Amid falling student scores and renewed debates about how the subject should be taught, math is in the spotlight once again.
The pandemic, which affected student learning across the board, had particularly devastating effects in math. Experts agree that supporting students in the subject will require time, money, and additional services like tutoring. But exactly what instructional approaches are likely to move the needle is the subject of decades-long debate.
The field is littered with enduring pedagogical disagreements. Among them:
- Whether teachers should spend more time explicitly teaching math procedures and content, or give students more time to puzzle out problems on their own;
- How to balance procedural knowledge, fluency, and conceptual understanding; and
- When—if ever—it makes sense to group students by ability in classrooms.
Those core disagreements are not easily resolved, in part because perspectives about explicit teaching vs. an inquiry-based approach map onto larger philosophical arguments about the purpose of education—and in part because researchers in math education and cognitive science fields often come to different conclusions about what best practice should look like.
As part of our coverage of math education, Education Week wanted to shed some light on where these divisions come from and why. To understand more about how teachers are prepared to teach math, the EdWeek Research Center surveyed a nationally representative sample of 373 postsecondary math and math education instructors in June and July of this year. Of this group, 126 taught only math courses, 142 taught only math education courses (typically as part of teacher education programs), and 105 taught both.
(The Bill & Melinda Gates Foundation provided financial support for the survey. EdWeek designed the instrument and maintains sole control over articles informed by the results.)
While K-12 teachers learn new content and techniques over time, this university education forms the foundation of their knowledge base—and just as significantly, their philosophy of education.
This first of three stories on these survey results explores how math and math education professors shape their courses: Which scholars do they introduce to students? What documents do they rely on? And what topics and practices do they cover with aspiring teachers, and expect them to master?
In sum, the results show that programs teach a mix of strategies—both explicit and more constructivist. They seem to rely less on empirical research than on textbooks and other materials; and special education gets less attention than some advocates would like. All of those findings are likely to raise fresh questions about whether programs are using the right recipe.
The experts who show up on math professors’ syllabi
When asked about which math scholars’, experts’, or practitioners’ work instructors introduce to their students, Jo Boaler topped the list, with 36 percent of math education and math instructors naming her.
Boaler, a professor of education at Stanford University, is a major figure in the math education world. Her work focuses on developing students’ math mindset—helping students see themselves as “math people” who are capable in the subject—and promoting equity in math classrooms.
“I would imagine that I’m high on the list because I have spent the last 10 years getting mathematics education out through the website YouCubed,” said Boaler, referencing a Stanford hub for math activities, lessons, and teaching guidance. (An earlier EdWeek Research Center survey, of K-12 math teachers, found that no one source, including YouCubed, was dominant in teachers’ use of instructional materials.)
“Particularly we wanted to get out the newer science that was out at that time that any student can get anything, and teachers should not promote the idea that some students don’t have a math brain,” Boaler said.
Boaler has a devoted teacher following, and she recently served as part of the writing committee for the new California Math Framework, which in general reflects many of her ideas about math. But she also has fierce critics, who argue that she has overstated research findings to promote teaching methods that are not evidence-based. Boaler has pushed back against these claims.
About a quarter of respondents listed names not included on the list of response choices. In open-ended responses, several survey participants named historical mathematicians rather than math education scholars: Fibonacci, Brahmagupta, Euclid, Carl Friedrich Gauss, Leonhard Euler, and René Descartes were all listed as examples. (Respondents to this question included both math education instructors and math professors who taught at least some future teachers.)
The survey of math and math education professors that underpins this story is part of a new thread of math coverage at Education Week. Here’s more of our math reporting:
Math Foundations: In a special report, reporters examined foundational math issues: Fact fluency, early word problems, and what we know about dyscalculia.
What’s Driving Declines in Math: For a special series, reporter Sarah Sparks investigated declines in students’ knowledge of data literacy and statistics.
A New Math Framework: Read about California’s controversial new math framework, which embodies many of the longstanding tensions in math education.
Complete coverage: Browse the latest news, analysis, and opinion about math instruction.
Still, many answers included well-known textbook authors, some of whom are or were also university professors, such as John Van de Walle, whose book Elementary and Middle School Mathematics: Teaching Developmentally was cited several times in open-ended survey responses. That finding makes sense given that many university instructors use textbooks or other instructional guides in their courses, said Sarah Powell, an associate professor of special education who studies math instruction at the University of Texas at Austin.
But it’s also a figure that gives her pause. “Books typically don’t undergo any peer review,” she said.
This is in contrast to research articles in scientific journals, which go through a rigorous peer review process. In research universities, publishing in journals matters for career advancement, Powell said. It’s a factor that’s considered when academics are up for tenure. Writing a book often doesn’t carry the same weight.
“There’s this disconnect between what’s expected in research-heavy positions and what’s expected in other positions,” she said. “Many people who write books don’t have a heavy research agenda.”
Documents that inform math education courses
In addition to math education scholars, university instructors also use some core documents to inform their classes.
Many of these have direct classroom relevance. When asked what foundational documents they use to inform their courses or introduce to their students, 77 percent of math education instructors said that they used the Common Core State Standards or state-level standards. Seventy-four percent said they used publications from the National Council of Teachers of Mathematics. The teacher professional organization is the largest math education organization in the country, and holds that math learning “is maximized when teachers focus on mathematical thinking and reasoning.”
But other practice-oriented resources weren’t as popular. Only 16 percent of instructors said that they used the What Works Clearinghouse Practice Guides in math from the Institute of Education Sciences, the U.S. Department of Education’s research wing. The practice guides are based on empirical evidence, weighted toward random-assignment studies with control groups.
It’s a figure that troubled Nicole McNeil, a professor cognitive psychology who studies math learning at the University of Notre Dame.
“It’s the best thing that they could use in my opinion,” she said, of the guides. “I don’t know why it is that IES hasn’t seemed to be able to crack through the PK-12 space to be seen as a leader, as a place for guidance. But to me, in our tutoring program, that’s what we use. That’s our No. 1 thing. Because it’s so well-resourced.”
The guides are written by researchers and outline best practices for specific grade levels, such as how to increase algebra knowledge in middle and high school students, or how to support problem-solving among 4th through 8th graders. They also include recommendations for interventions for struggling students.
When IES first started releasing these guides, they were focused heavily on findings from cognitive science and experimental psychology, rather than from the field of math education, which could have alienated researchers in that discipline, McNeil said. That’s since changed somewhat, but there’s still a “disconnect” between the fields, she said. “The world of education and schools of education haven’t yet connected up with that world of experimental psychology, math cognition.”
Other math educators weren’t as surprised to see that the What Works Clearinghouse practice guides didn’t top the list. “Classroom teachers usually do not interact a lot with research,” said Kyndall Brown, the executive director of the California Mathematics Project, a professional development network.
“They might get it secondhand from someone who’s writing about the research. Very seldom are teachers reading journal articles or research articles,” he said.
For Brown, guides and documents from organizations like NCTM are a viable alternative, he said: “[Teachers] are much more likely to read something like that than to read an actual research article.”
Translating research into practice is a notoriously complex process for teachers and professional organizations.
How instructors use class time
Math education professors spend a large chunk of time working with future teachers on the skills they’ll use in the classroom. The most commonly practiced strategies were using multiple representations, connecting new math content to prior knowledge, and explicitly modeling math skills and strategies.
Seeing that other practices were further down the list was “extremely disappointing,” said Afi Wiggins, the interim managing director of the Dana Center, a math research and technical assistance organization at the University of Texas at Austin.
Wiggins would have wanted to see future teachers get more practice with what she described as 21st century skills—items such as identifying and responding to misconceptions in math knowledge, and connecting math content to students’ personal or cultural knowledge. “That research has been out there for many, many years as critical to helping students learn,” Wiggins said.
Teachers noted that the survey responses could obscure important differences in how these skills were taught. Take using multiple representations, for example, which was the most commonly cited answer.
Often, teachers are taught to show these representations with manipulatives. But the efficacy of manipulatives depends on how teachers use them, said Brian Bushart, a 4th grade teacher in West Irondequoit Schools in New York.
Sometimes, manipulatives can help show why math works the way it does and create an “aha” moment. But they could also lead to more confusion. Ideally, he said, teachers need to know: How do they prepare and coach a class so that the core math idea arises from use of manipulatives?
Math professors also reported frequent use of another strategy: productive struggle.
Productive struggle is the idea that math learners can benefit from puzzling out difficult problems, sometimes without much teacher prompting, even if it causes some discomfort.
“More recently math educators have been trying to support classroom teachers to really get students engaged and share their thinking,” said Brown. “It makes sense to me that math educators would be modeling these kinds of strategies for their students to be able to take back into the classroom.”
Productive struggle is also a key component of math education courses at Stanford, where instructors prepare teachers to use this approach in the classroom, said Boaler.
But productive struggle is hard to do well, because it’s based on finding the right level of challenge for each student, said Powell. “If you’re doing that in a classroom of students, you cannot have one activity that meets all students exactly where they are and moves them forward.”
Preparation for supporting student needs
The survey also asked teacher educators how much time they spent preparing future teachers to work with students who struggle in math, and students with math learning disabilities.
Fifty-eight percent of instructors said they spent up to a quarter of their course covering math learning disabilities.
“One to 25 percent is not an amazing number,” said Tara Warren, a math instructional coach in the Santa Monica-Malibu Unified school district. “But I thought it was better than it has been in the past.”
The percentages didn’t surprise Wiggins, of the Dana Center. When she took math methods courses, she remembers them focusing extensively on creativity, but not as much on differentiated learning for students who might need more help or who have a learning difference. She did learn about differentiation, but in separate courses.
“Things are isolated,” Wiggins said. “When I learned about differentiated instruction, it wasn’t in the context of content.”
Approximately 5 to 7 percent of students have dyscalculia, a processing disorder that makes it harder to learn math, particularly how number symbols represent quantity. Many other students struggle more generally with math.
Powell, who studies special education, said the results about math disabilities didn’t surprise her either. “Many people draw a line in the sand for special education vs. general education,” she said.
But the responses to a question about students who struggle more generally disappointed Powell. When teacher educators were asked what percentage of their courses they spent teaching educators to teach students who struggle with math, about half said less than 50 percent, and half said more than 50 percent.
Data from the National Assessment of Educational Progress show that the majority of students in this country struggle with math, she said, referencing students who scored below proficient on the test.
“They’re spending less than 50 percent of their time thinking about how to support the majority of students who are in U.S. classrooms,” said Powell. “It doesn’t really match the percentage of students in the United States.”
Coverage of math education is supported in part by a grant from the Bill & Melinda Gates Foundation, at www.gatesfoundation.org. Education Week retains sole editorial control over the content of this coverage.