# On fidget spinners & speeded math practice

Daniel Willingham –

*I was very pleased to collaborate with Daniel Ansari, (@NumCog) a renowned authority on the cognition of mathematics, for this blog. *

Just in case you have been away from this planet for the last few months, ‘Fidget Spinners’ are the latest toy sensation. Some have suggested (without any evidence) that this new gadget is “perfect for children with attention deficit hyperactivity disorder, autism, anxiety.” Although there’s no evidence for that, kids love them, which has prompted a flurry of interest in possible educational applications (see here), and educators have come up with creative ways of integrating spinners into educational activities (when they are not banning them, see here).

One such idea was the subject of a tweet by Dan on June 14th. The idea is simple: students use the spinner as a timer and try to solve as many math fact problems as possible while it is spinning.

This seems to us a simple, harmless and perhaps even fun thing to do, and most people on Twitter took it that way. Most, but not all.

Negative responses fell into two categories. One suggested that timed practice would lead to math anxiety. The other suggested that this kind of practice might legitimize the much maligned ‘drill and kill’ approach to teaching math.

If a teacher doesn’t like an activity, that’s obviously reason enough not to use it as far as we’re concerned—we’re not in the business of advocating for particular classroom work. But we can point to the research literature bearing on the two common concerns, and based on this research, we don’t think they have merit.

Regarding anxiety: This issue has been raised most prominently by Professor Jo Boaler of Stanford University. For example, she argued in a recent blog that “…timed tests are a major cause of this debilitating, often lifelong condition [referring to math anxiety].”

First, let’s note that the fidget spinner worksheet offers timed *practice*, not timed *assessment, *which Boaler mentions. It seems to us that in a zero-stakes situation like a worksheet, the main agent of anxiety would be social comparison, an issue that teachers have plenty of experience handling.

Second, when it comes to timed assessments, the evidence for an anxiety link is still lacking. Boaler cites Ramirez et al (2013) in her blog. This article examined the relationship between working memory and math anxiety and showed, perhaps counterintuitively, that math anxiety impacts students with high working memory more than it does those with relatively lower working memory capacity. The authors argue that because math anxiety affects working memory, through intrusive thoughts and ruminations (“I can’t do this”, “I am terrible at math”), that students who typically use working-memory-demanding strategies are hit the hardest. These data say nothing about speeded math practice–the measure of math achievement used by Ramirez et al was untimed.

In a review of Boaler’s book, *Mathematical Mindset* , Victoria Simms (@DrVicSimms) writes *“*…she 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)’ (p. 38). 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.”

Again, it seems obvious to us that if a teacher feels that this sort of activity would make her students anxious, she won’t use it. But it’s not accurate to claim that research shows that this sort of activity generally makes students anxious.

What of the second concern, that students should focus on developing a conceptual understanding of math rather than being able to recall math facts speedily?

Arguments for speeded recall of math facts are not arguments against building students’ conceptual understanding of mathematics. As @MrReddyMath put it:

But cognitive scientists have long argued that there is an iterative, bidirectional relationship between the development of procedural math skills (such as being able to recall your math facts) and conceptual understanding (such as understanding the inverse relationship between addition and subtraction). That was the conclusion of the final report of the National Mathematics Advisory Panel in 2008.

It was also the conclusion of Professor Bethany Rittle-Johnson, a developmental psychologist at Vanderbilt who has extensively researched the relationship between procedures and concepts in math learning. When asked about the debate regarding memorizing math facts vs. developing conceptual understanding in a 2016 interview she said* “**Actually, I think it’s a silly argument because the evidence is pretty clear that children really need to do both things. Understanding is super-important, but understanding relies on knowing enough that you can understand it. If you have to spend all your time figuring out what two plus three is, then you can’t notice relationships between number pairs, [for example].”* Practicing math facts should be ** one** of the methods used to help students build solid foundations to scaffold their learning of mathematics.

Fine, but why, you might ask, apply the pressure of timing practice? Does speed matter?

It does. When working a complex problem you not only want to pull simple math facts from memory, you want to do so quickly, so that the other work can proceed apace. Indeed, adults with stronger higher-level math achievement retrieve math facts faster (Hecht, 1999).

And speed matters not just in *using* math facts but in learning them. Methe et al (2012) conducted a meta-analysis of interventions for basic math in single-case research and reported “we found interventions involving practice under speeded conditions and a carefully controlled instructional sequence produced the strongest effects,” echoing results from Powell et al (2009) who reported that timed practice (vs. untimed) was crucial to an intervention for struggling 3rd-graders to learn math facts, and Fuchs et al. (2013) reporting similar results for 1st graders..

It is clear, as is the case with any learning, that such speeded practice of math facts must be adaptive and appropriate for the level of the learning, and should be scaled gradually. And like everything else in a classroom, it will ideally be engaging. That’s challenging when you’re trying to develop automaticity, because it implies a certain amount of repetition. That’s why we liked the fidget spinner idea; it’s a little twist on a familiar task. It won’t be to every teacher’s taste, but we can say that there is no evidence it will prompt the problems that some feared.

Source: *On fidget spinners & speeded math practice – Daniel Willingham–Science & Education*

Wow. This article quickly moved from the topic of fidget spinners into antiquated ideas of math learning that can quite honestly be harmful to students. Instead of ranting with my reactions, here are some of the innumerable opposing viewpoints found in just a few minutes online…

From http://www.edweek.org/ew/articles/2012/07/03/36boaler.h31.html :

Until recently, we have not known the causes of math anxiety and how it affects the brain, but the introduction of brain-imaging research has given us new and important evidence. Sian Beilock, an associate professor of psychology at the University of Chicago, for example, has found that when children are put under math stress, they are unable to execute math problems successfully. The stress impedes their working memory—the area of the brain where we hold math facts. Beilock found that stressful math situations cause worries that compete for the working memory, causing it to be blocked. She also found that math anxiety has an impact on those with high, rather than low amounts of working memory—the very students who have the potential to take mathematics to higher levels.

From http://www.mctm.org/mespa/FasterIsntSmarter.pdf

Overemphasizing fast fact recall at the expense of problem solving and conceptual experiences gives students a distorted idea of the nature of mathematics and of their ability to do mathematics. Some students never survive this experience and they turn away from mathematics for years, sometimes forever. Having experienced timed tests when they were students, many adults believe that accurate, fast computation is the most significant part of mathematics. When pressed, many of these adults who dislike or fear mathematics attribute these negative feelings to experiences from their school years, especially the use of timed tests.

In addition to her own research, here are sources Jo Boaler has sited supporting the damaging effects of timed tests in mathematics (from her 2014 article, “Research suggests timed tests cause math anxiety”):

Ashcraft, Mark H. 2002. “Math Anxiety: Personal, Educational and Cognitive Consequences.” Current Directions in Psychological Science 11 (5): 181–85.

Beilock, Sian L. 2011. Choke: What The Secrets of the Brain Reveal about Get- ting it Right When You Have To. New York: Simon and Schuster, Free Press.

Beilock, Sian L., Elizabeth A. Gunderson, Gerardo Ramirez, and Susan C. Levine. 2009. “Female Teachers’ Math Anxiety Affects Girls’ Math Achievement.” Proceedings of the National Academy of Sciences 107 (5): 1860–1863. doi:10.1073/pnas.0910967107

Engle, Randall W. 2002. “Working Memory Capacity as Executive Attention.”Current Directions in Psychological Science 11:19–23.

Faust, Michael W. 1992. Analysis of Physiological Reactivity in Mathematics Anxiety. Ph.D. diss. Bowling Green State University, Ohio.

Gray, Eddie M., and David O. Tall. 1994. “Duality, Ambiguity, and Flexibility: A ‘Proceptual’ View of Simple Arithmetic.” Journal for Research in Mathemat- ics Education 25 (March): 116–40.

Harris, Pamela W. 2001. Building (Power- ful) Numeracy for Middle and High School Students. Portsmouth NH: Heinemann.

Hembree, Ray. 1990. “The Nature, Effects, and Relief of Mathematics Anxiety.” Journal for Research in Mathematics Education 21 (January): 33–46.

Kazemi, Elham, Magdalene Lampert, and Hala Ghousseini. 2007. Conceptualizing and Using Routines of Practice in Mathematics Teaching to Advance Professional Education. Report to the Spencer Foundation. Ann Arbor, Michigan, 2007.

Lambert, R. 2013. Pers. Communication. Parker, Ruth. 1993. Mathematical Power: Lessons from a Classroom. Heinemann Press.

Parrish, Sherry. 2010. Number Talks, Grades K–5: Helping Children Build Mental Math and Computation Strategies. Math Solutions: Sausalito.

Ramirez, Gerardo, Elizabeth A. Gunderson, Susan C. Levine, and Sian L. Beilock. 2013. “Math Anxiety, Working Memory and Math Achievement in Early Elementary School.” Journal of Cognition and Development 14 (2): 187–202.

Richardson, Frank C., and Robert L. Woolfolk. 1980. “Mathematics Anxiety.” In Test Anxiety: Theory, Research, and Application, edited by Irwin G. Sarason, pp. 271–88. Hillsdale, NJ: Lawrence Erlbaum Associates.

Richardson, Kathy. 2011. “What Is the Distinction between a Lesson and a Number Talk?” http://mathperspectives .com/pdf_docs/mp_lesson_ntalks_ distinction.pdf

Schwartz, Laurent. 2001. A Mathemati- cian Grappling with His Century. Bern: Birkhäuser Basel

Seeley, Cathy. 2009. Faster Isn’t Smarter. Sausalito, CA: Math Solutions Publications.

Young, C.B., Sarah Wu, and Vinod Menon. 2012. “The Neurodevelopmental Basis of Math Anxiety.” Psychological Science Online First. March 20, 2012. doi:10.1177/0956797611429134

The problem isn’t about a two minute speed drill it’s the belief from pushing content over mastery of facts is the only way. Wouldn’t you want to make sure all the kids could do their tables with speed and accuracy?