Do Arithmetic Drills Do Anything for Adults?

In 2004, Ryuta Kawashima and colleagues at Tohoku University in Japan published a study that used fMRI to look at the brain during simple arithmetic. Eight children aged 9 to 14 and eight adults in their forties did single-digit addition, subtraction and multiplication in their heads. In both groups, areas including part of the left frontal lobe were active. Only a few areas showed statistically clear differences between the types of calculation, or between children and adults.

Kawashima went on to lend his name to arithmetic workbooks for adults in Japan and to the Brain Age games. Bookshops sell arithmetic workbooks for grown-ups. Is there any point in an adult doing sums meant for schoolchildren? In this post I look at research on arithmetic and the brain, both the studies that found effects and the more cautious ones, and then write about the point of arithmetic for adults.

Being active is not the same as getting better

The first thing to separate is this: an area of the brain being active during arithmetic is one thing, and that area working better after you keep doing arithmetic is another.

What an fMRI study shows is where blood flow increased while people did a task. “The frontal lobe is active during arithmetic” means arithmetic uses the frontal lobe. On its own, it does not tell you whether doing more arithmetic improves the frontal lobe, or helps with anything else. To find that out, you need experiments that compare people who kept doing arithmetic with people who did not.

Experiments with daily arithmetic

Kawashima’s lab has run such experiments too.

In a 2008 randomized controlled trial by Uchida and Kawashima, 124 people aged 70 to 86 were split into two groups. One group did basic reading and arithmetic tasks every day for six months. That group improved on a test of frontal lobe function and on a processing speed test that pairs digits with symbols. The group that did nothing did not improve. I covered this study in more detail in Reading Aloud for Adults: How to Do It as Brain Training.

In a 2012 study by Rui Nouchi and colleagues, 32 older adults played either a brain training game that includes arithmetic tasks, or Tetris, for about 15 minutes a day, at least five days a week, for four weeks. The brain training group improved more than the Tetris group on tests of executive function and processing speed. There was no difference on a test of overall cognitive status or on attention tests. A study with the same design in 32 young adults followed in 2013.

These studies have limits, though. In the 2008 study, the comparison group did nothing at all. That makes it hard to separate the effect of arithmetic from the effect of doing any task every day, or of simply getting used to the tests. The 2012 study, after dropouts, had 14 people per group, and the paper itself says the results need replication in larger samples and that long-term effects and relevance to everyday life remain uncertain. The paper also states that one of the researchers created the game and that his university receives royalties from it.

The cautious side

Large studies and reviews, on the other hand, are cautious about effects beyond the trained tasks.

In a 2010 study in Nature, Adrian Owen and colleagues had 11,430 people practice reasoning, memory and other tasks online for six weeks. They got better at the tasks they practiced, but there was no effect on untrained tasks, even closely related ones.

A 2016 review by Daniel Simons and colleagues went through the studies that brain training companies cite as evidence, one by one. Its conclusion: there is extensive evidence that training improves the trained tasks, less evidence for closely related tasks, and little evidence for distantly related tasks or everyday cognitive performance.

In the ACTIVE study of 2,832 older Americans, a 10-year follow-up found that the group trained in speed of processing still kept gains in that ability. But that training was a task of picking out things flashed briefly on a screen, which is not an arithmetic drill. I went through these studies in more detail in Does Brain Training Work? What Research Shows and What It Doesn’t.

What we know and what we don’t

Putting the research side by side, it can be summed up like this.

If you keep doing arithmetic drills, you get faster and more accurate at arithmetic. That much is certain. Every study agrees that people improve at what they practice.

Whether it spreads to other abilities, such as attention or processing speed, is less clear: small studies found that it did, while large studies and reviews are cautious. It is not settled. And there is not enough evidence to say arithmetic drills prevent mental decline.

What arithmetic is for, as an adult

Even so, some see a point to adults doing arithmetic. Looking at the parts of the research that are certain, rather than the unsettled ones, there are three.

Arithmetic itself becomes usable in daily life. Splitting a bill, a price with tax, 30 percent off, checking a receipt. Sums that are not worth getting out a calculator for come up almost every day. A child’s arithmetic workbook is for learning the answers. Adults already know them. An adult’s arithmetic drill is practice in retrieving answers you already know, quickly and without mistakes.

It gives you a short stretch of focusing on one thing. In an arithmetic drill the problems keep coming, the end is clear, and your own time is something to measure against. When a worry won’t leave your head, arithmetic is one way to spend a few minutes looking only at the problem in front of you.

It is an easy first habit. Arithmetic needs no explanation of the rules, so it is easy to make it the first item in a daily routine.

In the BrainDojo developer interview, when I was asked how much I believe brain training works, I said, “I think it depends on the content of the training”, and went on:

Even if you stop strength training and your muscles waste away, nobody says strength training is pointless. In the same way, brain training is a habit of activating the brain. It is like how people with a habit of reading or jogging are better at those things. It is not that you do brain training and instantly become smart.

Arithmetic drills can be seen the same way: not a tool that makes you smart overnight, but a habit that keeps the arithmetic side of your mind in use for as long as you keep it up.

Paper workbooks and apps

A paper workbook lets you see the whole page at once, leaves a trace of what you wrote, and keeps you off screens. When you mark your own answers, you also see clearly where you went wrong.

An app checks your answers and records your time for you, gives you different problems every time, and goes wherever your phone goes. With a paper workbook, doing the same page twice can mean you remember the answers. That is less likely in an app.

Among apps, some have you tap the answer on buttons and some have you write it by hand. The second kind is closer to the writing in a workbook. Rather than one being better, you can split them by place: paper at home, the app when you are out.

Where to start if arithmetic is hard for you

Start with single-digit addition. If you feel arithmetic is not your thing, start with single-digit addition, without worrying about time. First make sure you can get them all right.

Accuracy before speed. Trying to cut your time increases mistakes. Once mistakes have almost disappeared, speed up a little at a time. I wrote about speed and accuracy in How to Think Faster: Reaction Speed vs Thinking Speed.

Add subtraction, then multiplication. Once addition feels easy, add one thing at a time: subtraction, then the times tables. Moving on to two-digit by one-digit sums can wait until after that.

Bring it back to daily life. Add up your shopping in your head and compare it with the total at the till. Using what you practiced in real situations is how you feel the point of the practice.

A few minutes a day is enough. There is no need for long sessions. How long to keep going each day is in How Many Minutes a Day Should You Do Brain Training?

What BrainDojo offers

BrainDojo is a brain training app for iPhone and iPad that I make, with handwriting, reading aloud, calculation, memory and attention trainings.

The calculation trainings sit together in the Calculation Boost lane. The most basic, Quick Math, gives you short calculation problems one after another. You write each answer with your finger, and at the end you see your time. You can compare it with last time, so it becomes a contest with your own record. There is also Speed Calc Long, 100 problems in a row, and How Much?, where you give the total of the coins and notes on screen. How Much? is the training closest to the everyday arithmetic above. Each training is described in BrainDojo’s Mini Games: What Calculation, Reading Aloud and Handwriting Train.

Because you write the answer with your finger instead of tapping a button, the practice is close to the writing in a paper workbook. Today’s Training is picked for you each day, and when you finish, you stamp the calendar.

Every training except the newest ones is free to play, and the free version shows ads. BrainDojo Plus removes the ads and lets you play the new trainings at any time. Your first session is covered in Getting Started with BrainDojo.