Divisions over how fast youths can learn math
A debate over how to teach math in California is heating up as state officials look to redefine success in the subject, with calculus no longer the gold standard of achievement, and a move to push Algebra 1 out of middle schools.
The proposed revamping of the state’s math framework for its 6 million K12 students has sparked yet another math war. It is one of many over the decades as parents, politicians and mathematicians battle over not only when and how to teach fractions, functions and quadratic equations, but what topics shouldn’t be taught at all.
The debates comes as the country has slowly lost ground in math to dozens of others, a potential liability in a global economy, and as Republicans and Democrats are battling over
equity issues in education, with math a common flash point.
California decided to require Algebra 1 in eighth grade about 25 years ago, then made it an option 10 years ago. State officials are now recommending a delay in offering the course until high school, which would eliminate the need to track students into accelerated programs in middle school, a controversial decision San Francisco made in 2014.
The goal is a deeper understanding of concepts rather than a race through memorized skill sets, supporters say.
Critics, however, question whether the effort will be an attempt to sacrifice advanced students on the altar of equity amid a desire to keep students together in math class until junior year in high school.
State officials have pushed back on the concerns with a mountain of research and support from university experts, who say the goal of racing through math courses to reach calculus too often results in a cursory understanding of the topic. That can lead to student burnout and a hatred of math that sticks with them for the rest of their lives.
“Traditionally, particularly in secondary math education, there’s been very much this notion we can measure what students know by how far they go,” said Michael Steele, associate professor of math education at the University of Wisconsin. “There’s really been an acceleration in this mathematics coursetaking arms race.”
In other words, there is a general belief that the quicker you get to calculus, the smarter you are. Increasingly, colleges and universities are rejecting that notion, eliminating the expectation students must complete calculus to be competitive for admission.
“It’s not about the names of courses,” Steele said. “It’s about the learning that happens inside of it.”
Many disagree, holding fast to the notion that the farther you get in math, the better.
“The 21st Century requires more education, not less,” said Rep. Ted Lieu, DTorrance (Los Angeles County), said in a tweet last week lambasting the proposed framework. “Your proposed math framework takes our state backwards. You will be hurting an entire generation of children and our future. Do not do this.”
The guidelines also look to eliminate the belief that some kids are good at math and should be propelled forward, while others are not, left to lag behind. While the framework would not be mandatory for districts even if passed by the state Board of Education later this year, the recommendations could be aligned with future state policies related to funding or standardized testing.
“Students internalize these messages to such a degree that undoing a selfidentity that is ‘bad at math’ to one that ‘loves math’ is rare,” according to the framework.
Under the current proposal, the state recommends students stay together in the same math sequence through sophomore year geometry, with opportunities for accelerated coursework after that. Currently, many districts offer students the chance to take more advanced math courses starting in middle school.
Despite accusations by critics, the 800page document does not recommend eliminating calculus.
“We’re not kicking calculus to the curb,” said Linda DarlingHammond, president of the state Board of Education. “It does present the research that the rush to calculus without the depth of understanding is not beneficial to longterm math (achievement).”
The framework is still a work in progress, with the first round of public comment complete. The draft will be revised and then pushed through another round of public vetting this summer. The state school board is expected to vote on it in November.
The document includes examples of how to teach various concepts as well as three types of math course sequences through high school, which would allow higherlevel math including calculus, statistics or data science.
Yet Orinda parent Chris van Löben Sels believes the recommendations would decrease opportunities for advanced students. The further in math you go in high school, the better, he said, with increased odds for college acceptances and scholarships.
In his son’s school district, students can take Algebra 1 in seventh grade, geometry at the local high school in eighth grade and calculus by sophomore year.
“Progress is getting more kids to get further in math,” he said. “Regardless of what our hopes may be, getting into college is competitive and when kids are able to get further in math, it helps them compete.”
In part, state officials drafting the framework looked to San Francisco Unified, which pushed Algebra 1 out of middle school in 2014, a decision that remains controversial even now.
But by 2019, the district saw a dramatic increase in the number of students who passed Algebra 1, said Lizzy Hull Barnes, the district’s Mathematics & Computer Science supervisor.
In addition, the number of students taking Advanced Placement math courses soared to 1,819 students, up from 1,641 in 2016, despite high school enrollment staying flat, and those taking the courses include more students of color, Barnes said.
Enrollment in calculus has dipped slightly to 1,085 this year, about 50 fewer students than five years ago, but at the same time enrollment in Advanced Placement Statistics has increased nearly 50%, to 734 enrolled in the course.
Despite the example of success and consistent research associated with slowing down the pace, “it causes fear and anxiety,” said Rachael Maves, California Department of Education deputy superintendent for Instruction and Measurement.
“Some of this is based on a misunderstanding and misconception of what we’re trying to accomplish here, which pushes against traditional notions and thinking,” she said. “The importance and outcome of math is providing a depth of understanding around mathematical concepts, not necessarily how quickly can we get to the top.”
Piedmont dad Mike Malione, who has read all 800plus pages of the draft framework, disagrees, saying there is too much focus on the beauty and joy students should have for math rather than the necessary skills. It’s like teaching an art appreciation class rather than teaching how to make art.
“It sort of forces everyone into one slow lane,” he said. “The ones who are capable are never going to be able to move fast enough.”