On February 28th Stanford Professor Jo Boaler and one of her students, Tanya Lamar, published an article that we think is a fine example of how not to draw educational conclusions from neuroscientific data. While we’re more interested in applauding great work than pointing out problems, we feel we can’t ignore an article in a high-profile venue like Time Magazine.

The backbone of their piece includes three points:

- Science has a new understanding of brain plasticity (the ability of the brain to change in response to experience), and this new understanding shows that the current teaching methods for struggling students are bad. These methods include identifying learning disabilities, providing accommodations, and working to students’ strengths.
- These new findings imply that “learning disabilities are no longer a barrier to mathematical achievement” because we now understand that the brain can be changed, if we intervene in the right way.
- The authors have evidence that students who thought they were “not math people” can be high math achievers, given the right environment.

There are a number of problems in this piece.

First, we know of no evidence that conceptions of brain plasticity or (in prior decades) lack of plasticity, had much (if any) influence on educators’ thinking about how to help struggling students. More to the point, conceptions of cellular processes should not influence specific educational plans or general educational outlook. The notion of the brain lacking plasticity obviously was not taken at face value by educators, nor should it have been—an unchangeable brain would be a brain incapable of learning. (For more on the difficulty of drawing educational implications from neuroscientific findings, see here and here)

Second, Boaler and Lamar mischaracterize “traditional” approaches to specific learning disability. Yes, most educators advocate for appropriate accommodations, but that does not mean educators don’t try intensive and inventive methods of practice for skills that students find difficult. Standard practice for students with a specific reading disability, for example, includes intensive practice in decoding and yes, educators have thought of the idea of trying methods other than the ones that a student seems not to learn from—methods that the authors, at the end of the article, mention were suggested for her daughter with dyslexia and auditory processing difficulties.

Third, Boaler and Lamar advocate for diversity of practice for typically developing students that we think would be unremarkable to most math educators: “making conjectures, problem-solving, communicating, reasoning, drawing, modeling, making connections, and using multiple representations.” More surprising is their charge that “There are many problems with the procedural approach to mathematics that emphasizes memorization of methods, instead of deep understanding.“ We agree with the National Mathematics Advisory Panel report that students should learn (and memorize) math facts and algorithms. We also agree with the Panel (and with Boaler and Lamar) that American students struggle with conceptual understanding. Deep understanding is always more difficult than memorization, and it’s the aspect of mathematics that most kids struggle with, but that doesn’t mean that most math educators don’t care if their students understand math. In our view there is no need to reinvigorate the math wars since an overwhelming body of scientific evidence has demonstrated that students need both – procedural fluency and conceptual understanding. One cannot develop one without the other. In our view it is best to lay this false dichotomy to rest and avoid emotive and value laden arguments such as that students who are strong in conceptual understanding of math are more creative.

Fourth, we think it’s inaccurate to suggest that “A number of different studies have shown that when students are given the freedom to think in ways that make sense to them, learning disabilities are no longer a barrier to . Yet many teachers have not been trained to teach in this way.” We have no desire to argue for student limitations and absolutely agree with Boaler and Lamar’s call for educators to applaud student achievement, to set high expectations, and to express (realistic) confidence that students can reach them. But it’s inaccurate to suggest that with the “right teaching” learning disabilities in math would greatly diminish or even vanish. For some students difficulties persist despite excellent education. We don’t know which article Boaler & Lamar meant to link to in support of this point—the one linked to concerns different methods of research for typical students vs students identified with a disability.

Do some students struggle with math because of bad teaching? We’re sure some do, and we have no idea how frequently this occurs. To suggest, however, that it’s the principal reason students struggle ignores a vast literature on learning disability in mathematics. This formulation sets up teachers to shoulder the blame for “bad teaching” when students struggle.

As to the final point—that Boaler & Lamar have evidence from a mathematics camp showing that, given the right instruction, students who find math difficult can gain 2.7 years of achievement in the course of a summer—we’re excited! We look forward to seeing the peer-reviewed report detailing how it worked.

In sum, we think that findings from studies of brain plasticity do not support the implications that Boaler and Lamar suggest they do. Further, we think they have mischaracterized both the typical goals of math instructors, and the typical profile of a student with math disability.