The Bridge Between Arithmetic and Algebra is Broken. Which Means Math Education is Broken.
The second sentence of the title was inserted not to belie the great work of math educators everywhere, but rather remind us all that maybe the shading of arithmetic/algebra into obscurity is blinding us to the magnitude of our failures…
Peter Harrison, my mentor who I taught with for 4 years from 1998 to 2002, and who was a huge influence in the landscape of math education during his career, started losing hope for its future a few years after his retirement.
Once over dinner, I distinctly remember him saying “…they should just turn math into Latin”. Implying that mathematics was losing its lustre as a language, and maybe just offer it as an “option” for anyone who is interested in honoring its central theme — the connection between arithmetic to algebra.
I don’t know anyone past or present who thought as deeply about building an organic and accessible bridge between these two powerful ideas more than Peter Harrison.
Unfortunately, the disjointedness between arithmetic and algebra has only gotten worse. Andrew Hacker’s New York Times article, Is Algebra Necessary, only widened the divide. Ironically, I agreed with much of Hacker’s article.
But, Hacker, like so many others, are lamenting about algebra in its present state of delivery — the way that it is taught. And, because of the way it taught, I would beat him to the front of the line of “Get Rid of Algebra”. Peter Harrison would have walked through that door 20 years ago…
However, the erosion of algebra in our education system has been going on for 50 years. What kids were able to do algebraically in the 60’s/70’s by the beginning of high school is what we hope our kids exiting high school can aspire to do. Somewhere along the way, a whole generation of students has become several years behind in algebraic thinking. If we trace the breadcrumbs, we will see that the “land” on the other side of the bridge — that was never been built for everyone to journey across safely and enthusiastically — is just as parched as algebra.
That would be arithmetic.
The treatment of Arithmetic in school is an abomination. What should be a joyful excursion of numbers, teeming with play, historical development, and deep connections, gets reduced to algorithms which are prefaced by the word “standard”. Its only headlining gig are those — as in the words of my 12 year-old son — boring PEDMAS/BEDMAS questions.
Algebra is the generalization of arithmetic. Separating the two is criminal.
Arithmetic and Algebra, once highly prized and valued — and connected — now have their discussions in math education’s discount bins. If these things could be thought of as wine, then their current status should put them on par with a jug of Carlo Rossi.
If we are truncating the experience of arithmetic, then we are definitely going to be shortchanging algebra. So yes Andrew Hacker, with the current state of the mathematical union, let’s ditch algebra.
But, I am not prepared to ditch algebra or arithmetic. I am prepared to fight valiantly for its resurrection through a prism of historical delight and imagination. The current lens of practicality and perfunctory practice is a complete distortion. It’s broken. It’s murky. It’s waste of time.
Students and teachers deserve better. Hopefully, the current road of play that math education seems to be embarked on, will guarantee some sightings of authentic arithmetic and algebra. And just maybe, enough will begin to understand and care about the idea that any restoration of mathematics must go beyond fixing and maintaining the bridge between these two giants of mathematics.
It must be celebrating. You can learn a new language out of practicality or for pleasure. Mathematics should be learned for both — and, for me, that includes a rich exploration of arithmetic and algebra.