Students who excel at math use rote memory to solve simple arithmetic problems, while weak students calculate, concludes a new study, Why Mental Arithmetic Counts, published in the Journal of Neuroscience.

Researchers scanned students’ brains while they were solving problems.

Higher-level mathematical skills are built on “arithmetic fluency, the speed and efficiency with which correct solutions to numerical computations are generated,” researchers wrote.

This “buttresses the Common Core’s call for ‘automaticity‘ of math facts in the early grades, writes *Education Gadfly*.

It’s been my observation that students who are strong math students use mental “shortcuts” rather than calculating. It’s not rote memory because they don’t have the answers learned by heart. But they are very good at simplifying problems so that they can solve them more quickly.

I believe they are talking about stuff like 5 + 20 = 25, or 5 x 5 = 25. I dare say none of us do the calculation, but have memorized the fact this is so. The greater the ability to do this, the better. Have the kids memorize the times tables. Have the kids memorize arithmatic patterns.

The ability to do this also makes greater speed possible and, on the kinds of tests that matter, speed is a necessary component. If you don’t finish, you lose points.

This sure looks like Kahneman’s system 1 and system 2:

“System 1 represents what we may call intuition. It tirelessly provides us with quick impressions, intentions and feelings. System 2, on the other hand, represents reason, self-control and intelligence. … most of the time, System 1 is acting on its own, without your being aware of it. It’s System 1 that decides whether you like a person, which thoughts or associations come to mind, and what you feel about something. All of this happens automatically. You can’t help it, and yet you often base your decisions on it. … System 1 can never be switched off. You can’t stop it from doing its thing. System 2, on the other hand, is lazy and only becomes active when necessary. Slow, deliberate thinking is hard work. It consumes chemical resources in the brain, and people usually don’t like that.”

You can’t do a hard system 2-intensive problem unless a lot of it can be easily done by system 1. If you have to think hard about the simple stuff, you can’t get to the more complicated stuff.

This sounds very consistent with experience, but without a linked source it’s not as credible as it deserves to be.

Actually, rote memory of math facts for me came from endless hours of ‘drill and kill’ memorization of math facts in both elementary and middle school.

Flash cards, worksheets, etc. After a while, you just knew that 5 x 5 = 25, or 8 x 9 = 72, you didn’t even have to think it, you just blurted out the answer.

There is some truth to the fact that knowing your multiplication, and basic addition and subtraction helps a student in math, rather than being a crutch.

Of course, the overuse of the calculator has ruined the math ability of at least 1.5 generations of school age

students, IMO.

Even worse, they don’t know how to use the calculator to solve a real-world problem, like calculating sales tax. Apparently, they only learned how to solve problems for which the format/equation was provided.

Momof4, I’ve seen that too many times in my lifetime to count, unfortunately.

8% of $11 = 88 cents…not all that hard.