QED “Squad Goals”: Stop, Start, and Continue for Mathematics Education
QED, the greatest Medium publication on Earth dedicated to mathematics education, I can honestly say, with no conflict of interest (it’s my “squad”), asks us to thing about what we would:
Stop
Start
Continue
in mathematics education.
QED squad goals: bring a new and improved mathematics education into being.
Me, my mission is to help kids and adults to live and love mathematics. I can articulate my mission in these simple terms. Can you? Can you strip away the clutter, jargon, overcomplicated theories, and edu-babble, and articulate what you want for your math students? How about you, as an adult who has mathematics in your life?
You say, there are too many barriers in our way. I say, and did say, in my book I just wrote (yeah, I get to say that, when I accomplished my childhood dream), that this mathematics can be brought into being.
If we can think of it, and dream it up, and bring it into the world, it exists. Define some school mathematics that is better than what we have today, that keeps the best of the past, while driving into the future.
It will exist, it must exist.
There Exists a School Mathematics, Better Than What We Have Now.
Think like a mathematician, come up with your own classroom axioms, and proceed from them. Stick to your vision.
STOP:
Our curricular materials would mostly be recognizable to Gauss, or Euler, or Newton. This is depressing. Imagine if Science education ignored everything that has been developed in the last 300 to 400 years. Yeah, that wouldn’t work. Modern mathematics is applicable and interesting
It is time that Mount Calculus and Mount Algebra moved aside-they don’t need to be the top of every K-12 curricular model.
New math needs to be fit into our curriculum.
Here is a short list of things that might be interesting:
Graph theory- making graphs to show connections. Okay, that is vastly oversimplified, but the diagrammatic nature of graph theory is well-suited to teaching to kids. Let them play with the Travelling Salesman. This may connect to computer science, and data literacy. It should. Making graphs, in the graph theory sense (connecting “things”) would fit nicely.
Topological surfaces: so yeah, we teach a lot about…triangles. Which are awesome. And other polygons. We teach about prisms well. And pyramids. But what about other shapes, and surfaces?
And this leads us to:
Non-Euclidean geometry. What are we worried about, they are still going to know what a triangle is. Now how about when that triangle is drawn on a balloon
Game Theory: making better decisions. Developing strategies for games, but also for LIFE. Yeah, this one is important. It ties in to how impoverished our “probability” curriculum is- 8 straight years of playing with dice and cards? I think we can broaden out from there.
This is the challenge for curriculum developers and mathematicians. Get together and bring MODERN MATHEMATICS into classrooms.
By the way, you should probably throw out that old poster that show Pluto as a planet. You are embarrassing yourself. The world has moved on.
START:
Let kids be messy.
Yeah, this is how we roll. Talking, thinking, conjecturing, wondering.
Teach kids to talk in math classrooms. Honestly, I have no idea why we traditionally don’t talk much about the mathematics we are doing. It is interesting to talk about mathematics. It also normalizes talking about mathematics. Why shouldn’t it be normal to talk about mathematics? We talk about everything else.
Playing With Numbers
Reading lots and lots of popular books about mathematics has shown me what I was missing.
Numbers are meant to be played with-torn apart into their prime elements, operated on in our minds, befriended.
Ramanujan loved 1729. What number do you love? Why?
Numbers have personalities, just like you.
Number theory is another impoverished area of math curricula. It’s as if we feel the need to hide things from kids, because they might not be able to “handle it”. Meanwhile, that 5 year old over there is staring at the stars, wondering about infinity. That 7 year old wants to know if she can count to a billion. Some 12 year old in your class wants to know how prime numbers work.
Numbers are interesting. We usually just use them in operations. We treat numbers like nuisances-pluck them out of word problems, and operate on them, then forget about them.
For that matter, we try and get counting out of the way as soon as possible.
Why? So we can get to arithmetic. How about we show them how counting is the basis of arithmetic? Paul Lockhart did in his book Arithmetic.
Play games to learn about numbers. YES KIDS NEED TO KNOW THEIR TIMES TABLES. This debate is so incredibly boring. Yup, they do. We spend our blood fighting over that same inch, that tiny slice of mathematics. It’s all in how we do it. Play games to learn number facts. Kids love games, and so do you.
Actually, we need to reclaim “arithmetic” from educational traditionalists. Algorithmic arithmetic is not the only arithmetic. We need better arithmetical foundations.
Computers compute, and humans think. It is what we do best, except when we try to avoid it.
Assume your students are all capable of high levels of mathematical thought. Teach them the concepts and skills (in whatever order you like- I am bored and tired of the trite, tired, and cliche “old math”/”new math” poles).
CONTINUE:
Being interesting. Give interesting tasks and problems, and let kids think. If you treat mathematics like broccoli, kids will probably try and avoid it. Treat it like the world’s most delicious cake. Stop pretending it’s just some medicine that must be taken. Make it all interesting. Yes, you can. There is not a single topic in K-12 math curricula that you can’t make interesting.
Kids want to think. Kids want to learn. They want to learn about mathematics. Start with that assumption.
Mathematics is where the wild things are. Wild, strange things. Be like Max in Sendak’s book. Take a trip to where they are. Make mathematics weird again. Mathematics has been tamed by curricula, and conservative interpretations of it.
Math curricula is Shania Twain, when it should be Johnny Cash.
Math curricula is the Eagles, when it should be the Ramones.
Math curricula is Sheryl Crow, when it should be the Pretenders.
Math curricula is Elvis Presley (Vegas period), when it should be Elvis Costello (circa 1977).
Math curricula is MC Hammer, when it should be GangStarr. *
*Quibbles about these comparisons can go in the comments. I will take no flack on Sheryl Crow though-”Every Day is a Winding Road” is the worst song in the history of recorded music.
We have kind of made it so. Institutions have made it so. Make mathematics more punk rock is a good goal.
Make mathematics punk rock, psychedelic rock. outlaw country. And bring it to the masses. Our tastes have been diluted by the bland. We can help fix that.
Write your own stop and continue for mathematics education. Join QED on Facebook.
Write your own riposte to this piece? Think I am wrong?* Write your own piece. I took the time to write this, so should you. Agree with some of these points? Say so.
*I firmly stand with The Dude on the issue of The Eagles, so don’t even bother with that one. I checked out of “Hotel California” long ago-contrary to popular belief, you can leave.
