Algorithms for Mastering Math

In a Brooklyn, N.Y. middle school, three walls have been knocked down to create one giant classroom where four seventh grade math teachers circulate among 120 students. Four different learning areas are signified by shelving and different colored carpets and chairs. An airport style monitor just outside the door tells kids where to go.

The program, Teach to One, is designed to let each student learn at his or her own level, and master each skill before moving on to a next step. Tina Rosenberg, in her New York Times column "Fixes," notes that kids who have missed an essential math skill or concept in an early grade are likely to keep falling further behind in successive grades, eventually joining a permanent math underclass of students who find math incomprehensible.

This classroom combines many learning methods and activities with a range of sophistication. . Some children work at computers, some use work sheets in groups, and some solve equations. The subjects include manipulating fractions and negative numbers, graphing expressions on a number line, and working out a multi-day probability project. Some worksheets show wrong answers and ask students to identify the mistakes that led to them.

At the end of each session, student take a short quiz testing their mastery of the subject, letting student and teacher know the successes and deficits of the moment. Rosenberg says the next step is the real innovation. Each student's quiz is fed into an algorithm, which produces the next day's lesson for that student based on individual mastery, and even on what has been shown to be the best learning modality for the student-such as learning best with games, or liking to learn alone. (Teachers get a preview and can override the computerized schedule if they think it necessary). The program identifies 77 math skills, and has a library of 12,000 lessons to teach them. Some lessons are created by staff, others bought from education companies.

Teach to One evolved from School of One, a math teaching program created by Joel Rose, an education expert, and Chris Rush, an educational consultant, both of whom had worked for the New York City Department of Education. The two formed Classroom Innovation Partners, and Rosenberg reports the model is being used in 30 schools in New York, New Jersey, Washington DC, Georgia and North Carolina. Early results have been very promising some schools and less so in others. The initiative has not been without controversy.

New Classrooms funded a study by scholars at Teachers College of Columbia University, to measure results. In the first year, math progress for Teach for One kids was about at the national average. The New York Daily News blasted the program as a pricy reject, and it was expensive. One school spent $140,000 on computers for every child. Second year results were much more encouraging, with progress of the kids ranging from 47 percent to 60 percent above the national average. In a thoughtful piece in Forbes, Michael Horn wrote that innovations are rarely instant successes. Instead, he said, they tend to require messy experimentation with many modifications and iterations. Further, Horn wrote, formative evaluation that measures grade level achievement doesn't identify nuanced individual progress of youngsters who have come from behind and those who have soared.

Horn suggests the second year improvements indicate that earlier gaps in math knowledge may have been filled during that first year. A middle school in Charlotte Mecklenburg reports with enthusiasm on its program. Rosenberg calls it a work in progress worthy of continued use and experimentation. "School of One takes comprehensive advantage of technology in ways that let teachers concentrate on teaching," she said. "That's worth getting right."

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