Professor Jo Boaler of Stanford University in the U.S. has released a statement on the Stanford website. It appears she has been contacted by a journalist working on a story and this is her preemptive response.

In the statement, Boaler outlines some appalling incidents of threats and abuse. I condemn these threats and this abuse. Such incidents are deplorable. If anyone who reads this Substack has participated in or condones such behaviour then please unsubscribe now.

I also think Boaler is profoundly wrong about mathematics education. In her statement, Boaler writes that, “Academic disagreement is an inevitable consequence of academic freedom, and I welcome it.” It is in this spirit that I write the rest of this post.

Embedded in Boaler’s statement is a link to a document in which she responds in detail to some of the criticisms levelled at her. These criticisms are quite different from threats and abuse. One of them addresses, “Research on Timed Testing and Math Anxiety.”

Maths anxiety is different to anxiety more generally. It is a debilitating condition that affects maths performance and can lead to students avoiding maths. Combatting maths anxiety is therefore a key issue for maths educators.

For many years, Boaler has claimed a connection between timed maths tests and maths anxiety. For instance, in 2012, Boaler claimed, “…research… has shown that timed tests are the direct cause of the early onset of math anxiety.” There is no reference provided for this claim. In 2018, Boaler made a similar claim in *American Educator* that, “For about one-third of students, the onset of timed testing is the beginning of math anxiety.” This time, Boaler provided a reference to a page on her YouCubed website.

When I read the *American Educator *article, I was reminded of a similar claim made in Boaler’s 2015 book, *Mathematical Mindsets *that used the same reference. Reviewing this book, Professor Victoria Simms, an academic from Northern Ireland, noted that the references Boaler gave for this claim led to a dead end:

“[Boaler] discusses a purported causal connection between drill practice and long-term mathematical anxiety, a claim for which she provides no evidence, beyond a reference to “Boaler (2014c)” (p38). After due investigation it appears that this reference is an online article which repeats the same claim, this time referencing “Boaler (2014)”, an article which does not appear in the reference list, or on Boaler’s website.”

The 2018 article in *American Educator* led to the same dead end. I therefore contacted the editor of *American Educator*. After I did this, the article on the *YouCubed *website was updated. The claim that, “For about one third of students the onset of timed testing is the beginning of math anxiety,” now references this paper that Boaler wrote for the *National Council of Teachers of Mathematics (NCTM)* in April 2014 — although at the time of writing, the link to it from the *YouCubed* site appears to be broken.

It is hard to find a smoking gun in the *NCTM* paper. At one point, Boaler explains how she asked students to write about how they felt about tests and about a quarter of the students’ responses indicated anxiety. However, there is no reference for this research so we cannot evaluate the design of the study. And a quarter does not equal a third.

The closest we approach to a directly relevant paper is the following:

“…researchers now know that students experience stress on timed tests that they do not experience even when working on the same math questions in untimed conditions.”

If substantiated, this would imply that timed tests cause anxiety because that is the only factor varying between the two conditions. I would still want to see how the study was done and whether it showed this happened for a third of students, as claimed. There would probably be room for discussion and debate, but at least we would have a reference relating to the original claim. Unfortunately, the reference given is ‘Engle 2002’. Looking this up in the references takes us to the article *Engle, Randall W. 2002. “Working Memory Capacity as Executive Attention.” Current Directions in Psychological Science 11:19–23. *As the name of the article implies, this has nothing at all to do with timed tests and maths anxiety.

This appears to be a simple error because this paper is referenced elsewhere in the *NCTM* paper in a way that makes sense. It looks like we are missing a reference and that Boaler could clear this up if she pointed us to the reference she intended to make.

In her recent statement, Boaler has not chosen to do this. Instead, Boaler makes the following point about the claim that, “For about one third of students the onset of timed testing is the beginning of math anxiety…”:

“I have responded [to the journalist] that this statement is clearly an estimate, that draws from different scientific papers and decades of work in schools.”

Clearly an estimate? Really? What, then, was the research Boaler was referring to in 2012 when she wrote that, “…research… has shown that timed tests are the direct cause of the early onset of math anxiety.” Where does the figure of one-third come from? Is it really just an estimate? What was the paper that Boaler intended to reference in the *NCTM *article?

It is not clear.

Boaler then lists a series of six papers that she suggests, “support my estimate and the links between anxiety and timed testing.” It seems odd to me that two of them date from 2016 and 2019 i.e. after Boaler first started making her claims about timed testing and maths anxiety.

I have not reviewed all these papers. A quick look at the first paper shows that in its discussion of timed tests, it references the third paper, so there are plenty more rabbit holes to explore.

Why does this matter? Given some of the awful comments Boaler has endured, should I simply stay away from this whole area?

It matters if teachers are avoiding the use of timed tests because they believe that ‘research shows’ they cause maths anxiety. Timed tests have the potential to ensure maths facts are embedded in long-term memory and there is evidence that interventions that target such facts through timed tests improve students’ maths skills. In one case, Boaler has cited such a study herself.

For what it’s worth, I think timed tests *could* induce maths anxiety, depending on how they are presented to students by the teacher. If they are seen as high-stakes make-or-break competitions, then I can imagine this freaking students out. On the other hand, if the teacher plays them down, makes them fun and suggests the stakes are low, they could be an effective and productive teaching strategy.

*Update: The story has now been published in The Chronicle of Higher Education*

There's no such thing as math anxiety.

OK, I admit that's provocative. After all, lots of people take math and experience anxiety, so how can it make sense to say that there's no such thing as math anxiety? What I question is Boaler's (and others') claim that there are lots of students who are highly proficient in math who experience a mysterious surge in anxiety when they are in a testing situation, and as a result can't function properly. In my experience, this never happens. Instead, when a student comes to me and explains that they "really understand the concepts" but when the test came along they experienced some sort of "math anxiety", I inevitably find with a few simple questions that in reality they don't understand the material and can't solve the problems, even in a low-stress environment. Instead, they vastly overestimate their competence (see Dunning-Kruger).

A lot of math education in the US is based on collaboration and group work. Also, many instructors are less concerned with getting the correct answer, and will grade charitably if the student can somehow display some form of "conceptual" understanding. Whatever the merits of this approach, it allows weak students to drift along, delusional in their belief that they are developing strong math skills. Once they get into a test however, they can't rely on the group to carry them through, and the test is marked so that they really do have to get the right answers.

So, sure, students experience anxiety on math tests. Even I concede that. But that anxiety isn't some mysterious psychological affliction that descends on talented students with strong math skills. Rather, the anxiety is caused because it's only on the test that students are confronted with the fact that they don't really understand the material. To be honest, I've been there myself, and I know firsthand that it's a very unpleasant experience -- after all, you can fake your way through an English exam, but if you can't solve a problem it's difficult to hide that fact.

Here's my cool innovative idea for resolving math anxiety: explicitly teach students methods for solving problems, and then give them lots of hands-on practice to develop procedural fluency. I do, we do, you do.

From my experience a lot of anxiety students have about high stakes testing comes from teachers themselves.