Under the Common Core State Standards, Algebra 1 is a much tougher course than what was taught previously in most states, teachers and standards experts say, in part because many of the concepts that historically were covered in that high school class have been bumped down into middle school math.
Some say those changes could complicate efforts around the country to put 8th graders in Algebra 1—a still-debated trend that’s grown over the past two decades.
In fact, at least a few districts are already reconsidering their stances on Algebra 1 in middle school. The San Francisco school system, for instance, went from requiring all 8th graders to take Algebra 1 to just the opposite policy under the common core—as of this year, all students must take Algebra 1 in 9th grade.
And while that kind of move can disappoint some parents, educators point out it doesn’t mean 8th graders aren’t learning algebra.
Under the new standards, California students would learn many of the concepts traditionally taught in Algebra 1 in 8th grade math—as well as some concepts not previously taught in either course, according to mathematician Hung-Hsi Wu.
Source: Hung-Hsi Wu, professor emeritus at the University of California, Berkeley
“There’s big confusion between the Algebra 1 course with a capital A and algebra, the mathematical subject,” said William G. McCallum, a mathematics education professor at the University of Arizona, in Tucson, and one of the lead writers of the common standards. “If you follow common core, there’s now tons of algebra content in the 8th grade.”
“Traditionally in Algebra 1, a lot of time was spent looking at linear functions,” said Diane J. Briars, the president of the Reston, Va.-based National Council of Teachers of Mathematics. “But a lot of that work now has been moved into 8th grade common core.
“The common core,” she said, “built much higher expectations for conceptual understanding regarding ratio and proportional relationships [in 8th grade] to prepare students to understand the ideas of slope and rate of change.”
Simultaneous linear equations and functions and their graphs—concepts also typically taught in Algebra 1—are now also taught in 8th grade under the common core.
The idea is that by the time students get to Algebra 1, they will have developed deep understanding of some basic algebraic concepts, and can dive into more complicated coursework.
Adding in Concepts
There are also algebra concepts taught in the 8th grade common-core standards that were not taught at all in most previous state standards, according to Hung-Hsi Wu, a professor emeritus of mathematics at the University of California, Berkeley. Those include the concepts of congruence and similarity as related to algebra, and the fact that the slope is the same between any two points on a nonvertical line.
The common standards for the elementary grades help get students ready for algebra as well, said Jonathan A. Wray, the instructional facilitator for secondary-math curricular programs in Maryland’s 52,000-student Howard County public schools. “You can back-map all the way to grades 3, 4, and 5 and see there’s better preparation there than there ever has been before.”
He visualizes it this way: In the past, at least in his own state, K-12 math courses became increasingly harder over the years, with the demand really taking off in Algebra 1. “I think now if you illustrate the way the common-core standards were designed,” he said, “it’s a little more in a steady line all the way up through Algebra 2.”
But the reality is that in many places, students don’t take 8th grade math—they take Algebra 1.
Both California and Minnesota approved policies mandating 8th grade Algebra 1 for all about seven years ago, though California later backed off and made the practice optional for districts. Some individual districts require students to take Algebra 1 before the end of 8th grade as well.
Between 1990 and 2011, the share of 8th graders enrolled in Algebra 1 or a higher math course nearly tripled, from 16 percent to 47 percent, according to a study by Tom Loveless, a senior fellow at the Brookings Institution in Washington.
Under the common standards, that may be changing, Mr. Loveless said. “I’m expecting the numbers to decline significantly,” he said.
Mr. McCallum of the University of Arizona agrees such decreases are possible, at least for a while. “Initially, we might have fewer 8th graders in the course because it will be a more serious course,” he said.
That’s already happened in the 53,000-student San Francisco school district, which went from a blanket policy placing all 8th graders in Algebra 1 to a policy that puts all 9th graders in it.
Too many students were failing Algebra 1 in 8th grade, said James Ryan, the STEM executive director for the district. But also, “the material is different than what it used to be,” he said. “We’re taking what was the Algebra 1 course and ... spreading it over two years [8th and 9th grades], and also interspersing in there the mathematics that allows students to see why they would ever want to learn it.”
That is, students are focused on applying the algebra they’re learning, rather than seeing it as a series of procedures and algorithms.
For instance, rather than doing a set of problems from the textbook, Mr. Ryan said, students in Algebra 1 might collect data on the weight of students’ backpacks, plot them on a graph, and model them with an algebraic function.
Parent Reactions
Of course, such logistical changes can be a hard pill to swallow for some parents.
“There is a vocal minority in San Francisco that feels students should be able to rush forward more quickly, but that is a minority of parents,” Mr. Ryan said.
Parents were outspoken in the nearby San Mateo-Foster City Elementary School District, in Foster City, Calif., when they learned that fewer students would be taking Algebra 1 in middle school, reported the San Mateo Daily Journal. Many parents in that Silicon Valley district were concerned that their children would be bored or wouldn’t be able to take calculus before they graduated.
“That’s been one of the challenges,” said Ms. Briars of the math teachers’ council. “How do you help parents understand that if fewer kids are going into 8th grade Algebra 1, it’s not that we’re dummying down the curriculum, it’s that the whole curriculum is elevated?”
For Mr. Ryan, community outreach has been critical. “In the common core, one of the things that’s embedded is that algebra is not really a course, it’s really a domain of knowledge that starts in kindergarten and goes through high school,” he said. “That is a very different way of thinking about their child’s experience than [parents] had in the past, and that kind of shift takes time and repeated conversations to take hold.”
And while the common-standards document strongly advises against skipping material, acceleration is still possible, and districts can do it several ways. The appendix of the common-core math standards suggests a three-years-in-two option, in which students take the content of 7th grade math, 8th grade math, and Algebra 1 in the last two years of middle school. The San Mateo-Foster City district plans to use that option.
In San Francisco, students will be able to accelerate later in high school, taking a compressed version of Algebra 2 in 10th grade that also includes precalculus topics. Then they can take calculus senior year.
Some students in Howard County schools are learning above-grade-level material in elementary school, for instance, doing some 6th and 7th grade work in grade 5. Mr. Wray is looking into ways to compact the early grades’ standards as well—for instance, whether K-4 math concepts and skills could be taught in K-3.
So far in Howard County, which has been implementing the common standards for several years now, enrollment in 8th grade Algebra 1 hasn’t declined, Mr. Wray noted.
“What that says is that either students are meeting that challenge [of higher standards] and/or the preparation that the common core presents through a more-smooth trajectory has resulted in students being just as prepared—or even more prepared—to succeed in algebra,” he said.
