The great divide: Set up 'productive struggle' or teach math step by step?

When I was a kid, some people thought that if you threw a kid in the water, he'd learn how to swim. Others thought that was too risky. Maybe the athletically talented would swim, but many would sink.

Leading math education researchers think students will understand math more deeply if they try to solve challenging, open-ended problems before they're explicitly taught, writes Sarah Schwartz in Education Week. It's called "productive struggle."

Special-education researchers argue that direct, systematic instruction -- teaching math step by step, with chances for students to practice -- is more effective. Many students -- not just those with disabilities -- struggle with math, they say. Adding struggle is more frustrating than productive, they argue.

"States such as California and major math education groups have embraced inquiry-based math education, writes Schwartz. Students are supposed to discuss math ideas and develop theories before the teacher provides guidance.

But the “science of math” movement, led by special education professors, is pushing back. Drawing on the success of the “science of reading,” they argue that students need "systematic, explicit instruction and guided practice . . . to develop foundational knowledge."

Both general and special educators want to students to develop conceptual understanding, concludes a new paper based on interviews with researchers. However, special educators measured math success by outcomes such as mastering standards and being prepared for more advanced courses in high school and college, while generalists focused on "broader goals, like finding 'joy' in math, or using it to engage in civic life," Schwartz writes. They more often wanted "to reimagine why we learn mathematics.”

The math generalists "prioritized inquiry, arguing that classrooms should be weighted toward student discourse over teacher-directed instruction, and that students should try tackling problems first before teachers modeled how to solve them," she writes. Special education researchers reversed the order, saying "teachers should use explicit instruction to break down complicated processes first, guide them through examples, and then give students the opportunity to try challenging problems."

Schools are adopting new instructional materials that rely on "inquiry approaches and discourse-heavy pedagogy,” said Julie Cohen, a University of Virginia education professor who was lead author on the study. Students who struggle in math will need extra scaffolding and guidance, she predicts. But, top math education researchers don't want step-by-step instruction for anyone.

General education researchers had little familiarity with math disabilities, the study found. Special ed researchers rarely discussed "how social factors, like race and power, could influence classroom dynamics and shape whether kids saw themselves as math people," said Cohen.

Some states are requiring schools to use "evidence-based" math teaching, writes Schwartz. But there's no consensus on what the evidence says.

In 2024, the National Council of Teachers of Mathematics and the Council for Exceptional Children issued a joint statement in an attempt to reach common ground, she writes. It said students with disabilities should be “provided with appropriate supports.” Among the recommendations are that teachers “position students with disabilities as valuable owners of and contributors to the mathematics being learned,” and “build meaningful connections between concepts and procedures.”

More than 30 special education researchers signed a letter calling many of the recommendations “merely beliefs and philosophies without significant and rigorous research to support them.” The letter called it "educational malpractice" to ignore the strong research base supporting systematic, explicit instruction.

When I was an op-ed columnist, my goal was to motivate people who read the first sentence to read the second sentence. The second sentence would make them want to read the third sentence, and so on. Sometimes, I'd be very clear, but other times I'd plunge into a scene or anecdote and not explain it till the second or third paragraph. A little mystery -- what's happening here? -- would hook readers, I thought. But too much would be confusing, and readers would bail. You can't make people struggle for very long before they give up.