Research

That Matters

The Math Field as Battlefield

The gloves have come off in the “Math Wars” in Washington State.

In one corner are the traditionalists, protectors of “real” math, true math. They’ll fight to the end for tried-and-true facts, principles and procedures. When they look across the ring, they see opponents who they believe have lost their way — new-age teachers who indulge students, allow noisy free-for-alls in the classroom, engage in “fuzzy” math, press students to draw pictures, play games and “discover” why 3x4=12.

In the other corner are the upstarts, the reformists, the math educators who strive for “deep understanding” in the classroom. When they look across the ring, they believe they see rote-and-drill advocates who muzzle students, never make them think. They see “control freaks” who stand in front of a class making mathematical pronouncements for students to repeat, memorize. Their classrooms are lifeless, their students miserable as they work through dull, repetitive, meaningless exercises.

Such simplistic stereotypes dominate today’s divisive knock-down drag-outs over math and science education. “Rarely does anyone come into the debate saying ‘Oh, I‘m a little of both.’ People self-identify with one side or the other, “ says UW associate professor Mark Windschitl, who teaches science education and serves as chair of curriculum and instruction in the College of Education.
In truth, he points out, the best traditionalists stand in front of the class, make math fascinating through storytelling and clear explanations of concepts, give lots of examples and engage student attention.

The best reformists facilitate complex mathematical thinking. They elicit students’ ideas to find out what they already know and build instruction on the findings. They ensure students not only engage in mathematical activities that lead to mathematical procedures, but know when to put those procedures into action to solve problems.

Both sides want students of all backgrounds and abilities to improve their mathematics skills, and both agree that math teachers in this state need extensive subject matter knowledge to do their job.

Teaching Math So why have people who care so deeply about student success turned the math field into a battlefield?

The question intrigues Windschitl. He has studied the language and images used by both camps in the virulent math and science battles — camps that stake out their positions daily on editorial pages, Internet sites, blogs, sound-offs. “It’s hard to overestimate how nasty this debate is nationally,” says Windschitl.

Words used by traditionalists to describe reformist methods include “ineffective, inefficient, cumbersome.” Words used by reformists for their counterparts’ methods include “rigid, authoritarian, outmoded.”

What makes it so hard for the two camps to talk are deeply held underlying values and beliefs. Many educators say the wars have as much to do with politics as they do with education. Even discussions about a seemingly neutral topic such as student thinking rarely play out in a productive way.

“To traditionalists, student thinking means comprehending,
integrating, applying knowledge — specifically, how the teacher comprehends, integrates, and applies knowledge. The students’ job is to figure out how the teacher made the connection, how to reconstruct the teacher’s thinking, and
how to memorize it,” says Windschitl.

“To reformists, thinking means sense-making. It means students going beyond the information given by the teacher and making connections for themselves.”

“In the one view, knowledge is acquired from teachers. In the other, it is learned via sense-making by one’s self.”

Both camps point to the low scores on the Washington Assessment of Student Learning (WASL) math test as proof that their opponents’ methods are not working. Is reform math curricula hurting WASL performance? Or is it the rigidity of traditionalist teaching that leaves all but high-level students in the math-track dust? “The WASL is like holding up a mirror to ourselves right now,” says Windschitl.

Low student performance may be reflecting the field’s lack of consensus on what matters in mathematics.

The high-stakes test, tied to high-school graduation, is one force behind the venting. Another is the “gate-keeping” role of mathematics. Students who don’t take advanced high-school math head down a different path than their college-bound counterparts, whose math track can lead to high-paying jobs in science, technology, and engineering. Is this the education everyone, under new legislative mandates, should be getting?

For students, the warring ideologies have too often resulted in a mishmash of teaching styles. While moves are afoot to adopt more consistent math curricula statewide, many districts remain a checkerboard of reform and traditionalist methods. Some schools vary grade to grade.

That can turn campuses into their own battlegrounds. Windschitl cites the example of a high school where the traditional vs. reform argument was so heated that administrators had to cancel all department meetings.

In all the noise, some important voices are drowned out, says Windschitl. And it may be the quietest ones that need to be heard, the voices of teachers who shy away from divisive words and concentrate on teaching.

They’re the teachers who don’t separate curricula into enemy camps, don’t buy into either/or thinking, but assimilate the best ideas from both methods to tailor their teaching to individual student’s needs. They‘re the teachers who know each child learns differently from every other child.

“Most good teachers use both active learning strategies and direct instruction, group work and seatwork, scripted exercises and individual student investigations,” says Windschitl. “They want students to make sense of both the procedures and the underlying mathematical concepts.”

Their success advocates for a lower-volume, more reasoned discussion of mathematics education, one that addresses shared goals for student learning and a shared understanding that there are many ways to teach. Amid that variety, however, students need to experience coherence from one class to the next.
Can a measured discussion happen amid such rancor? Are warring camps ready to put down their rhetorical weapons and enter peace negotiations?

It’s a hard call. “A change in rhetoric is the only way to move the conversation off the battlefield and onto productive ground,” says Windschitl. “The only thing you can do is start a dialogue and that means not talking ideology, not using straw men, not using stereotypes. It means trying to understand the other person’s point of view.”

With sides so firmly entrenched, it could fall on the next generation of K-12 teachers to broker a truce. At the UW College of Education, students are expected to initiate these dialogues when they take inquiry-based math methods out into schools, says Windschitl.