Mathematics is an Emotional Roller Coaster: Let’s Teach it That Way!
One of the pillars of Social and Emotional Learning(SEL) is the healthy development of all the emotions of our students, and the consequent management of them in their learning.
In mathematics, SEL does not play a significant enough role in the learning — and appreciation — of mathematics. While emotions like anger/frustration compete with joy/elation on the other end, these emotions are outputs after the mathematics has been done. And, for the most part, they just wander and drift aimlessly from student to student. So yes, anger exists and joy exists. But, so do others.
What if we got in front of all the emotions, and gave mathematical ideas/problems that elicit all the important/integrated emotions that we as humans should experience? Is it really healthy to only emphasize joy — especially if it’s not there? There’s no joy in decimals, but there is boredom — right? Sorry, but these emotions, to have an honest and varied experience with mathematics, must all be present.
This is — well, should be — the most important emotion to underscore in mathematics. Since the entire history of mathematical development is based on failure — slow failure — the emotion of frustration has been a fairly predominant one in the history of exploring mathematics. Paul Zeitz has a nice twist on this word — funstration!
A great example of ensuring frustration from every student is doing a problem that has no solution, but has enough intrigue to carry out several trials/strategies before the towel is thrown in.
Below is one of the best examples. It appeared in The Guardian(Alex Bellos).
Simple problem. Get all three coins out of the square bank. When you remove a coin, you must replace it with one below and one to the right — and yes, there must be room.
Go ahead and try. It’s impossible, and the solution to its impossibility is bloody elegant. So, there will be a collective energy of frustration that might demand this proof.
There are many stories of sadness in mathematics. Many. I wrote about them in my book, Chasing Rabbits: A Curious Guide to a Lifetime of Mathematical Wellness. The story of Sophie Germain, while exemplary of her bravery in the harsh conditions of sexism, is also a sad story — how much could she have accomplished if the same doors that were open to men were open to her?
What about the story of Christopher Jackson, the man who found a love for mathematics while in jail? While we should feel happiness on one hand, there is also a sadness to the systemic issues that led a Black man to spend much of his formative years in prison. And yet, from the sadness, blooms the beautiful book that Francis Su wrote, summoning the most binding and human reason for doing mathematics — flourishing.
A good chunk of K to 12 mathematics is boring. But, don’t ask me. Ask the thousands that turn to social media to air their somniferous grievances regarding math.
Boredom needs to have a seat in the classroom. It needs to participate in critiquing a question. Sure, there will be moments where questions and explanations lack color, but they can’t dominate the landscape as they currently do. Show boring questions and call them out. That way, there is some baseline reference. Students can see what makes one problem a snooze fest and another a compelling mystery.
One of the key traits of being a good teacher is honesty. As such, allow your students to be honest about when boredom shows up — call it out. Show them you are human and trustworthy.
Show them multiplying decimals or dividing fractions with denominators that nobody would ever care about. Enjoy the boredom with your students.
This emotion needs to rise to the top. It needs to pierce routine and rituals. We can’t always be throwing 80 mph fastballs. Throw a curve or two. Maybe a hard slider. Even a knuckleball that gets away from you.
Here is one I did last year in my 6th Grade Math Recess class at Dexter Learning. We had finished wrapping up exponents, and I wrote this on the Jamboard.
Some of the kids answered 81 and some of the kids responded with that I wrote the exponent in the wrong place. I kind of played along for a bit, and then said “No, this question is written correctly — and the answer is not 81”
Curiosity always tends to hang around the emotion of surprise. First of all, we went over the expected response of 3 x 3 x 3 x 3, which is exponentiation. I think quipped something about if exponentiation is related to repeated multiplication, what could be…next?
Oh yes, I milked it.
I then wrote this.
The surprise came delivered in the familiar — a small tower of exponents, which all of them could calculate in their heads. The final answer 7,625, 597, 484, 987 was almost no longer relevant. The enormity of the number was realized — and, it could all be written with 3 and 4.
The beautiful thing about surprise, mathematics, and large numbers is that they occupy a space beyond even what our imaginations can hold. Below is an image that begins the journey to unpack Graham’s Number. It was the number that sparked my interest in numbers/math when I came across it in 1977’s Guinness World Book of Records.
This is the emotion that might be the most underrated, but unfortunately, really an invited guest in our classrooms. Even if it is, we put a stopwatch on it, and kind of shame it.
Mathematics is nothing without confusion. All the charm, whimsy, magic, awe, and wonder is locked here. Being confused by mathematics is to be enchanted with mathematics. Sense-making and deep understanding takes time. Sending our students through the Drive-Thru for algorithms separates them from their rightful — human — journey of being baffled and bewildered by mathematics.
Stop “GPSing” everything to #$#@! death — allow our students to be lost in mathematics. Just like the millions before them.
I not only confusion. I encourage. As a mutual learner, I show it myself. I tell students once I stop confusing you, I will have run out of mathematics to show you. Teaching simply for correctness and all the right moves all the time is not honoring the human complexity in flourishing with mathematics(Su).
A student’s first reaction is an organic moment to capture. We should honor all the emotions. Better yet, let’s just teach with them.