Introducing letters to represent quantities, as in these first-grade math problems, helps students prepare for algebra. (Source: Curriculum Research and Development Group, Univ. of Hawaii)
Volume 28, Number 3
May/June 2012
The Algebra Problem
How to elicit algebraic thinking in students before eighth grade
By LAURA PAPPANO
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.
