The dean of the School of Education is in the center of a horseshoe of tables surrounded by 27 incoming Ypsilanti fifth-graders.
Deborah Ball, one of the nation’s leading math education experts, spends two weeks each summer at the helm of U-M’s Elementary Mathematics Laboratory (EML). While the fifth-graders study math, more than 20 faculty members and graduate students from U-M and the University of California, Berkeley study the young students.
Joining the team every day are more than 50 additional teachers, researchers, mathematicians and student teachers who watch the class quietly from risers on the edge of the room and then brainstorm after class about the best ways to improve instruction. A larger group watches live video feed of the class from other rooms.
In the afternoon, U-M student teachers work with the fifth-graders in small-group tutorials, honing their own instructional skills while simultaneously providing an extra boost to the children. The entire enterprise is carefully video- and audio-recorded for later analysis.
“Why am I giving you pens instead of pencils?” Ball asks the young class. “So you can keep a record of everything you do on these problems and learn from your mistakes.”
Despite decades of federal and state education reforms, U.S. students have trailed most industrialized nations in math ability for the past 50 years.
Ball has devoted her career to understanding the problem and crafting solutions. She recently served on a White House panel to resolve the so-called math wars, working to bring the two camps together. Her research has developed “mathematical knowledge for teaching” that improves instruction and increases the level of understanding of students.
The Math Lab combines research, teacher education and community outreach, and the techniques developed in it can be applied to school subject areas other than math. It is all part of the School of Education Teacher Education Initiative, an ambitious long-term plan to redesign fundamentally how teachers teach, and to create tools and resources that will serve the field broadly.
One problem on the first day of class demonstrated how early math mistakes can compound, leaving children lost and struggling 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.”
The debate both in the class and among the teachers afterward went on.
Education can’t end when a teacher graduates from college, 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 doesn’t mean you’re good at teaching math, good at understanding how a child came up with a solution and whether they can do it again,” Ball says.
