Should High Schools Rethink How They Sequence Math Courses?
Most students don't aspire to careers that will require calculus, so high schools must create sequences of math courses that reflect the wide variety of young people's occupational goals, a math advocacy group argues in a report published Wednesday.
"Mathematics education needs to support students' transitions to and through college, whether they're pursuing STEM disciplines or other promising majors that prepare students for careers in other fields like law, politics, design and the media," says the report by Just Equations, a group that's trying to get school districts to consider the equity of their math offerings.
Too often, "irrelevant math hurdles" are becoming stumbling blocks for students who don't aspire to careers in science, technology, engineering, or math. Additionally, schools do poorly at nurturing and recruiting black and Latino students into challenging math classes, the report says.
To serve all students well, schools must start thinking differently about their math courses, write co-authors Phil Daro, a lead author of the Common Core State Standards in math, and Harold Asturias, the director of University of California-Berkeley's Center for Mathematics Excellence and Equity.
The authors propose a model that would eliminate the classic Algebra 1-Geometry-Algebra 2 model in favor of a pattern that would have all students in the same math classes in 9th and 10th grade, followed by a set of choices beginning in 11th grade.
Some of those choices would be aimed at students who will need the highest levels of math, while others would be for students in what the authors call "branch" fields—a term they coined to distinguish these students from STEM students in general, and from those who aspire to jobs that require calculus.
Courses Designed With All Students in Mind
An 11th grade course for "branch" students might delve into statistics, game theory, and math modeling. They could build students' skills at symbolic notation, and use functions to model real-world situations. They "should not be watered-down versions of STEM topics, but instead topics with their own heft and potential relevance in branch fields" like data science, statistics, probability, digital graphics, decision theory, robotics, and game design, the report said.
All courses and pathways should be rigorous, and prepare students for college without demanding that they master types of math they won't need down the road, the report says.
The report includes examples of course sequences from districts that have ventured into this work.
The five high schools in Escondido Unified School District in California now use common math courses for all 9th and 10th graders, and offer a choice of two courses for 11th grade. Math 3C includes precalculus, while Math 3S is "common-core math with statistics," Abi Leaf, a math content specialist for the district, said during a webinar Tuesday. In their senior year, STEM-oriented students can take AP Calculus their senior year, and other students can choose between Math 4 or AP Statistics.
Escondido teachers and counselors use a "decision tree" to help students think through their math options, starting with questions about their career goals. Leaf said the district has also eliminated remedial classes, and does its best to provide support for students where they need it. Teachers are participating in "teaching studios" to help them get used to "having all students in their classes," and to absorb the district's new "value system" in math, Leaf said.
Even still, after a few years of using the new approach, Escondido is concerned that the Math 3S is "considered a pathway for students of color," Leaf said, with more white students opting for Math 3C. "It's one of the biases of our system that we're working against," she said.
Read about San Francisco's work to "de-track" math.
Oregon has been rethinking its math pathways, too. About 50 high schools are piloting versions of a new model that has common courses in 9th and 10th grade, followed by options in 11th. State content specialists in math and career-tech-ed designed the pathways together, in recognition of students' widely varying goals and needs.
The 9th and 10th grade courses cover a year's worth of Algebra, and a half year each of geometry and data science, said Mark Freed, a math specialist with the state department of education. Schools can cover that content sequentially, or integrate it over the two years, he said. Courses in 11th grade include Algebra 2/precalculus, for students who aspire to careers that would require calculus, and, for other students, a variety of applied math classes, such as "construction geometry," "financial algebra," and "math in computer science."
"The idea is to create math systems that all our students can see themselves in, and see the relevance of math," Freed said. "We have a system that works for [future] math majors. We need one where all students see themselves as 'math people.'"
Choosing Instead of Placing
Rethinking math courses should go hand-in-hand with shifting the way schools think about assigning students to courses, Daro and Asturias wrote in the new report. Instead of "placing" students in classes based on adults' perceptions of their mastery, schools should engage in a dialogue with students, asking what their career goals are and offering information about each math pathway so students and their families can decide the best match.
That approach will likely mean that many students need support to be successful in their chosen math classes, the report said, so schools will have to provide things like summer bridge courses, or classes that students can take alongside their regular math classes—a model colleges call "co-requisite" courses—instead of getting mired in remedial math courses.
Teachers will need to shift instructional strategies as well, from a model that values the students who quickly raise their hands to a model that encourages "curious and thoughtful" dialogue that includes all students, the report says. Teachers and counselors will need to work with students to heal their "damaged math identities," it said, since so many students, ill-suited to the classic math course progression, end up feeling like they're bad at math.
For the new kinds of courses and sequences to work in high school, colleges will have to embrace supportive policies, the report said. Too often, colleges require completion of Algebra 2, or use calculus as a "signal" of students' potential, the report said. Some universities are starting to crack those doors open, dropping the Algebra 2 expectation and using courses like Advanced Placement statistics as signs of a wider variety of math mastery, the report said.
The themes in the new report aren't new. "Catalyzing Change in High School Mathematics," released last year by the National Council of Teachers of Mathematics, urged schools to end tracking and create new pathways that would have shared courses for the first two years, and then diverge into various options in students' third and fourth years that reflect their goals and interests.
A joint statement in 2012 by NCTM and the Mathematics Association of America urged schools to leave calculus to universities, and cultivate high school students' expertise in algebra, geometry, and trigonometry.