It’s Time To Throw Away The Dickensian Culture of Math Education
Strike while the iron is hot…
One of my kindred spirits, Peter Harrison, who I had the honor of being mentored by early in my teaching career, used to give out these insanely hard math problem sets. However, he encouraged students to get help from any teacher in the school — or even outside the school. You just couldn’t ask him.
Peter didn’t really care about the actual answer/solution. His goal — sly and subversive — was to have the math conversations exit the classroom and have a large as radius as possible.
Dammit. He just wanted people talking about math. He also created the most exquisite idea of bridging arithmetic to algebra back in the 80's — Cows In The Classroom. In the link, click on “Purpose and Rationale”. Below are the opening paragraphs.
Similarly, my recent Medium article was written to stir much needed discussion. To invite ideas/thoughts/perspectives from all the different/unique biographies that K to 12 math teachers bring to the table.
Agreement is fine. Disagreement is fine. Just don’t be quiet. That has been the Achilles Heel for math education to have any measurable effect beyond ripples in distant and isolated ponds. Oh, don’t get me wrong. People have tried to trigger mathematical tsunamis. Have they ever.
Paul. Your lament for math education was a shot heard around the world a decade ago.
Dan. Your wry makeover for the math classroom catapulted you to deserved fame and critical leadership in the age of social media.
And then there is the zero subtlety of Jason Wilkes…
The intentions have been more than earnest and heartfelt. Yet, the shifts of change didn’t manifest measurably with the intended targets in terms of content. Classrooms, by and large, handcuffed by their own anachronism — sporadically checked — heard these lamentations like trees falling in a forest.
Meanwhile, on YouTube, mathematics was beginning to strut its feathers with channels like — Vi Hart, Numberphile, VSauce, etc. Having each over one million subscribers, these channels now dazzle and challenge viewers with some of the deepest and most wondrous ideas about mathematics freely — and joyfully.
Social media was the great emancipator of mathematics — not education.
You see, the greatest efforts of the greatest math leaders barely laid a dent in the Wall of math education — Roger Waters might not have been a math teacher, but he told millions about the machinery that would ensnare — and eventually emaciate — the heart and soul of mathematics. Staying with music and surfing the “wall” theme…Just replace “words” with “math”.
Is there anybody listening?
Is there anyone that sees what’s going on?
Read between the lines, criticize the words they’re selling
Think for yourself and feel the walls
Become sand beneath your feet
Geoff Tate, Is There Anybody Listening?
And then there are the inspiring lyrics of This Is The Sea by The Waterboys. Isn’t our current math curriculum a meandering — and soulless — river?
Part of the challenges of even wanting to contemplate something new is that teachers, generally speaking, are a conservative group, resistant to change. And, the long familiarity with even the most rigid and antiquated ideas about the math curriculum outweighs the possibility of discarding it all — and this is the destructive byproduct of the institutionalization of mathematics: math education becomes the dominant and accepted culture. Everything else becomes foreign and alien.
The tail(education) wags the dog(mathematics).
Schools(some) are nicer looking. Textbooks have glossier finishes. Social media connecting/learning has never been more fervent. That’s all nice. The problem is that the general culture/design of math curriculum seems dated — really dated.
I quit teaching in 2013 because I just got fed up with it all — the boring curriculum, the asinine emphasis on assessment, the lies, the deceit, and the lack of empathy/understanding for students who have to ingest such harrowing, disconnected pap. I tried, with my limited voice, to evoke even the discussion for change. Complete. Waste. Of. Time.
The math curriculum, already narrow in its scope, worships performance and practicality — and really unrealistic trig applications. The latter is tragically ironic, for in terms of trying to find authentic practicality, you might be better off collecting needles in haystacks.
The question below is one of my favorite math questions I have ever seen. But, not for the the reasons you might think. It’s so ridiculously stupid, that one might think that it was purposefully written to be nutzoid! A truck rambling down the highway at a clip of 170 mph, with the driver having the “observation” skills of a superhero, is more fascinated with a hovering object than road safety. Insert face palm. I don’t even have the patience to address the significant figures malfunction of the answer.
I agree that everyone needs mathematics and should have access to the highest quality of teaching and resources. I just happen to think that kids who played GO and Chess for 4 years in high school would be “better prepared” for the “real world” than dining on the cliched fare of polynomials, trig, and quadratic equations. They used to teach conic sections when I went to high school. I loved conic sections. But, good luck finding a curriculum that still teaches eccentricity and directrix.
Curriculum changes alright. But, I believe erosion moves faster.
I still think they should teach these things. I just don’t think they should be mandated after grade 8. There has to be other options for kids who desire to think mathematically, but might be getting turned off by the growing syntax, jargon, etc.
Classical mathematics should always have a place in high school, but jeez Louise, it is kind of time for a status update in 2018 to include more modern ways of thinking mathematically!
Also, as it has been mentioned many times, mathematics is a soulless sojourn without deep nods to its global history. Junaid Mubeen, co-editor with me at Q.E.D, summed it up all too well with Mathematics Without History is Soulless
But critiquing math education is a micro-audit activity. It operates in the larger antiquated mill of education. Sir Ken Robinson’s animated examination of the sifting/sorting/packaging/etc. students answered the bell on the macro picture of education.
My own personal lament is that the holy trinity of theories — number, graph, and game — are nowhere to be seen in most K to 12 math curricula. Prime numbers are merely a definition. Mathematical mavericks like Martin Gardner, John Conway, Ivan Moscovich, etc. are unknowns. Algebra pops out of a can in high school — with a sequel to boot. There is no organic and seamless bridge between arithmetic and algebra. Teaching algebra as an appendage to teenagers as opposed to teaching it as a circulatory system earlier on is one of the clearest indicators of the mismanagement of mathematics by education. It’s like going to hardware store. Aisle 3, top shelf: nails, washers, and Algebra I.
Mathematical expectation, one of the most powerful math concepts — that can be learned by almost anyone in the time it take to boil an egg — remains relegated in upper level high school courses. Logarithms, exponents themselves, are mysteriously separated from exponents by sometimes as much as three years. Etcetera.
Sorry. Tweak this and tweak that never worked — only for publishing companies. It all has to come down. Decimals on Monday. Fractions on Tuesday. Kids identifying math by where they are in the textbook — I am on 7.3 — and just general, isolating soup can delivery of math has to stop. It is kind of insane — and accepted(which makes it more insane)And, for some, fear of the unknown/what to do will be natural reactions. That is okay.
Now…to the drawing board…literally.
Early this year, Daniel Torres-Rangel, a kindred math spirit I met at NCTM 2016 in San Francisco, and I had some rough ruminations about what a “fantasy” K to 12 math curriculum would look like. We started with some broad ideas, filled in some holes, and asked others to join our mission.
Below are some screen shots of the Google document.
I always envied English teachers. They always seemed to have more flexibility in choosing the books we read. Shouldn’t math teachers have the same autonomy to choose their favorite math topics/problems? I mean, the brain isn’t partitioned by math topics. There is no lobe/hemisphere that is starving for the double-angle trig formulas. The brain simply wants its axons and synapses firing and blood flowing like a raging river — maybe, we should just have kids doing Suduko and its variants for 12 years.
At least give teachers/local school communities the space/respect to create their own K to 12 math curriculum — or at least temper it.
I am unclear how someone can love mathematics so much and watch it suffer in cramped cages, fed a constant diet of tests/assessment, and orchestrated with bureaucratic agendas — especially since it has been rightfully assailed for the better part of this century.
I can think of no better way to end this than with Lockhart…and a few choice words for the soul crushing bureaucracy that still chokes the bloody life out of mathematics.
I am not here to praise the math curriculum, I am here to bury it.