Algebra: The Great Education Tragedy
Around 30 years after Shakespeare penned my favorite tragedy, King Lear, Rene Descartes, one of the most revered minds of the Renaissance era, wrote one of the most important books in terms of modern mathematics — Discours de la méthode” (the “Discourse on Method”). This book contained the symbols for both known(a, b, c) and unknown quantities(x,y, z) in algebra.
This was the first time that a textbook would resemble the modern mathematics textbooks of today. Unfortunately, the excitement and importance of that event in the long, long story of algebra, has been long, long forgotten. So much so, that algebra is only spoken derisively now by both students and math educators. The cascade of bitterness has been happening for some time now, with its christening occurring with this now famous article in The New York Times.
If you distill the article down to its key ideas, Hacker argues through a lens of usefulness and success — hardly things which champion the logistic beauty and rich story of algebra. But, strangely, I do agree with Hacker. Not that the idea of algebra should be rendered easily disposable, but that algebra in its current state of high school isolation with cliched exploration/problems is something that has a declining currency.
Any math story which makes it to mainstream media often explores stereotypical ideas of mathematical concern — homework, false ideas of Common Core, and of course, the **usefulness** of algebra.
Going down the utility/practicality road with mathematics is selling it wrong and horribly short — I am still waiting to apply my understanding of the tragedy of King Lear to my daily routine of housework, shopping, and raising kids.
The problem has never been with algebra per say, it has to do with how it has been incorrectly isolated and re-branded as a course of study reserved for teenagers — usually disgruntled and apathetic teenagers.
One of the problems could be is that students don’t travel back far enough to begin algebra/algebraic thinking. They start with modern notation — the cliched Western narrative — and it all quickly dissolves into thoroughly inane questions about unknown ages of family members and other desperate attempts at applications.
The problem is not algebra. The problem is how education took magnificent bottles of vintage wine and some how turned it into character-less draft beer that everybody wants to spit out.
Algebra has gotten decades of bad PR. Time to fire its publicist.
A place of beginning some reconciliation might be learning the whole, beautiful story of algebra’s birth — not just its teenage adolescence of mostly white males. There is no better place to start than with Keith Devlin and his presentation on its birth and migration from the East to the West — where Islamic mathematicians studied it passionately for, get this, practical applications of inheritance, commerce, and trade.
The Islamic mathematicians didn’t need symbols to think algebraically. Perhaps that is where we should start with our students, in whatever native language they speak.
One of the things that gets wonderfully unpacked in Devlin’s presentation is the clear idea what algebra is about.
To be honest, we are not teaching algebra. There is no historical context. Arithmetic thinking, a necessary precursor for algebraic thinking, isn’t developed enough in our K to 12 education system — it’s a pretty wonky bridge. But, we only need to look at the results. Students dread all things “algebra”. Mainstream media — remember justifiably so — is calling for its termination in high school as a college requirement. And, educators like myself just want to pull the plug on this cheap facsimile of a mathematical masterpiece. How did we get from the poetry of something like Euler’s equation to an angry medieval, theatre mob hurling rotten food at it…?
In the next 7 to 10 days, I should finish my first course that I am writing for Mathigon. It will, like all courses, be freely available(sometime in Spring 2021).
My main goal for this course is for students to not just develop early, functional literacy for this magical idea of mathematics, but — as is implied by its beautiful place in this subject — an honest, human curiosity for it.
Right now, math education is struggling to get beyond creating literate illiterates in mathematics. The historical dehumanization of the subject with its marginalization of its history, neglect of its thematic development through various races/cultures, and false characterization of its scope/purpose has left one of its children — algebra — poorly clothed, malnourished, and generally abandoned.
A few weeks ago, I shared the following question with my 6th graders in my Math Recess course at Dexter Learning. I posed them the following question.
a + b = 8
I asked kids to come up with solutions to this problem. Sure enough, they exhausted all the positive solutions first. And, one student the brilliant answer that a or b could be zero. I then asked, “Is that all”? There was pause. Then one student offered an answer with negatives. The floodgates opened. Infinite solutions was the answer. I then added another equation.
a + b = 8
a — b = 2
After the kids locked down that there was only one solution of a = 5 and b = 3, I then proceeded to do this question formally with algebra — with the answer already known. Mathematics has been about searching for answers and enjoying the adventurous thinking to get there. Algebra is a powerful intellectual journey of logic/creativity. That is where its magic lies — always has laid. Teaching algebra as some dead appendage of throwing symbols into a Cuisinart to solve painfully contrived problems in which educated guessing is the faster algorithm is an embarrassment to mathematics and teaching.
Math education created this tragedy. Math education, however, has a chance to rewrite the ending. Not sure if we will get it right, but we won’t know if we don’t try.
The answer, as always, will always lie in the attempt. The attempt has to start now.