Jun 18, 2018
Prime Numbers: Their General Exclusion From Math Education Is Inexcusable
I have written most of my articles through a macro lens, trying to find the biggest picture possible for learning mathematics — you know, the whole Humanity or Bust thing — but, now I want to take a closer look at an idea which underscores the problems in math education.
Prime numbers.
Prime numbers? Of course kids know about prime numbers! You can’t divide them by any other number besides 1 and themselves, right? Yes. That is the classic definition, which is more often dispensed like it came out of a fortune cookie — some novelty piece of information that gets shared without too much fanfare.
Problem: Kids Should Discover Primes Not Memorize A Definition
As soon as kids learn about shapes, specifically squares and rectangles, it is time to dive right into the deep end of mathematics — prime numbers. Almost every elementary class has access to those unafix cubes. Get kids to build towers of numbers. Even that simple activity reinforces counting, and it is the first subconscious foray into number theory(triangle numbers: 1, 3, 6, 10, etc.)
Now ask them to take each number and see if it can be fashioned into different looking rectangle. Kids will quickly see that 1 and 2 are easily dismissed here in terms of constructing a new one. The number 3, while probably intuitively impossible as well, might invite some unsnapping and snapping of blocks — yes! The number 4, which can be constructed into a square, should invite the question is a square a rectangle? Yup! A nice ancillary benefit from this adventure into mathematics’ most famous rabbit hole — prime numbers.
Only because the death of Anthony Bourdain is still fresh on my mind, I need to inject a chef/cooking/food metaphor here to shed light on how we as teachers need to do a much better job in understanding our craft. The teaching of mathematics is a creative and noble profession like chefs. But, I highly doubt there is chef of any reputability in the world who is not fluent in the history of one or two cuisines and cannot rhyme off a myriad of their favorite dishes. They also probably all possess some mandatory kitchen skills like this:25 Skills Every Cook Should Know.
Primes are so bloody fundamental to mathematics. And, they shouldn’t be relegated to only being a part of some tragically inert definition in the appendices of math textbooks — for kids to stumble upon in puberty. No. They should be actively explored when imagination and curiosity is most ripe — elementary school.
Having children explore primes early on not only strengthens their arithmetic, but it goes to the heart and soul of mathematics — that being a mathematician is about being a pattern-searcher.
Once kids visually see which numbers stubbornly refuse to be another rectangle — its fun to inject some animated language — their collective curiosities will want to find the next one, and the next one , and the next one…
And, however, long it takes, let a question like “How many primes are there”? bubble up to the surface of the class.
It is that question, coming from a student, that will take students to the opening of the rabbit hole — that is several thousand years deep. You, as a teacher, also get to mention it has already been proven that there are infinite number of primes, but they only get rarer and rarer, fainter and fainter, as you count into the millions, billions, etc..
Who proved this? When was this proven? Hopefully these questions also get elicited. The history of mathematics awaits…Here’s looking at Euclid…
No. These young students won’t be going through the Looking Glass and into the world of imaginary numbers, where the potential bounty of prime number research lies(The Riemann Hypothesis). But, you should tell them that the “erratic behavior” of these primes — that these kids observed through constructive play — is now part of the most famous problem in mathematics. And, not only will anyone who solves this mystery will get one million dollars, but their face will appear on the front page of every newspaper in the world.
They will automatically join the legends of Euclid, Descartes, Germain, Gauss, Ramajunan, etc.
That is a pretty powerful moment. Fusing burgeoning curiosity with completely unexpected information of mythical proportions is what will inspire kids to become pattern-searchers, problems solvers, and mathematicians like Marcus Du Satoy.
Primes are connected to so many things that are within the intellectual reach of our students — The Goldbach Conjecture, prime factorization, basic ideas of encryption, etc. Yet, none of those things will have any depth if the initial exploration of primes is a shallow/perfunctory one.
For all the rage of “Number Talks”, if there isn’t any homage to the importance of primes — to both the history of mathematics and to the pedagogy of teaching mathematics — then we are hardly in love with mathematics. If we aren’t going to be in love, neither will our students.
It then not too ironic that Dan Finkel, one of the founders of the website, mathforlove, helped create the game, Prime Climb, which took the power of primes and turned it into a wonderfully tactical game.
Math Education’s general disinterest in primes — conscious or not — is unconscionable. Disregarding building blocks for math and for deep learning of arithmetic garners a harsh verdict. Skipping over primes would be like a great chef who couldn’t make an omelette or chop onions properly and didn’t know how to make something like French Onion Soup…
It is just one more example of how math education has no interest in math history, and only wants to peddle something soulless like canned and prepackaged meals that are kind of bland.
Pedagogy = Cookbooks. Mathematics = What’s For Dinner?
All I know its not French Onion Soup…
