In my gut. That is where the whole back-to-basics movement has been gnawing at. And, up until today, I couldn’t consolidate my fear and worry of that call to have kids learn their times tables, be introduced to fractions earlier, and get drilled on long division. I mean, math facts are important, right?
And then I saw this post come across my Facebook page — a quote from Kylene Beers.
The parallel to learning basic math facts is frightening.
Math facts are important. But, the BTB movement implies there is a Canon of math facts centred around the most cliched idea of times tables. How important are they? When I taught calculus, I had a few kids score into the 90’s who struggled with times tables. While it would have been nice to quickly know what 12 x 7 is, it didn’t preclude them from doing well in areas of mathematics like calculus — which is a highly visual course.
Times tables are really low-hanging fruit of math facts. Sure, 7 x 6 = 42 is a something nice to know. But, you what is better? 7 x 2 x 3 = 42. That students can break down every composite number — another math fact — into its primes. That is math fact has little more teeth than 7 x 6.
Dan Finkel’s creation, Prime Climb, was the “rabbit” my own kids chased down into the Rabbit Hole of mathematics — number theory. Not only is this place filled with “math facts”, it has people like Gauss and Germain to romp around with — always ensuring that the thirst for mathematics is never quenched. The picture below is what should hang above every rabbit hole — every math classroom.
Why do we wait to teach prime factorization until middle school? To me, that is kind of late. That is a topic that can be taught in elementary school — that is IF students physically construct prime numbers with block earlier on.
But, just having a bag of math facts doesn’t mean much. You might have some basic literacy — some basic mathematical grammar. But, are you now armed with mathematics that makes you seek out more mathematics?
No. Who would pine for mathematics after learning a square grid of times tables that arbitrarily stops at 12 x 12? Oh, just wait until they start multiply fractions with denominators of 7 and 11,then they will be salivating for long division.
On top of all of that, students are repeatedly tested on these things. If we didn’t make mathematics mandatory, kids would be running for the door at the end of elementary school — and never coming back. And, just because they sit their quietly and obediently in the math class, doesn’t mean they haven’t checked out emotionally/spiritually.
Once you lose the heart, the mind will follow — want to follow.
It doesn’t work like that. It never has worked like that. There is no inspiring light at the end of this tunnel. Just a delirious demand that students need to be able factor polynomials.
Championing for a hardcore retreat to learning mathematics with glorified flash cards is a familiar recipe to quash any love for mathematics. And, that is why I am so vehemently opposed to the back-to-basics movement. The collective myopia they brandish calls for a short-term, low-stakes math literacy. Naively, they think that a strong foundation here automatically parlays that into STEM jobs.
STEM is a 21st century construct. Times Tables and inordinate sweating over fractions is a 20th century fixation. Good luck squaring that circle.
Thanks to my kids, I have picked my fascination with prime numbers. Do you want to know a cool math fact?
How many prime numbers are there in this list:
115, 117, 119, 121, 123, 125
I would have gotten this question wrong as recently as six months ago. There are zero primes numbers in this list. The largest gap of primes from 1 to 100 is eight(89 to 97). After that, it skips to 14(113 to 127). Which means we — my kids and I — investigated what numbers multiply to these prime suspects.
119 = 17 x 7. At the age of 54, I absorbed another math fact. There is no “tablets” of facts that fit into a square array. You will always be learning math facts, and the better the math fact, the tighter your factual fluency will be. But, perhaps more importantly, you will stumble closer to falling through the rabbit holes of mathematical lore and love.
The literate illiterate. That is the endgame of learning to read without the love of reading. It is the same terminal for mathematics. But, don’t listen to me.
Listen to Alfred North Whitehead, the famed mathematician that co-wrote Principia Mathematica, the 23rd most important non-fiction book according to Modern Library.
Times tables are useful, but they are precariously close to being inert. And, if they lead students away from loving mathematics, then they indeed can be harmful if we build our math education ideas around them.