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Research That Matters
Do the Math: Engagement Equals Academic Success
The topic of math education comes laden with baggage. Myths abound. You either get it or you don’t.
Even if you do get it, the only way to learn it is to master one step before moving onto another. You memorize. You drill. You test. Maybe you pass. Maybe — if math doesn’t catch your imagination — you fail.
When 75-80 percent of the students at an urban high school in Washington State received D's and F's in their introductory math class, teachers decided it was time for change. Traditional teaching and curriculum weren't working with these low-achieving students. Teachers were frustrated.
"The freshmen and sophomores had virtually no skills. They could crank out worksheets, but if you gave them a quiz, they looked as though they knew nothing," says one veteran teacher. She was on the verge of quitting.
The school, a magnet school, is both an academic flagship for the district and a poster child for the city's growing academic gap that divides along demographic lines. In honors classes, most of the students are white or Asian. In remedial classes, most of the students are non-Asian minorities. For many of them, college is someone else's dream, and math — the gateway to college for high-achievers — is too hard, too boring, too irrelevant.
"The kids say math doesn't have meaning in their lives. They ask: 'What’s the point of this?'" says Ilana Horn, professor of mathematics education at the UW College of Education. "But if you can get them to buy in to an introductory course, if you can turn them onto math, you can turn them onto going to college."
The first years of high school math mark a critical juncture for all students. Nationally, about 50 percent of students drop out of the math track altogether after they hit ninth grade. They don't get it, and they can't get away from it fast enough.
It’s hard for math teachers — who found math easy themselves— to tackle the problem. But the frustrated math teachers at this urban high school decided to try. In an effort to update their teaching skills and to find a curriculum that would engage struggling students, they partnered with a UW team. It was led by Horn, whose work focuses on the underperformance of American secondary students in school mathematics, and by Jim King, a UW math professor.
Horn believes high-level mathematics should be accessible to all students, including low-achievers often excluded from the curriculum. Keeping underachieving students from working on probability because they haven't mastered fractions may be stopping them in their academic tracks, she suggests. Students having trouble with one mathematical concept may need a different door into mathematical thinking.
"There's a common assumption that the kids who struggle are not capable of engaging in higher level thinking," says Horn. "They often can be really good at math, but the way they get there is not the traditional route."
Under a National Science Foundation grant to the UW Department of Mathematics, the university team worked with the high school teachers on revamping the math program, adapting a new interactive curriculum focused on problem-solving, and changing their methods of teaching.
The UW team asked teachers to visit one another’s classrooms and collect data on the kinds of questions being asked. Most, the teachers realized, were procedural questions, and inside the classrooms the teachers were doing most of the talking. "The students were doing whatever they wanted while I stood up and lectured," says the department chair, a 25-year-plus teaching veteran.
She estimated only 20 percent of students in introductory math classes were engaged participants under the old model. After a year of intense change in her classroom, she estimated at least 90 percent of students were participating.
The UW team observed in classrooms, often with video cameras trained on students. Later, they screened clips for teachers in a "Video Club," posing questions: Were the students engaged? What was their understanding of the problem? "It’s like video playback when you're training athletes," explains Horn. "You analyze the plays, then debrief."
Another grant from the Carnegie Foundation allowed the UW to help the school hire an additional math teacher for a year, freeing up an extra planning period for the staff. The team of teachers used the time for one-on-ones with students and parents, and for group strategizing. They found that working collaboratively, instead of isolated within their own classrooms, helped them more effectively hone curriculum and teaching methods to students' needs.
"There is this mythology in America of the lone super-star hero teacher, the Jaime Escalante," says Horn, referring to the Los Angeles math teacher made famous in the movie Stand and Deliver. "But you can't do it alone. A single teacher cannot close the achievement gap."
The teachers decided to use a new curriculum that had been developed through a collaboration of university researchers and classroom teachers from across the country. The UW team offered training and support to help implement the curriculum effectively. Essentially, the curriculum engages students in applied but complex mathematical problems: How can you predict the length of a shadow? How much time would it take — and what would it cost — to make a pioneering 2,400 mile trek on the Overland Trail?
Students, working in groups, began to debate central mathematical issues as teachers assured them "You can do this!" Even the most reluctant students began to weigh in. "Everyone has different mathematical abilities," says Horn. "If you have a place for that, if you allow kids to be smart, the kids start to value each other."
By year’s end, changes in the first-year math classrooms were dramatic. Students were engaged, and they were engaged in higher-level math thinking. In prior years, they might still be studying fractions come springtime. This spring, they were tackling standard deviation and other statistical concepts.
Passing rates – numbers of students with C’s or higher — in first-year math classes rose from 20 percent to 60 percent. And teachers reported seeing higher levels of understanding and engagement, even among students who were not passing.
For the math teachers, who described it as both the hardest and the best year they have spent in a classroom, it all added up. "This is by far the most growth I’ve ever made as a professional," says one classroom veteran.
Horn and the UW team are continuing their collaboration with the school, determined to help the teachers accomplish their goal of increasing student pass rates still further next year.
For more information
Video Interviews
Ilana Horn
Assistant Professor,
Curriculum & Instruction
9th grade is a critical year for learning math.
Watch video 
Math interventions for students improved their promotion to 10th grade math.
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There are many ways to be good at math, not just computation skills, but making connections.
Watch video
Math education is best with multiple teachers demonstrating problem solving skills.
Watch video
Video clubs for teachers take clips of classes to see what students are understanding.
Watch video
Video clips show where students get stuck and how they make sense of problems.
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How to improve teaching at high needs schools.
Watch video
The achievement gap is not intractable.
Watch video
Note: QuickTime and a high-speed connection are required to view videos.
...There’s a common assumption that the kids who struggle are not capable . . . They often can be really good at math, but the way they get there is not the traditional route.
—Ilana Horn
—Ilana Horn