In an Age of Calculators, Do We Still Need to Know Our Times tables?

Fluency – for reading and for math

I’m working with my younger sons on their reading, and they are at the point where thy can sound out the letters “c,” “a,” and “t” to make the word “cat,” but they would struggle if I handed them something like the play Hamlet.  Yeah, they could technically do it, probably, but it would be so onerous that they’d begin to hate reading.  By the time they'd have sounded out "Denmark," they'd have forgotten the beginning of the sentence.  The meaning, the rhythm, the point of the play would get buried under the sheer mechanical effort of decoding letters into sounds.

The same problem presents itself with some of my students in math, where they’re trying to factor a rational polynomial (the math equivalent of Shakespeare) or even just add regular fractions when they don’t know their times tables.  Without knowing that 7 × 8 is 56, automatically, instantly, without thinking, it becomes a slow, arduous process, and math becomes a drag.  Even with a calculator, it can feel like banging your head against a wall!

Now, I love reading, and I can’t imagine what my life would be like without having the decoding ability that lets me read and access imaginative stories, delicious recipes, and reflective essays.  I don’t have to think about what letters make what sounds anymore – it’s just obvious that “v” makes a “vee” sound.  I hope (and expect) that my boys will also get to the point where they know their letters automatically and build from there to read independently for information, enrichment, and entertainment.  In the same way, I know that it will be difficult for them to progress with math to the point of finding some level of enjoyment and flow (not to mention effectiveness) without knowing their times tables just as automatically as they should know their letters. 

Fluency as a Foundation

There's a concept in education called cognitive load.  Your working memory (the mental scratch pad you use to hold information while you work on a problem) can only hold so much at once.  When a skill is fluent, it takes up almost no space on that scratch pad.  When a skill is not fluent, it hogs the whole thing.

A student who reads fluently doesn't think about letter sounds anymore.  That mental effort is freed up entirely for comprehension: for noticing that Hamlet is stalling, for catching the humor in puns, for following the plot, etc.  A student who doesn't read fluently spends all their mental energy just decoding, and has nothing left over for understanding.

Multiplication facts work the same way.  A student who knows instantly that 6 × 7 = 42 has a free mental scratch pad to think about why they're multiplying, what the problem is actually asking, and how to combine that step with the next one.  A student who must stop and calculate (or reach for a calculator) spends their limited mental energy on arithmetic and has nothing left to think about the actual math.

What This Looks Like in Real Tutoring Sessions

I had a middle schooler recently who needed to find the lowest common denominator for a fraction problem.  A student with fluent times tables sees 4 and 6 and just knows, almost instantly, that 12 works as the least common multiple (LCM), but this student didn't have that fluency, so his only available strategy was to painstakingly list out multiples of each number: 4, 8, 12, 16... 6, 12, 18...  until he found a match.  It worked, but it took longer, required a lot more writing (and I’m usually  a proponent of writing things down in math), introduced more chances for a careless error, and left the student mentally exhausted before we'd even gotten to the actual point of the lesson, which was understanding fraction addition.  It was no surprise that the student didn’t enjoy math.    

I commonly see this with students who struggle with fractions.  It's almost never that they don't understand the concept of a common denominator, but that they can't execute the mechanics fast enough to keep the concept in view.  Sometimes we simply cannot make progress on fractions until we've gone back and shored up the times tables.  The higher skill is trying to stand on a foundation that isn't there yet.

The Calculator Trap

With my high schoolers, it shows up differently.  They are finally allowed calculators, which can become a crutch for those who never really solidified their times tables.  A calculator can genuinely work fine for a single, isolated arithmetic step or higher-order operations that don’t make sense to try mentally.  The trouble is that real math problems are rarely a single step.  Problem-solving like finding roots, simplifying radicals, or writing a geometric proof requires a chain of small arithmetic decisions made quickly, one after another, while holding the bigger structure of the problem in mind.

Consider a student trying to find the greatest common factor in a trinomial with coefficients of 18, 30, and 56.  A student fluent in their times tables scans the numbers and notices that the first two are multiples of 6 and the last one is a multiple of 8, so they probably only have a 2 in common (and not a 6).  It might take a few seconds to mentally double-check that, but they have an idea of where to start.  A student who isn't fluent has to pick up the calculator and do some hunting and pecking, going from their shaky memory and guessing: are they all divisible by 3?  So they punch in 18÷3, 30÷3, and 56÷3, only stopping when they find that 56 isn’t divisible by three like the others.  Back to square one… they try another number, maybe 5, again finding that they’re not all divisible by 5, either.  Eventually they might try 4, and when that fails, just whittle it down to 2.  They can do it, and it can work for them (as long as they don’t accidentally press the wrong buttons on the calculator), but this process of elimination method is so slow and effortful that they lose the thread of what factoring is even for.  And often, this will just be one step of many on the way to finding the roots of the quadratic trinomial.  It’s too much!  They start to dread problems that a fluent student would breeze through.  Over time, that dread compounds.  Math starts to feel like it's supposed to be a slow, grinding slog, and the student never gets to experience what it feels like when math really flows.

Often the Highest-Leverage Thing We Can Fix

For a lot of students, probably the slight majority of those I work with, the single intervention that would most reliably boost their confidence and unlock progress across the board would be sitting down and building real, automatic fluency with the multiplication facts.  That would mean getting some flashcards (or a good math app) and practicing.  If you can get each one within three seconds, great!  If not, keep working on it until you can. 

Few students, especially high school students, want to go back and work on those skills, though, particularly when there’s a calculator on hand.  A lot of them have years of struggling in math in their history and are just hoping to get through the class so that they can avoid ever having to do math again.  And I get that – there are things I’m not good at (juggling, auto repair, photography) and probably don’t care enough to invest the time and effort to ever get good at. 

But it feels like such a waste.  It could have gone differently for these struggling students if there had been a bit more invested up front.  It didn’t have to be such a slog this whole time.  Just like a student can't fall in love with Hamlet while still sounding out three-letter words, a student can't fall in love with, or even feel competent at, algebra while still counting on their fingers to find 7 × 8.

What Parents Can Do

When I’m first talking with a parent of a potential new student and trying to get to know where they’re coming from, one of my first questions is “How are they with their times tables?”  If your student is struggling with fractions, algebra, or just seems to find math exhausting rather than engaging, it's worth asking a simple diagnostic question: can they answer basic multiplication facts (through 12×12) in a couple of seconds, without counting or calculating?  If not, that's often the highest-leverage place to start — not because it's glamorous, but because everything else is standing on it.