Research in Action: The Mathematics of School Improvement

Leinwand and classWhat's 9 + 8? Simple, right?

If only school improvement were so easy. It's not. Neither is helping mathematics teachers in struggling schools move beyond drilling for right answers. But Steve Leinwand, math specialist at AIR, says supporting teachers as they work to create classroom conversations around, for example, why and how 9 + 8 equals 17, is a critical part of strengthening instruction. "That's what builds understanding in classrooms," Leinwand says.

The approach is getting results at a high-poverty elementary school of nearly 400 students in the Mid-Atlantic region, where Leinwand is part of an AIR team leading school turnaround. During the past year at the school, which serves students in pre-Kindergarten through Grade 8, the proportion of students who are proficient in math has gone up 21 percentage points.

The gain in math proficiency followed an AIR audit of the school's math program and implementation of a set of targeted activities for improvement. The audit revealed that appropriate curriculum, standards, and resources were in place, but the overall quality of instruction and the collaborative structures (such as professional learning communities) were not as strong as they needed to be.

Classroom coaching and modeling of professional collaboration have enabled the school's teachers to better focus on analyzing student performance data, planning and providing mutual support, and sharing effective instructional methods.

For AIR, building relationships with the administration and teachers—and making sure that all parties are aligned to support the development of student understanding—is critical for success.

Leinwand, who spends two days a month at the school, might co-teach a math lesson or demonstrate how to spur discussion by asking during a class how students know that the sum of 9 + 8 is 17. One student might explain the addition of 9 + 8 as "double 8 plus 1," while another might see the calculation as "double 10 minus 3." The point, Leinwand says, is that students need opportunities to work on strategies for thinking and should be expected to explain their reasoning. When a student is confused, effective teachers turn to a different approach or representation—for example, demonstrating fractions with a ruler instead of denominations of money.

Steve Leinwand with students"We're not doing test prep," Leinwand says. "We're trying to build effective teaching and learning of mathematics skills and concepts. The tests take care of themselves if the students understand."

Leinwand—who has visited more than 2,000 schools and observed more than 5,000 math classes during his career—talks with teachers after class. In a positive and constructive manner, he provides three or four points for improvement.

"I care deeply about what teachers are doing with and for their students," Leinwand says, "and they know I know how hard it is to do well. These kids can't afford mediocrity."

Principal Researcher