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Campus Ideals Meet Classroom Realities

Teachers-in-training at the UW College of Education — which incorporates real-world classroom immersion into math methods instruction — encounter low-achieving students who claim “I don’t do math” and high-achieving students who can successfully complete computations, but have no idea what they mean.
They find Muslim students who spend the first 15 minutes of a 50-minute class in prayer, and struggling English language learners who leave teachers wondering:

“Should I modify the lesson for them? Is that fair? What do they already know? How do I find out?”

The UW students, many white and from suburban backgrounds, encounter immigrant children whose parents work three jobs to make ends meet, students of color who challenge them on issues of race, teens who don’t want to lose face in front of their friends by trying in school, and kids who have never seen a point to studying.

For Alayne Cartales, a recent graduate of the UW College of Education’s teacher education program, the ideals of campus met the realities of the 21st-century classroom when she was assigned to student-teach in a math classroom where almost half the pupils were special-education students. Her job:
to get them up to speed while keeping a handful of advanced students mathematically challenged. “I just tried to keep my head above water and reach as many kids as possible,” says Cartales.

These on-the-ground experiences are eye-opening, both for UW students and the faculty researchers who closely follow them into their first years as teachers. “When we’re at the university talking about teaching, there are many aspects of the classroom we can bring to life: lesson plans, activities, even student-teacher role play. But none of this does justice to the complexity, the particularity of students in an urban classroom,” says UW mathematics education professor Ilana Horn, whose research team intensively studies the gaps between academic theory and real educational practice.

Horn says would-be math teachers often come into UW classes expecting tips and tricks, not the complex concepts and practices instructors use in math education. “They think they can follow a recipe and magic will happen,” says Horn. “But good teaching is more about problem-solving than deploying some particular method.”

It’s a lesson brought home for math education students who, over the past two years, have spent part of their first quarter at the UW in a Puget Sound urban high school, observing in classrooms, studying lesson plans, debriefing with teachers about what happened in class and why, pairing up with high school students struggling with math.

“Students who go through this field-based methods class are much more humble about how hard teaching is,” says Horn. “We want to send student teachers out with the idea they have something to learn from any competent teacher out there.”
The UW students are typically high achievers who “got” math in school. They’re surprised to find students who don’t even know how to add fractions. “For them, it’s a shock to see the level of math these students are doing. They, themselves, got it at that age. They didn’t struggle. It’s a reality check,” says UW research assistant Sara Sunshine Campbell, who teaches math methods classes.
Many of the UW students were taught traditional college-prep math curricula in school. They memorized algorithms, worked step-by-step through curricula. In that one-track world, there was a single right answer to a problem, and one way to get there. Teachers lectured. Students memorized. “Slow learners” were assumed to be missing the logical skills needed to do higher math. “Fast learners” often arrived at answers without understanding the mathematical process that got them there. But who noticed?

In the urban classrooms where Horn and her students work, the UW students find that what worked for them does not necessarily work for struggling and disengaged students. Instead of dumbing down curriculum, the teachers are learning methods to help students engage in important mathematical ideas –– despite gaps in their prior learning. As they engage with challenging content, they can learn some of the math they may have not had opportunities to understand in their earlier education. To make this work, one student may need visuals to grasp mathematical concepts; another may do best with hands-on projects. Discussion and argument, not lecturing, may be the best way to challenge them mathematically.

These aren’t the quiet classrooms most UW students remember from their childhoods — classrooms where pupils, sitting in neat rows of desks, kept their nose in a book, and where talking might be considered cheating. But, at a time when federal laws demand unilateral academic equity, these are classrooms that must open doors into mathematical understanding for diverse student populations. “The way math was taught in the past did not give all kids access. It wasn’t fair, and that’s why so many students didn’t succeed,” says Campbell.
Not all teachers agree. In their field assignments, UW students see teachers using reform-based methods as well as veteran teachers who believe that such changes might reduce the rigor of the traditional curriculum. Some of the veteran teachers frankly state that they don’t believe in group work, “But go ahead and try it if you want to.” High school students, too, sometimes balk at new methods. “Of course, they may give you push back,” says Campbell. “You are asking them to do the thinking. Before, the teacher did all the thinking for them. You’re asking them to do something harder, to do more work.”

Even some math education students are initially skeptical of the inquiry-based approach to teaching. Alayne Cartales was one of them. “My understanding of this instructional approach when I started was that students didn’t ever have to memorize or learn algorithms, they’d just create them themselves. I thought, ‘That’s baloney. They just have to memorize some stuff.’”
“Now I realize that students do have to memorize some algorithms, but besides just memorizing, they have to understand the mathematical concepts involved. People keep saying they want students to be critical thinkers. Well, first you have to make them think. They don’t always have to think when they apply an algorithm.”