I went to the grocery store today and at the self checkout, one of my items was not recognized by the barcode scanner. It scanned successfully, but it wasn’t in the system and couldn’t give a price. An employee came over to help. He was young, no older than his 20s, though he looked like he could have been still in high school. He went to enter a price manually and asked me if I knew how much it cost. I said I didn’t. He responded that he thought it was about $1.69 and I said that sounded reasonable. (He was actually undercharging me quite a bit, as I later looked up the price and found it to be at least $6.)

Here’s the problem: I was buying two of them, so the employee had to double $1.69 in his head. For the record, that’s $3.38. He initially typed in $3.52, paused for a moment, then said “Wait, that’s not right,” and erased it. He was visibly struggling to think of the number, and after several seconds typed in $3.32. “I think that’s right. Right?” I answered that it was fine and he hit the confirm button.

He had unfortunately picked a hard number to double. He also probably felt under pressure. I, too, have trouble doing mental math under pressure. I wouldn’t have wanted to double $1.69 in his position and I probably would have gotten it wrong too.

Being able to do mental math effectively requires two things: number facts and number sense (or numeracy). Number facts are the basic facts of integer arithmetic, fractions, decimals, and percentages, which must be able to be recalled in order to perform calculations. Number sense is a largely intuitive understanding of how numbers are related that enables problem-solving and accurate approximation. There has long been controversy surrounding these skills because they involve rote memorization and repetitive practice to learn, not deep thinking. Rote memorization is usually grouped under “traditional” math education, while deep thinking is associated with “progressive” math education. Over the past decades this pendulum has swung back and forth as both approaches have advantages and disadvantages.

Many people, both educators and non-educators, see problems with allowing students to use calculators. There is now a genuine argument that students will walk around with a calculator in their pocket at all times, so what use is mental math? For one, it just comes up sometimes, like in the grocery store. There are different ways that situation might have gone: the employee could have entered $1.69 twice, he could have pulled out his phone or even a paper and pencil, and so on. But he didn’t do any of that, he did the math in his head. The fact that there could always be a way to avoid mental math in principle doesn’t mean any given person will actually avoid it all the time. It may be that these situations are fewer and farther between than they used to be, but at this point it’s still an important skill.