The algebra problem
It’s Crazy Hair Day at Marshall Elementary School in Boston’s Dorchester neighborhood—which is perfect, because Tufts University researcher Bárbara Brizuela has brought a hat.
In the stovepipe style and made from oaktag paper, the hat is one foot tall. Brizuela then asks, “If I’m five and a half feet tall, how tall will I be with the hat on?” Second-grader Jasmine, smiley in a pink sweatsuit, answers, “Six and a half feet.” Rather than say, “Right!” Brizuela offers another question: “How do you know?”
Thus begins a math conversation that researchers like Brizuela believe may hold the key to tackling one of our biggest school bugaboos: algebra.
As they talk, Jasmine uses words, bar graphs, and a table to describe how tall each person they discuss will be if they put on the hat. Jasmine creates a rule—“add one foot to the number you already had”—and applies it to an imaginary person 100 feet tall.
Brizuela even throws out a variable. “So, to show someone whose height I don’t know, I will use z feet,” she says, adding a z to Jasmine’s table. “What should I do now?” Jasmine pauses. “This is kind of hard,” she says. Brizuela, whose pilot study explores mathematical thinking among children in grades K–2, understands. “Would you like to use a different letter?” she asks, erasing the z and replacing it with a y. Jasmine smiles. She picks up her pencil and easily jots down the rule: y + 1 = z feet.
Algebra – A Dreaded, Scary Subject
It may seem adorable that young children are stumped if asked to add 1 to z but not if asked to add 1 to y, but to Brizuela, director of the Mathematics, Science, Technology, and Engineering Education Program in Tuft’s education department, it reveals the reasoning capacity of young minds and the need to engage them in thinking about algebra long before it becomes a dreaded and scary subject.
To many, algebra is about the first or last three letters of the alphabet, and it provokes groaning, trash talk (think Forever 21’s “Allergic to Algebra” T-shirt), and heated debate. Should it be mandated? At what grade? Algebra’s status as a “gatekeeper course” has made it a touchstone on matters of access and equity. As a result, in many places it’s become a graduation requirement.
Back in the early 1980s, one-quarter of high school graduates never even took algebra, says Daniel Chazen, director of the Center for Mathematics Education at the University of Maryland. Today, educators are pushing students to take algebra even before high school. According to the National Assessment of Educational Progress (NAEP), the number of students taking Algebra I in eighth grade more than doubled between 1986 and 2011, from 16 to 34 percent. Strikingly, eighth-grade NAEP math test scores have edged up too, with 43 percent scoring advanced or proficient in 2011, compared with 27 percent in 1996.
But amid the good news is a troubling reality: Many kids are failing algebra. In California, where standards call for Algebra I in grade 8, a 2011 EdSource report shows that nearly one-third of those who took the course—or 80,000 students—scored “below basic” or “far below basic.” In districts across the country, failure rates for Algebra I vary but run as high as 40 or 50 percent, raising questions about how students are prepared—and how the subject is taught.
Starting Algebra Early… continue reading
Thank you Laura Pappano, a Freelance education writer and author for the Harvard Education Letter.