# PROOF POINTS: Do math drills help children learn?

One of the most hotly contested teaching practices concerns a single minute of math class.

Should teachers pull out their stopwatches and administer one-page worksheets in addition, subtraction, multiplication and division? Speed drills are such a routine part of the weekly rhythms of many math classrooms that they’re often called Mad Minute Mondays. Critics say these timed drills aren’t useful and instead provoke math anxiety in many children. The National Council of Teachers of Mathematics urges teachers to “avoid” timed tests. But advocates insist that these tests, which last one to five minutes, help children memorize math facts, freeing up their brains to tackle more challenging math problems.

This long-running debate captured my attention again because a group of more than a dozen education researchers, who founded an organization they call the “Science of Math,” declared that the stopwatch skeptics are wrong. The researchers built an entire webpage to set the record straight and devoted a section of a 2022 paper to explaining why it’s a myth that timed tests cause anxiety. A few readers contacted me after I first wrote about the Science of Math movement earlier in May 2023, urging me to look at the group’s claims about timed tests. After looking at the research, I think the evidence is not quite as clear as the Science of Math group indicates.

The group argues there is no evidence that timed tests cause math anxiety. They also contend that timed tests improve math performance. Some researchers contest both points.

“Time tests don’t cause math anxiety?” said Jo Boaler, an education professor at Stanford University who is a prominent opponent of timed tests. “I could counter their studies with many more that show the opposite. And yes, you could conclude it’s a contested field, that there’s different evidence. But you can’t conclude that this is a myth.”

#### Dueling evidence

There isn’t much dispute about the lack of empirical evidence. I interviewed more than a half dozen math experts who confirmed there aren’t well-designed experiments that prove timed tests cause math anxiety. The Science of Math group could find only two experimental studies that have attempted to test the hypothesis and neither concluded that tests produce anxiety.

Math anxiety is difficult to measure, and even children who enjoy timed drills may experience an elevated heart rate, an aspect of anxiety, as they race through a sheet of sums. Distinguishing productive adrenaline rush from detrimental anxiety isn’t easy. It’s also complicated to disentangle whether timed tests are making matters worse for children who already have math anxiety from other causes. There’s evidence for and against even within studies.

Ideally, you would need to design a multi-year study — where some children were randomly given speed drills and others not, but were all taught the same way — and see what their math achievement and math anxiety levels were at the end of high school. That study doesn’t exist.

What does exist are dozens, perhaps hundreds, of studies that document the stories of people who describe how much they hated timed tests. Interview excerpts like this one from a 1999 study of college students who were training to become math teachers are typical:

“If I am timed, I get nervous and forget everything. I do the ones I know, but then I get stressed that I’m not thinking fast enough and forget. I worry about finishing, and I can’t remember it even if I do know it. It is horrible. I get nervous just thinking about it.”

Others explained how they decided they weren’t a “math person” during these time-pressured moments and lost interest in the subject.

First-person testimonials are sufficient evidence for some that timed tests are harmful. For others, subjective reflections like this, no matter how many and how emotionally compelling, still fall short of scientific proof. At the same time, we also don’t have compelling scientific evidence to prove that timed tests aren’t harming children. I think it remains unknown.

#### Citation clash

Several math education experts questioned the Science of Math group’s scientific evidence on their second claim, that “timed tactics improve math performance.” One critic, Rachel Lambert, an associate professor in both special education and mathematics education at University of California Santa Barbara, had one of her classes analyze the group’s citations about timed tests, as an assignment on how to analyze education research. She showed me a spreadsheet of instances where the citations didn’t back their claims. In some cases, the studies contradicted their claims and found that students performed worse under timed conditions. “They’re calling themselves the Science of Math,” said Lambert. “But they’re not being careful in their citations.”

I found several of the citations confusing, too. Corey Peltier, an assistant professor of special education at the University of Oklahoma and one of the founders of the Science of Math group, explained that the primary purpose of the webpage and the article was to dispel the myth that timed tests and other timed activities cause anxiety. “We weren’t writing about how timing affects math performance,” he said via email. “Rather we were writing about whether timing causes math anxiety.”

Confusing citations or not, the more pressing question for math teachers and parents is whether there is evidence in favor of timed tests. The U.S. Department of Education seems to side with the Science of Math folks and against the National Council of Teachers of Mathematics. A 2021 guide for teachers on how to assist elementary school students who struggle with math recommends regular timed activities – not necessarily tests – to help children build fluency with addition, subtraction, multiplication and division. The What Works Clearinghouse, a unit of the Department of Education that vets research, and an expert panel found 27 studies to back timed practice and called that a “strong” level of evidence.

#### Games vs. the stopwatch

These 27 studies suggest that timed activities – not in isolation, but in conjunction with larger interventions – help children learn math. In one 2013 study, struggling first graders received math tutoring three times a week and were split into two groups. One played untimed games to reinforce the lessons. The other was subjected to speed practice, where the children worked in groups to try to answer as many math flashcards correctly as possible within 60 seconds. Each time they were encouraged to “meet or beat” their previous score. After 16 weeks, the children in the speed practice group had much higher math achievement than the children who had played untimed games.

Children in the speed group answered more math facts correctly each day, the researchers found. The sheer volume of correct responses helped the children commit more math facts to long-term memory, according to Lynn Fuchs, who led the study. Cognitive scientists call that spaced retrieval practice, a proven way of building long-term memories, and children in the speed group got more of it.

“That gives children an advantage as they progress through the math curriculum,” said Fuchs, a professor of education at Vanderbilt University. “A lot of kids will develop fluency on their own without any fluency building practice. But to say we can’t do that in classrooms is to deny the opportunity to develop fluency for a significant portion of children.”

Fuchs and other advocates question why timed practice is so controversial in math when it’s common in other fields. Musicians repeat scales by the rapid tick of a metronome and athletes do speed drills to build muscle memory. “In all walks of life, the strongest musicians, the most skillful athletes, they do drills and practice, drill and practice,” said Fuchs.

Opponents of timed tests also want children to automatically know that seven times eight is 56 instead of conceptually thinking it out each time (7+7+7+7+7+7+7+7), but they say that there are games and other less stressful ways to do it. Fuchs’s study is one of the few to directly test timed versus untimed conditions and we need more studies to replicate her findings before we can conclude that speed is considerably more effective and harmless to children.

Both sides of this debate are concerned with working memory, the ability to temporarily hold information in your head in order to process it, think and solve. One side worries that timed tests can produce so much anxiety that it overwhelms the working memory and prevents a child from learning. The other side wants to free up working memory to handle more complicated math problems by making basic arithmetic calculations automatic, and it believes the most effective road to automaticity is through speed drills. While the causes of math anxiety are debated and mysterious, many in the pro-drill camp suspect that children might feel less math anxiety if they became more proficient in the subject, which is something that drills might help accomplish.

#### Advice for math teachers

What can classroom teachers take away from this debate? I turned to a veteran researcher, Art Baroody, professor emeritus at the University of Illinois at Urbana-Champaign, who spent his career studying the best ways to teach counting, numbers and arithmetic concepts to young children.

He agrees that timed tests can be used effectively, but he is apprehensive about a blanket recommendation for teachers to use them. “Timed tests are an educational tool and like any tool can be used to good, no, or bad effect,” he said. “Unfortunately, the tool is often misused with poor or even devastating results. I have seen the damage timed tests can do to some children.”

Baroody thinks it’s critical that children first understand conceptually what addition and subtraction mean and develop number sense before they are given timed tests. Too often students are taught mathematical operations through rote memorization, like random numbers, he said, and arithmetic learned this way is easily forgotten, no matter how much it’s drilled.

But once a child understands the math, he believes that timed worksheets are beneficial. Baroody said that if he were teaching in an elementary school classroom, he would administer timed tests at least once a week, and even** **more often depending on the topic and how much children have learned.

Fuchs is even more circumspect in her advice to teachers on how to use timed tests effectively without harming children in the process. Not only should students first** **master concepts, they should have already demonstrated that they know the correct answers in an untimed setting. “You don’t want to give students a page full of problems and they’re kind of lost,” said Fuchs.

Immediate feedback is important too. “When you make an error, your teacher or your partner can say, ‘Hey, let’s fix that’,” said Fuchs. “You want to stop a student when they make an error because what you’re trying to do is practice correct responses. You don’t want students to practice incorrect responses.”

Advocates of timed practice disagree about the details. Some say students should be given long lists of calculations so that no one can finish in time and slam their pencils down, which leaves slower children feeling bad about themselves. However, Fuchs favors flashcards because she fears the sight of a long list of problems overwhelms some children. This is an area that needs more research to guide teachers on best practices.

The Science of Math group concurs that not all timed practice is good, and says the research shows that timed activities or tests shouldn’t start until after a child can calculate accurately. They also say that teachers should never count these tests toward students’ grades; the tests should be low-stakes practice.

“Much like any instructional activity, if it is used inappropriately, it will yield minimal benefits and in some cases could be harmful,” said Peltier. Timing students on “a skill they don’t know – not only is this a waste of time, it also can be demoralizing and harmful. Imagine being timed to parallel park a car at the age of 16!”

*This story about math drills was written by Jill Barshay and produced by *The Hechinger Report*, a nonprofit, independent news organization focused on inequality and innovation in education. Sign up for **Proof Points** and other **Hechinger newsletters**.*