On the docket today: multiple-variable equations. Swanson stands beneath a bright green sign — "Math Is . . . The Wrecking Ball Which Knocks Down the Door to College" — and aims for relevance. This, he says, is the sort of equation that might come in handy in chemistry class or in choosing a cell phone plan.
A 25-minute "workshop" period follows, with students paired off to solve their first multi-variable problem: Joel has 25 coins — some dimes and some quarters — totaling $4. How many of each?
Swanson passes out bags of foam — blue and yellow for some students, red and green for others — to represent the coins, but not before brainstorming a set of rules with the students: no throwing the foam, no eating the foam, no writing on the foam.
Classroom management is important. And Swanson has been working to improve his performance there and in all facets of the job. "Teaching is all about trying new things," he says. "What can I do to get that edge?"
Swanson moves from one group to the other, offering carefully calibrated questions and celebratory fist bumps. At the end — the 15-minute "closing" — a handful of kids are summoned to the front of class to explain how they wound up with 15 dimes and 10 quarters. One group reports a deliberate process, another a lucky guess.
McQueen, who was a TFA corps member in Phoenix, jots down notes that he'll turn into a bullet-point email later in the day. Swanson gets high marks for keeping students engaged and making the lesson relevant to their lives.
He might have done better, McQueen suggests, to model a multi-variable equation during the launch — thinking aloud about how he would approach it. And a countdown clock, he adds, might help to maintain focus during the paired-off problem solving.
McQueen will be back in a couple of weeks to check on Swanson's progress. But he seems pretty confident of what he'll find. In the first few months of school, Swanson's students have already doubled their math scores.
 ALUM IN ACTION Jeremy Chiapetta at the Rhode Island Mayoral Academies Blackstone Valley.
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This package — a determined corps and systematic support — has yielded strong results on the whole. Recent research out of Louisiana, North Carolina, and Tennessee found TFA instructors performing as well as, or better than, traditionally trained teachers.
Gary Henry, a professor of public policy at the University of North Carolina, conducted the research in his own state and counts himself impressed with the organization's approach. "They're simply not allowed to fail," he says, of TFA instructors.
But ask him if Teach For America can be scaled up in any significant way and his answer is swift and definitive: no.
The organization supplies a tiny sliver of North Carolina's teachers. And the numbers are just as modest in Rhode Island. If TFA hits its goal of 100 instructors in the state in a couple of years, the figure will account for less than 1 percent of the total teaching force.
"If we're going to change the achievement gap in Providence Public Schools, which we will, it's not going to be TFA," says Tom Brady, superintendent of the Providence schools and a supporter of Teach for America.