When my children were in grade school, I never let them do their math homework with calculators. They had to work out the numbers in their head or with pencil and paper. I kept thinking about my grandfather who could mentally sum long lists of numbers more quickly than I could punch those numbers into a calculator. That sort of mental agility stood him well in his work in garment factories and elsewhere. And his ability contrasts greatly with the skill of many of my college-age students who distrust their own mental computations. They reach for their calculators instead.
Does it matter? With the near ubiquity of electronic devices these days, maybe the ability to calculate in your head is no longer needed. So I was intrigued to read an article in a recent issue of the Journal of Neuroscience tilted, “Why mental arithmetic counts: Brain activation during single digit arithmetic predicts high school math scores.” Participants in this study were 33 high school students who were given simple addition and subtraction equations (i.e. 5 + 3 = 8 or 5 + 3 = 7) and then asked to indicate whether the equations were right or wrong. As they took this test (and a number of other control tests), their brains were imaged in an fMRI scanner. All the students did well on this test, but differences were found in the areas of the brain that they activated, and these differences correlated with their scores on the math subsection of the PSAT. Those students with higher math PSAT scores engaged parts of the brain, the left supramarginal gyrus and bilateral anterior cingulate cortex, which have been associated with arithmetic fact retrieval. In contrast, those students with lower math PSAT scores engaged the right intraparietal sulcus, a region involved with processing numerical quantity. In completing the test in the scanner then, students with the higher math PSAT scores relied more on their memory of arithmetic facts
The math section of the PSAT does not include the simple addition and subtraction problems that were used in the imaging experiments. Instead, it includes word problems, geometry, algebraic equations, and more complex arithmetic. However, performing higher level math skills may depend upon how fast and efficiently you can compute. If you have a good memory for “math facts,” such as simple sums and differences and the multiplication tables, then you don’t have to waste mental energy on performing these calculations and can concentrate instead on more sophisticated problems. If you’re given the algebraic equation, X - 3 = 5, for example, it will be easier for you to understand the way to solve the problem (X = 5 + 3) and arrive at its solution if the arithmetic is already automatic. Students who do better on their math PSATs may have, through the years, practiced their math facts more and thus have an easier time with mental calculations.
I don’t think this means we have to subject our children to endless drills involving simple addition, subtraction, multiplication, and division. But it might be wise to throw out the calculators in the years leading up to high school. Being able to calculate in your head is still an important skill for math and science classes, for developing a good memory, and, indeed, for life in general.