The University of Michigan’s School of Education dean will spend a week of her summer in Grand Rapids’ Steelcase headquarters, standing in the center of a horseshoe of tables surrounded by 27 incoming fifth-graders.
Deborah Ball is one of the nation's leading education experts (both the Obama and Bush administrations have sought her counsel). But she also spends two weeks each summer at the helm of U-M's Elementary Mathematics Laboratory (EML), a fishbowl style program in which Ball teaches a class of fifth-grade students while a range of professionals observe from the back of the room. The Ann Arbor-based EML attracts students and teachers from southeast Michigan, as well as a growing number of teachers and researchers from around the country. Inspired by the program’s success and hoping to expand its reach, this summer Ball will launch a second EML, this one in Grand Rapids.
While the west Michigan fifth-graders study math, more than 20 faculty members and graduate students from U-M as well as west Michigan educators and people from as far away as California will study the teaching and learning in the class.
Joining the group every day will be more than 50 additional teachers, researchers, and mathematicians who will watch the class quietly, taking notes and keeping close track of the students’ and the teacher’s work together. After class each day, the group will analyze what went on and discuss the teaching and plans for the next day’s lesson. Despite decades of federal and state education reforms, U.S. students have trailed most industrialized nations in math performance for the past 50 years.
Ball has devoted her career to understanding the problem and crafting solutions. She played a key role on a White House panel that synthesized research on mathematics teaching and learning, and seeking to reconcile the “math wars” that had plagued improvements over the past decade. Her research group has conducted significant investigations of the mathematical knowledge needed for effective instruction with students.
The Elementary Mathematics Laboratory combines research, teacher education and community outreach, and the techniques developed in it can be applied to school subject areas other than mathematics. It is all part of the School of Education Teacher Education Initiative, an ambitious long-term plan to redesign fundamentally how teachers are trained, and to create tools and resources that will serve the field broadly.
One mathematics problem in last summer’s class demonstrated how early mathematical misconceptions can compound, leading children to struggle as they reach higher levels of math. Ball shows students a square with one half divided into two equal pieces and the other half twice as large as the smaller portions. She colors in one of the smaller squares and asks what portion was shaded.
Half the students give the correct answer of one-fourth and half argue that it was one-third because there were three spaces and only one was shaded. Ball asks, "What if I draw a line here?" splitting the larger rectangle into four equal squares.
"But that's changing the problem! You can't change the problem!" one boy argues.
Another student asks, "But what if there were no lines? You'd see it's one fourth."
Through work on problems like this one, students come to understand the importance of “equal areas” in identifying fractional quantities. Meanwhile, the educators in the EML discuss the importance of delving into “errors” that students make, and of helping learners develop explicit understanding of key ideas. They consider the value of this approach to using errors rather than quickly correcting them or simply making students “feel better.”
Professional learning is not finished when a teacher completes initial training, Ball says, but must be ongoing and continuous as it is for members of other professions such as physicians and attorneys.
"Just because you're good at math yourself doesn't mean you're good at teaching math, or good at understanding how a student came up with a solution and what he was thinking, or how to help that student develop,'' Ball says. The Elementary Mathematics Laboratory offers one mechanism for ongoing professional learning among teachers. It is a model that Ball and her colleagues at the School of Education hope to expand in the next few years, reaching greater numbers of professionals from Michigan and from around the country every year.
Ball and the U-M School of Education’s efforts toward “Building a Better Teacher” were recently spotlighted in the New York Times Magazine
For more on Ball, visit: http://www-personal.umich.edu/~dball/
For more on the U-M School of Education, visit: http://www.soe.umich.edu