Long a staple of the high school curriculum, the mathematics-course sequence of Algebra 1, geometry, and Algebra 2 is facing a budding challenge as schools transition to the Common Core State Standards.
Students at a small but growing number of high schools across the country are moving toward an integrated-mathematics pathway, in which they learn a blend of topics like algebra, geometry, and statistics each year. Common internationally, the integrated sequence is meant to take math learning out of silos and teach students how to bridge connections among topics. There are three levels of integrated math, and students typically take the classes from freshman to junior year.
In the United States, integrated math has been in use sporadically since the 1990s. But the concept has gained ground recently, with the common core serving as a catalyst.
In Appendix A of the common standards for mathematics, both a traditional and an integrated pathway are laid out as viable progressions to convey the standards.
That made it easier for school districts and even some states to reflect on their curriculum and consider the integrated-math approach, said Carrie Heath Phillips, the program director for the common core at the Washington-based Council of Chief State School Officers.
The majority of states leave the decision to individual districts. But three states—North Carolina, West Virginia, and Utah—have recently mandated that all public high schools teach only integrated math. A handful of other states, including Arkansas and Florida, took the opposite approach, requiring a traditional pathway. Georgia, meanwhile, has required an integrated-math sequence since 2008, but, state officials say, has transitioned to more of a hybrid model recently.
The common core’s inclusion of the integrated-math approach opened the door to more districts implementing integrated courses, Tom Loveless, a nonresident senior fellow at the Washington-based Brookings Institution’s Brown Center on Education Policy, wrote in an essay this summer.
“Neutrality, in this case, is a tacit endorsement. And it carries significant consequences for implementation,” Mr. Loveless wrote. “State, district, and school administrators who have long wished and waited for an integrated sequence of math courses are licensed to push this approach as a ‘reform’ sanctioned by the CCSS.”
A Focus on Connections
Switching to integrated math poses resource and logistical challenges for schools and has plenty of detractors, including among math teachers. But for some educators, the introduction of the common core provided an opportune moment to make significant changes to the high school curriculum.
As Edward Logiudice, the math-department chairman at North Middlesex Regional High School in Townsend, Mass., put it: “If we stayed with a traditional pathway, we’d have to rewrite curriculum anyway to fit the new standards. The more we discussed it, and the more we looked at the standards, it just made sense for us to go to integrated.”
For some, the notion that making a significant change to course structure might give the new standards some added leverage was also a factor.
The Common Core State Standards lay out two pathways for teaching math in high school—the traditional Algebra 1-geometry-Algebra 2 sequence and an integrated sequence. The integrated math sequence blends the topic of algebra, geometry, probability, and statistics.
SOURCE: Common Core State Standards
“We knew that the common core was very different, and we were afraid that if we didn’t make some kind of statement about the differences, people would just do what they always did,” said Diana Suddreth, the interim director of teaching and learning at the Utah education department.
Integrated math has growing support in the mathematics-education community. A study published in the Journal for Research in Mathematics Education last year tracked students over three years and found that those who were being taught with an integrated-math curriculum outperformed their counterparts who were in a traditional sequence.
“We can’t say why, [but] the fact that they did [perform better] is an indication that curriculum matters,” said James E. Tarr, a professor of mathematics education at the University of Missouri, in Columbia, and one of the study’s authors. “Since our results have come out, I have heard from people throughout the world who did not find our results to be surprising.”
Many countries—including those whose students outperform the United States in international assessments—use an integrated-mathematics sequence at the secondary level. And many American teachers and administrators who have transitioned to a combined-math pathway say they have seen benefits.
Chat: ‘Integrated’ Math: A Transitional Approach to the Common Core
Dec. 1, 2014
2:30 to 3:30 p.m. ET
In this chat, educators from an Illinois district will discuss their choice to transition their high school math curriculum to an integrated course sequence and share what they’ve learned.
One of the most common arguments for integrated math is that it doesn’t make sense to teach the subject in silos, since in real-world applications, math topics are not neatly segmented.
“The advantage of integrated math is that it kind of blends those math topics together,” said Gina Ziccardi, the assistant superintendent for student learning at Community High School District 99 in Downers Grove, Ill., which is transitioning to an integrated-math curriculum. “It focuses on these connections instead of isolating [topics].”
Paul Stevenson, the math-department chairman at Downers Grove South High School in District 99, taught a level 1 integrated-math class last year after decades of teaching traditional math sequences. He said that, after some initial adjustment problems, he saw an improvement in his students’ learning.
“Students rose to the level of expectation we had for them, by and large,” he said. “They were doing much deeper thinking about practices and problems than even students we had in our [traditional math] program three years advance of them.”
Although integrated math predates the common core, educators say it reflects the standards’ emphasis on building conceptual understanding and making connections across mathematical expressions.
‘Pushback From Stakeholders’
Currently, “only a few math majors, maybe, make sense out of the mathematics, and that’s what we want for all students,” said LuAnn Malik, the coordinator of mathematics for K-12 in the Chapel Hill-Carrboro district, in North Carolina. “Most people hate math because they don’t understand it and [think] it’s just a bunch of procedures, and I think we need to change that as a society.”
In addition, instead of limiting a topic to one or two years in high school, an integrated-math pathway allows teachers to reinforce those math skills over time, said Diane J. Briars, the president of the Reston, Va.-based National Council of Teachers of Mathematics.
But not everyone is sold on the idea of moving away from the venerable Algebra 1-geometry-Algebra 2 approach.
“Integrated mathematics, at least in this country, is somewhat of a controversy,” the University of Missouri’s Mr. Tarr said. “It’s bucking tradition—more than a hundred years of tradition. Certainly when you try to change things in what is seen as in a dramatic way, there’s pushback from a lot of stakeholders.”
Parents, for example, have been vocal critics of integrated math, according to educators in several districts that have made the switch. They worry that colleges or scholarship programs won’t accept integrated-math credits on a transcript (though most, if not all, do), and they balk at the unfamiliarity of the textbooks and problems their children are bringing home.
“The fear of a lot of parents is that kids won’t be adequately prepared for calculus or college math,” the Brookings Institution’s Mr. Loveless said in an interview. “The fear comes from the basic idea that there’s the potential for topics to slip through the cracks [in an integrated-math approach].”
Mr. Loveless said it’s too early to see how effective the integrated math is compared with the traditional sequence, since in school districts that are newly transitioning, there aren’t enough years of test scores to compare. But parents, he said, don’t want to gamble on their children’s education.
Some teachers have also had problems with the switch.
According to a recent survey conducted for the Georgia board of education, nearly 85 percent of the 1,019 Georgia high school math teachers who responded said they would rather use the traditional pathway than the integrated model now mandated by the state.
“From a purely academic standpoint, I think I could be convinced that an integrated approach might make sense,” said Robert Avossa, the superintendent of the Fulton County school district, near Atlanta. He added, however, that teachers have not been adequately prepared to make the transition. “The state did very little work with teacher colleges, purchasing of materials, and quite frankly, training and preparing teachers to work on this model,” he said.
The state board may soon consider reinstating the traditional course sequence or give districts the option to choose, said Matt Cardoza, a spokesman for the Georgia education department.
Educators in other states express similar frustrations.
“It’s moving fast, teachers are kind of struggling to get their hands around it,” said Joanne Whitley, a high school math specialist for the Charlotte-Mecklenburg district in North Carolina. “It’s more difficult than I thought it would be.”
“There has been a learning curve for teachers. In many cases, we had teachers who have taught geometry for let’s say, 10 years, at a certain set of standards, and they’re used to those,” said Jennifer Curtis, the section chief of K-12 mathematics at the North Carolina education department.
Deborah A. Crocker, the president of the North Carolina Council of Teachers of Mathematics, said that teachers in the state are responding well to the professional development they’ve received in integrated math, but that financially strapped districts may be unable to provide sufficient training.
“I think the problem is whether we can provide enough professional development,” she said. “We’ve had such tough budget times [the past] seven or eight years, it’s definitely an issue across the state.”
Resource Questions
One of the biggest complaints from teachers and administrators transitioning to integrated math is the lack of accompanying curricular resources available, particularly ones that align with the common standards. Since the majority of schools teach a traditional sequence, publishers have tended to cater to that market.
“What we get to choose from would be so different if we were traditional,” said Derek Elison, a secondary-math specialist at the Alpine school district in American Fork, Utah.
To fill the curriculum void in integrated math, educators in Utah launched an online, open-source resource called Mathematics Vision Project. Other educators have patched together instructional resources from a variety of sources, including online venues.
Some schools have even decided to write their own textbooks. Mr. Logiudice, the math-department chairman in Townsend, Mass., said his school began the transition to an integrated-math curriculum in 2011, but his team was underwhelmed with the resources available. So the teachers crafted their own curriculum from online materials.
“I didn’t want to spend a lot of money on a textbook service that didn’t want to do what we wanted to do,” he said.
Testing has been another concern for schools with integrated-math programs. Several states, including Maryland and New Jersey, allow districts to choose which high school math pathway to offer but currently support only state assessments designed to reflect the traditional sequence.
As for the multistate consortia assessments, Nicole Siegel, a spokesperson for the Smarter Balanced Assessment Consortium, said that, while the group does not have a specific exam in integrated math, the grade 11 assessment is designed to work for students on either an integrated or traditional pathway. The Partnership for Assessment of Readiness for College and Careers does have specific assessments for integrated-math levels 1, 2, and 3, but states have to grant districts the option to use them. Spokesman David Connerty-Marin said demand for the exams has been low so far.
Despite such challenges and uncertainties, some educators say they see the integrated-math pathway as a development whose time has come in U.S. schools.
“It is challenging to completely change your curriculum, but this was the right thing to do because it’s about student learning—it’s about students really understanding math, not just getting the problem right,” said Ms. Ziccardi, the assistant superintendent in Downers Grove. “This is a much different level, more of a conceptual level.”
