In a new paper, Stanford professor Jo Boaler argues that math teachers should use more visual approaches in their classrooms, including encouraging students to use their fingers to count and represent quantities.
Boaler, a sometimes-divisive figure among math academics and educators, cites brain research showing that the dorsal visual pathway is involved when people do mathematics tasks. She also points to evidence that people visualize a representation of their fingers when they are doing math, even when they are not using their fingers in the calculation.
But in U.S. classrooms, math is “presented as an almost entirely numeric and symbolic subject,” she says, and students consequently miss out on enhancing their visual math skills.
“Despite the clear evidence on the importance of finger use, dangerous instructions to ban finger use are communicated to teachers and parents,” she writes. “Telling students not to use their fingers to count or represent quantities is akin to halting their mathematical development. Fingers are probably our most useful visual aid, critical to mathematical understanding and brain development, that endures well into adulthood.”
Finger perception is so important, she and her co-authors argue, it may explain why pianists and other musicians “often display higher mathematical understanding.” She and her colleagues have developed a variety of visual math activities available on her youcubed.org website.
Too Much Memorizing?
Boaler has long contended that math education in the United States puts far too much emphasis on memorization and timed tests. In an interview last year, she told me that she herself hasn’t memorized all her times tables—instead she uses number sense to come to the answers quickly. “It’s not that it’s not useful to memorize things, but we do way too much of it,” she said. “If kids get the idea that’s what math is, we have problems. And not just with them understanding it, but with them liking it.”
That blog post incited a host of comments—many of them angry—both from readers who defended memorization and from those who said Boaler misunderstands what’s going on in schools.
Much of Boaler’s recent work has looked at how growth mindsets can affect math achievement. At the recent National Council of Teachers of Mathematics conference, Boaler received a hero’s welcome, by some accounts. But previously, the validity of one of Boaler’s seminal research studies was questioned by fellow academics.
A version of this news article first appeared in the Curriculum Matters blog.