In search of the 'science of math'

Indiana revamped reading instruction two years ago, and now hopes to reform math instruction, reports Chalkbeat's Aleksandra Appleton. A bill in the legislature would require teacher preparation use "evidence-based" strategies to promote "conceptual understanding, procedural fluency and real-world problem solving." It also requires screening K-2 students, and providing tutoring or other help for those who need it. Middle-schoolers who test as proficient would be automatically enrolled in advanced classes.

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"But while Indiana followed in the footsteps of states like Mississippi to implement the principles of the science of reading, the template for overhauling math isn’t so clear-cut," writes Appleton.

In recent decades, schools have stressed conceptual understanding rather than procedural fluency, said Sarah Powell, a University of Texas professor. The problem is that “people learn through modeling or practice,” she said. “You watch a YouTube video, pause it, practice, and finally you can tile your bathroom.”

If students don't get enough modeling and practice in how to solve problems, they're confused, say advocates of explicit instruction. And they don't understand the concepts either.

Enrique Galindo, an associate professor of mathematics at Indiana University, believes legislators shouldn't mandate how to teach. He adds, that too much focus on procedures “doesn’t develop the kind of thinkers we need today to be successful in society. We need to prepare students who are problem solvers, who understand what they’re doing,” not just how to get to the right answer.

In both reading and math, progressive educators want to skip the boring basics to get to the "deeper learning." I don't think it works very well.

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New York City's plan to improve math achievement faces pushback from teachers, who says it leaves struggling students behind, reports Sarah Schwartz in Education Week.

NYC Solves requires high schools to adopt Illustrative Mathematics to teach Algebra 1, she writes. It "prioritizes a problem-based approach" focused on "grappling with, and discussing, real-world scenarios that involve math."

“So many of the questions are so overwhelming for kids, because they don’t allow for kids to process the information,” says Bobson Wong, an Algebra 2 teacher. “They don’t allow for kids to practice the requisite skills they need to solve the equations.”

As the creator of Illustrative Math sees it, learning to do math is like learning how to ride a bicycle. Kids don’t watch adults ride and pick up the skill that way; they have to get on and pedal themselves, said William McCallum, an emeritus professor of math at the University of Arizona. “There is an underlying principle that we believe in, that kids learn math by doing math rather than by watching someone else do math,” he said.

One side of the "math wars" argues that students will learn more if they work with classmates to tackle complex problems they haven't been taught how to solve, writes Schwartz. "Productive struggle" is better than memorizing procedures, say advocates.

The other side believes in explicit instruction. "Teachers model new skills, students practice them with teacher guidance, and only then do they apply them on their own," she writes. "Those who use this 'I do, we do, you do' method say that it shores up the crucial foundational skills students need to tackle higher-order concepts."

"Conceptual understanding and procedural fluency develop in tandem and build off of each other," research shows. "But there’s not much consensus about how to structure lessons and units in ways that attend to both of those two goals," writes Schwartz.

Wong thinks learning math isn't like riding a bicycle. “Math is a language. You learn a language by observing patterns and applying them.”