A Fantasy K to 12 Math Curriculum
…There is no life I know to compare with pure imagination
Living there you’ll be free if you truly wish to be…
Ed Frenkel once referred to mathematics representing “freedom”. Trying to synch Willy Wonka’s idea of imagination, it seems the nexus of these two ideas would — should — involve unbounded creativity. Most K to 12 curricula have moments of such free-range exploration, but certainly not enough to create a lasting legacy of the purest freedom to run wild in the fields of mathematics, and the associated intelligences that blossom here.
I think I have struggled for most of my career trying to envision something that constantly and consistently fosters a deep, intrinsic love for anything and everything mathematics — right from the earliest years of learning. I think I have something now, but again, this is only cobbled through my own experience as a teacher and the mathematicians and educators who have inspired me to look well outside the domain of the box I was placed in. Just climbing out took close to half my lifetime. I am guessing that I probably need a similar amount to construct a thirteen year path of mathematical learning that I would want to put my name on.
Well, this is what I have so far…
K to 3
Why reinvent the wheel on this one? I will just borrow the mathematical riffs of Paul Lockhart and almost avoid kids doing any formal mathematics.
Play games! Teach them Chess and Go, Hex and Backgammon, Sprouts and Nim, whatever. Make up a game. Do puzzles. Expose them to situations where deductive reasoning is necessary. Don’t worry about notation and technique, help them to become active and creative mathematical thinkers.
The two games that come quickly to mind are Dan Finkel’s delightful Tiny Polka Dot and Rich Buchner’s addictive Albert’s Insomnia — AI carries well into the latter years. I would also start the holy trinity of mathematical theories here — number, graph and game. Ironically, none of these are really formalized in most K to 12 math curricula. Number theory not only weaves in the needed patterning and arithmetic necessary for algebra — sorry, algebra is a part of my fantasy! — but it follows the historical narrative of how most mathematicians came to love mathematics. Love? Isn’t that what we are here for said Elton John in Love Song…I would also wear out the pages of James Tanton’s must-have book, Thinking Mathematics 1: Arithmetic = Gateway to All.
4 to 6
This would be the ideal time to roll out what is catching fire around the world and will be the roll-out activity for the ambitious and audacious Global Math Project this year(www.theglobalmathproject.org) — Exploding Dots! Students could never spend enough time here playing with dots, base machines and wormholes to high school mathematics — and beyond! I would also start to fold in — yes, I can never leave the food metaphor for learning mathematics — logic mazes(Robert Abbott), bucket full of number puzzles like KenKen, Strimko and crazy Sudoku variants. Also have kids to not only explore probability, but its cool cousin, expectation. To help start building a natural bridge from arithmetic to algebra, I would use what I consider still one of the best resources to this — Peter Harrison’s Cows in the Classroom(www.bovinemath.com). It sounds weird and silly, but the mathematics, like Tanton’s Exploding Dots, take elementary ideas of addition and subtraction to even eigen vectors. So yes…kids would still be in the cow pastures well into high school:) I would also begin to introduce the idea of proof to children. No. Not the buzz-killer trig proofs that made math Mondays seem like the longest week in one’s life, but just fun and creative analysis of what proof means to kids and what proof could mean in math.
7 and 8
Algebra. Algebra. Algebra. Remember, this is my fantasy curriculum. So, for someone like Andrew Hacker(author of Math Myth: And Other STEM Delusions) this would be a nightmare. Mathematics is an art form. Trying to extricate algebra from the learning of mathematics would be like throwing away all the colors and being forced to paint in black and white. Actually, I think there is probably a more depressing analogy to be found, but I don’t want to dwell on the dystopian world of mathematics that Hacker knuckles out in 37 shades of grey. But, the inclusion of algebra would be built upon that kids have loved mathematics so far — and they have the maturity, curiosity and discipline to start to really cross that critical bridge of arithmetic to the golden land of algebra. And, not to use algebra in an intrusive and contrived way to figure out ages of uncles, aunts and siblings — akin to putting on a lampshade at 2 am at a party you were already not invited to — but to push arithmetic and patterning solutions to their exhaustive brink and create an honest need for mathematics finest and most powerful tool.
9 to 12
This is where it gets pretty anarchistic. Would really focus on decision-making mathematics that involve games with complex thinking and/or have optimum strategy associated with them — yahtzee, poker, chess, GO. I would introduce the visual elements of calculus in grade 9. I mean kids learn slope at this grade don’t they? They have experienced roller coasters by now? Draw a whole bunch of tangent slopes and you are a 5 minute conversation away from talking about the second derivative — the “change of the change” with young teenagers. By this point, kids will have probably found areas of mathematics they want to explore further. I would allow and want this to happen. If some kid is jacked up on game theory — go to town, paint it red and comeback with some stories to tell.
Ahhh…and speaking of stories. Math history would be woven into almost every topic — especially the lost female heroes like Sophie Germain and Ada Lovelace. As well, at the end of it all, kids would know who the hell Martin Gardner was — since his books would make up half the collection of the shelves of their classrooms.
The only way I would know if this was a success would be if kids, at the end of all **this** would love mathematics well beyond any ability they would have picked up. That is my yardstick — simple and uncomplicated love for this dazzling beast of knowledge. It’s not perfect. Not meant to be. It’s just meant to be a happy dream. My happy dream…
We need others to create their own and share them…:)
Author, The Pi of Life: The Hidden Happiness of Mathematics