Special Report: Special Report:Leveling the Playing Field in Math
Are Math Coaches the Answer to Lagging Achievement?
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American children largely struggle in math, national and international exam results show. Could providing their teachers with dedicated math coaches help?

Educators say math is a subject that's particularly ripe for instructional coaching. There has long been concern that teachers' preparation in math content, especially in the elementary and middle grades, is weak. With the shift to tougher math standards over the past decade, teachers are also taxed with having to teach the subject in ways different from how many of them were taught. Plus, research suggests that teachers can subconsciously pass on their own attitudes about math to students, including anxiety, which can hurt student achievement.

Most important, a sizable body of research shows that one-on-one coaching can improve instructional practice and student achievement, more so than other professional-development offerings for teachers. Much of the research focuses on literacy coaching, but a growing number of studies have found positive effects in math coaching, too.

"You're helping teachers to understand the mathematics they're teaching so they know how to support the student experience," said Mona Toncheff, the president of the National Council of Supervisors of Mathematics, on the role of math coaches.

Just 3 percent of elementary teachers and 45 percent of middle school math teachers have a degree in mathematics or math education, according to the 2018 National Survey of Science and Mathematics Education. (In contrast, 79 percent of high school math teachers have a degree in their fields.) And analyses have shown that in many teacher-preparation programs, future teachers tend to take math-methods courses that cover instructional strategies rather than courses steeped in math content.

"Some K-5 teachers have literally told me, 'I became an elementary teacher because I didn't like math,' " Toncheff said. "Part of mathematical coaching is helping develop [teachers'] mathematical identity in a more positive way."

Because coaches are in the trenches with teachers, their help is relevant and timely, experts say. As a middle school math coach and interventionist in De Pere, Wis., Adrianne Burns offers resources, helps teachers thoroughly understand math content and the curriculum's progression, and guides teachers through deciding which direction they want to take in their lessons.

Instead of teachers attending stand-alone professional-development workshops, math coaching "just becomes part of our everyday meetings: This is what they're struggling with; let's talk about how they can do it," Burns said. "The coaching becomes just having another teammate."

According to 2015-16 federal data, the most recent available, 18 percent of the nation's public schools have a math coach. But coaching is costly, as much as six to 12 times more expensive than short-term PD workshops, according to a 2012 study by David S. Knight of the University of Texas at El Paso.

As school districts prepare to tighten their budgets in the wake of an anticipated coronavirus-inflicted recession, experts worry that the investments in math coaching will fall by the wayside. Already, in many districts, math coaches are tapped for administrative duties or other roles.

What Works

For math coaching to be successful, Toncheff and other experts say, coaches need to be full time and in the classroom as much as possible-observing teachers, listening to student conver-sations about math, and providing feedback about what makes good math instruction. They need access to student data. And they need their own professional development on how to support adult learners.

"It's not just, you go in the classroom once and expect a transformational change in instruction, but it's ongoing," Toncheff said. "There's follow-up."

This type of collaborative, intensive math coaching is hard to do if coaches have other responsibilities, experts warn. "Trying to empower teachers is at the forefront of a math coach's mind, and if they are tied to other things-teaching their own classes, spread across multiple subjects-it's much harder to do that," said Aimee Ellington, a math professor at Virginia Commonwealth University.

In a two-year study, published in 2017, Ellington and her colleagues found that when middle school teachers were highly engaged with math coaches, they were more likely to help students explore mathematics through making sense of the concepts for themselves rather than using predetermined algorithms or procedures. Their students also scored higher on the end-of-year math tests than their peers in classes where the teacher had access to the coaches but was not engaged.

"[A teacher] working regularly, consistently with the coach to improve math instruction for students is the key," Ellington said. "Just having somebody in the building to provide help if teachers happen to ask isn't enough."

It takes time for coaches to win teachers over, she said. Math coaches typically spend the first year of a new program getting to know teachers and helping them realize that their work is not evaluative. In the 2017 study, the percentage of teachers who were highly engaged with the coach increased from 40 percent in the first year to about 52 percent in year two.

After all, getting buy-in from teachers can be tricky. Coaching "can have that stigma that 'I'm not doing something right, and that's why the coach is in with me,' " said Burns, the Wisconsin coach.

This is just the second year that Burns has coached in the school-and the first time the De Pere school has ever had a math coach. Burns said she's trying to build a culture of support and continuous improvement through attending all the professional learning community meetings and offering help with evaluation goals. She wants teachers to see her as a valuable ally in math instruction.

"Everybody can improve their teaching-there's always things we recognize we can do better," she said. "Teachers don't know that they need a coach, because they didn't know there was this thing they could be doing that a coach could help with."

Threats to Quality

If coaching is going to fulfill what many see as its potential to lift the quality of math instruction, it will have to be scaled up-and, some say, it will have to cost less. Research has found that in general, the effectiveness of a coaching program declines as the number of teachers who are being coached increases. And yet more teachers in a program generally reduces the per-teacher cost.

"It's quite possible that in bringing coaching to scale, we're going to dilute its effectiveness so much that it's not an effective program," said Matthew Kraft, an associate professor of education and economics at Brown University.

To address concerns about cost and effectiveness, Kraft and Harvard University education professor Heather C. Hill created and studied a virtual math-coaching program that could potentially be a cheaper way for districts to have dedicated math coaches. The program was based on a framework that was co-developed by researchers at Harvard and the American Institutes for Research. It centered on practices aligned to the Common Core State Standards, such as rich meaning-making and encouraging student questions.

On average, teachers in Kraft and Hill's study participated in about 10 coaching cycles over the course of a school year. In each, they identified an instructional practice they wanted to work on, filmed a math lesson, and then received feedback remotely from a coach. The coach also helped them plan future instruction.

The coaching took place only during the first year of the study, but researchers continued to track participating teachers' work for a second year. They found that teachers were delivering richer, more student-centered instruction after participating in coaching, which was sustained even after the coaching stopped. Students also reported that their teachers' instruction improved. But there was a catch: Test results did not show a significant increase in student learning.

"We found that the distance-based coaching program, in not a small way but in a sizable, meaningful way, substantially changed the quality of mathematics instruction," Kraft said. "It was both surprising and disappointing that we didn't see a corresponding increase in either [student scores] on the state standardized test or a formative assessment."

That might have been the result of tests that didn't capture deeper learning, effects that were too small to distinguish from those that might be due to chance, or identification of the wrong teaching practices as effective, Kraft said.

Further research, he said, should focus on what type of coaching model is more effective-directive or reflective? in-house or distance-based?-as well as how many times a coach should meet with a teacher in order to get results. He also wants to find additional ways to maintain coaching's effectiveness while keeping it affordable for districts.

The price tag will be increasingly an issue this fall, as districts brace for a precipitous drop in state funding because of the pandemic's impact on the economy. In the past, said Ellington of Virginia Commonwealth University, districts have been creative in how they find funding for math coaching, but she's worried that those programs could now fall to the chopping block.

Even now, with school buildings closed, math coaches are playing an important role in instruction, she said. The math coaches she works with in Virginia have pulled together packets to send to parents, helped teachers do online remote instruction, and worked with administrators to decide how the math curriculum should look for the rest of the disrupted school year.

As budgets take shape for the coming school year, Ellington predicted, calls will be made for more classroom teachers and fewer coaches. But thinning the ranks of coaches would be a mistake, she said. They are the ones who "keep math [learning] moving during these times."

Special Report: Special Report:Leveling the Playing Field in Math