grasp of math concepts.

“It’s a lot less intimidating. It’s more about developing strategies, so if you don’t know how to solve a problem, if you have some tools in your bag you can find a way to solve it,” said Christina Rubalcava, a math teacher and teacher coach at Enochs High in Modesto.

Moreover, the integrated math series keeps bringing back earlier skills so they stay fresh, and foreshadowing next year’s lessons so the progression makes sense.

“Once students got to advanced algebra, I find they’re not retaining those algebra I skills. They treat geometry like a year off from algebra,” Rubalcava said. “But algebra and geometry are not two standalone subjects. They’re interrelated.”

Modesto City Schools had a pilot Common Core math 1 course three years ago, but districtwide launched the change at the last year possible in California, 2014-15. Ceres Unified shifted early to Common Core-style instruction, but only started integrated math courses last year. High schools in the sprawling Merced Union High School District kick-started the shift five years ago.

A better grasp of math matters to turn around dismal math readiness figures. In 2015, only about 1 in 5 high school juniors in Stanislaus and Merced counties tested at grade level in math. Nationally, more than half of students entering community college and 20 percent of freshmen at four-year universities needed remedial courses, notes a 2012 report by Complete College America.

Algebra is the pivot point in high school math – kids either get it and sail forward, or struggle and flail.

Under the old bubble tests, last taken in 2013, algebra was tested separately. Combining results from Merced and Stanislaus counties shows top students, roughly 6 percent of the class, took algebra in seventh grade and most passed. Other students did not fare as well, with about 1 in 5 students still trying, and most failing, to pass algebra as high school juniors.

It was the brick wall thousands of their students hit at algebra that brought Modesto City Schools to pilot several classes of integrated math 1 in 2013-14 with students taking a second stab at algebra. Rubalcava was one of those teachers, and has taught that first class for three years running. As seniors, those students are in what Modesto calls secondary math 3, the replacement for algebra II.

“They’re doing trigonometry, which they would never have been exposed to if they had repeated algebra I as sophomores,” she said. That first year changed their minds about math, parents told her. “Not only were their scores higher in algebra, for many of them it was the first time they actually enjoyed coming to math class,” Rubalcava said.

The switch from memorizing steps in a process came easy to teens who did not learn well that way, she said. But many students who excelled under the old style of math teaching – “Here’s the formula, plug in the numbers” – have struggled with the new and somewhat nebulous demand to explain their process.

“I never know what the right answer is,” admitted one straight-A high school student. Asked if she understood the concepts better under the Common Core method, she simply shrugged and said the process is much harder.

The ramp-up to calculus for high achievers has been the last piece in place for most districts. A year spent in pre-calculus stands between the end of standard integrated math 3 and the AP calculus course parents see as critical for entry to top-tier universities or math-heavy majors.

Modesto has wrapped early calculus skills into the third year of their pre-AP secondary math series.

Merced Union high schools are taking a different approach, condensing integrated math 1-3 into a two-year program for high achievers, said Albert Gonzalez, an associate principal at El Capitan High. Gonzalez helped with the district’s teacher-led switch to Common Core that started in 2011-12.

“Teachers who were interested met as a team and looked at current math standards for algebra, geometry and algebra II, and for Common Core, seeing how they were different,” Gonzalez said. The volunteer team included math teachers from all the district’s high schools, weighing the pros and cons of both systems.

“The decision was to go ahead and go with integrated pathway,” he said, with teachers developing materials to teach the more interactive, Common Core way, while covering the old standards teens would still face on state tests. Changing classes to Common Core was also voluntary, with students and parents notified, and rolled out differently at every campus.

“The content is very similar. Integrated math I covered mostly algebra standards anyway, but also introduced geometry. It’s more the way it is taught and the way assessments are done, with computers, (that’s different),” Gonzalez said. California tests using the Smarter Balanced computer-adapted system.

“What we tended to find through students enrolled in courses doing the integrated trials, was all year they answered open-ended questions, so as soon as we went to Smarter Balanced, they felt a lot more comfortable than the ones that weren’t,” he said.

That said, the first Smarter Balanced math scores districtwide were still lower than teachers had hoped, with 20 percent of Merced Union juniors testing at or above grade level. Most juniors would still have been taking the traditional algebra II course.

Gonzalez said the unfamiliar testing software threw even tech-savvy students for a loop. “Once they’ve had more experience with it, we’ll see the scores go up,” he predicted.

By the numbers, Modesto City Schools and Ceres Unified students scored about the same as the Merced group in math. This is Modesto’s second year of using integrated math. Like other districts, Modesto’s high schoolers already in the algebra-geometry-algebra II pipeline will finish up in the old sequence.

In an Enochs High demonstration lesson, Carolyn Viss of the the Stanislaus County Office of Education led students in the first level of Common Core integrated math through rotating an irregular shape on an x-y axis. The exercise covered some geometry, a little trigonometry and algebra.

At each step, Viss asked students to think it through and discuss their findings in pairs while a half-dozen Enochs teachers looked on with clipboards. The first-year students kept their heads down and said little. Only one student spoke of geometric concepts she could articulate with confidence.

“The shift is falling most heavily on this group of students,” Viss said.

“Growing pains. The growing pains of this year, because we have to get used to it,” said Randy Rubio, the regular Enochs class teacher. Even so, he said, he prefers integrated math to what he taught before.

In Ceres Unified, students with years of pair-sharing ideas and answering open-ended questions under their belts, were more talkative.

Central Valley High students in integrated math 1 and 2 courses either said they liked the Common Core courses better or seemed stumped by the question – algebra or geometry were courses their older siblings might have taken.

“It’s easy. The old way, it was too slow,” said Estevan Barragan.

“I like it better,” said Nasson Sanchez, “It involves a lot more writing – which is good. It helps us out with writing skills, too.”

For Jaime Morales, working together just makes more sense. “If you don’t understand, you can see how other people did it and understand a little more,” he said.

“We pay attention more. she goes at a faster pace,” said freshman Iran Torres as teacher Susanna Kandeel led the students through some hits and misses for that day’s lesson.

“I think we learn from the mistakes she shows us, so we know not to make them,” Torres added.

For her part, Kandeel said she sees real differences in how students grasp the reasoning behind the formulas.

“They’re able to express the content. There’s more of the concepts and not just can you do the skill. It’s a lot better than in my algebra days,” she said.

Central Valley math teacher Erica Guevara said she sees students who traditionally struggled in math doing better with the hands-on Common Core problems.

“Today it’s more about conceptual understanding, not so much computational,” she said.

“We didn’t do as many word problems before,” said Paul Rutishauser, Central Valley associate principal. “Now they have to hold a skill and a concept and apply it. They have to really use it.”

This story was originally published March 17, 2016 at 2:05 PM with the headline "Integrated math in the mix at high schools."