Math needs knowledge building, too

An interview with Sarah Powell on the role of knowledge in math success

Happy summer Friday, Bell Ringers! Today’s letter is shining a light on the role background knowledge plays in math, with professor and math education expert Sarah Powell. It’s not just the math content that students need stored in their long-term memory—read on for a new frame of how to think about knowledge building for math.

Over the last few years, schools and teachers have begun to realize the importance of building students’ background knowledge when it comes to new learning. Research has shown that background knowledge makes learning new material easier and richer for a variety of reasons—increased vocabulary and knowledge in art, history and science bolsters reading comprehension, for example, while greater stores of knowledge in long-term memory eases cognitive load and makes it easier for new knowledge to stick.

The idea that prior knowledge is key to learning—“What you know determines what you see,” as Paul Kirschner wrote more than 30 years ago—is a relatively new one to American education. Most teachers say they never learned about the role of knowledge, long-term memory and working memory in their training.

But now things are beginning to change. Books like Natalie Wexler’s The Knowledge Gap and the work of cognitive scientists like Dan Willingham have spurred national attention to helping increase kids’ knowledge of geography, history and science topics, including ‘knowledge-building’ ELA curricula like Core Knowledge and Wit & Wisdom. Academic texts like the recent Developing Curriculum for Deep Thinking: The Knowledge Revival (a recent Bell Ringer book club pick—you can watch our reader discussions here and here) outline how knowledge works in the brain, and then dissects how educators can help build the “web of knowledge” in students’ minds that leads to analyzing and deep thinking.

Yet the same push to focus on building background knowledge hasn’t happened in math—even though it plays just as important a role in student success. “Everything in math requires background knowledge and knowledge of math language,” said University of Texas at Austin professor and math education expert Sarah Powell.

“We really need to be thoughtful about how all of this knowledge works across grade levels and even into our adult life, so that people actually understand math instead of just all these bits and pieces of math,” she said.

Because math is entirely cumulative—new skills are built upon already mastered ones constantly—background knowledge plays an essential role in everything students do, Powell said, in ways that go beyond the basic math content. Students need knowledge of math vocabulary and strategies. Word problems, which are quite complex, require stores of knowledge in reading and language as well as being able to do the math.

Powell, who spends much of her time training math teachers, said a knowledge-building movement for math looks different than for reading. In a recent interview, she outlined how teachers and schools can think about intentionally building knowledge in math.

Building math knowledge

Math vocabulary is essential background knowledge, and often overlooked.