Volume 28, Number 3
May/June 2012

The Algebra Problem

How to elicit algebraic thinking in students before eighth grade

by Laura Pappano

 

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)

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.