How Feldenkrais made me the best math teacher

This year I was going to reconsider my choice of volonteering in a school as a math tutor. The amount of /pointless-mathematics that I would routinely see there would make me sick, and the sight of those poor teenagers struggling with a subject that had been expropriated of all sense and beauty drained my soul and filled me with pity every week. In a whole semester, I had not yet succeeded in giving any of them a different experience. They all just wanted a solution to their exercises, and they were pissed with all the questions I asked them. So I thought maybe I could, you know, light and candle and knit myself a pair of socks in those hours, rather than inflict damage on my spirit. Practice headstands. Get myself injured running from rabbits. Test the sharpness of needles. Stare at the void. Anything. But I work in tech so I have a perverse fascination for masochism, so I decided to stay one more year.

What I didn't yet know is that the Feldenkrais teacher training I had started just a few months earlier would turn the experience on its head.

---

I come in one day, and a boy and a girl are sitting at the back of the class and chuckle. The occasionally write something down, they text, they chuckle more. They are the modern incarnation of Waiting for Godot – idly fooling around, getting nothing done, heading in no particular direction, emptily gliding through life, waiting for something to happen. After half an hour they raise their hand. I go and sit between them.
"With this one exercise. I don't know what to do."
[Chuckles from the boy behind me and restrained chuckles from her. I ignore.]
I ask: "What's your thoughts on this? How have you approached it?"
[Silence]
"I don't know how to do it."
She's been taught that either you were born on the right side of math or you weren't; that in math either you read the exercise and already know the answer, or you don't and can't figure it out. She's accepted she was born among the unlucky half, that she doesn't know the answer, so she doesn't look for one. The exercise gives her a bunch of numbers (2, 4, 6, 8, 10) and asks to come up with a closed formula and a recursive formula for the progression those numbers hint at. I ask: "Do you know what closed and recursive formulas are?" And she, as if I'd just pointed at all her flaws: "Uhm... not really..." It's like if she was asked to go into an herbarium and come back with a Hibiscus, without knowing what an Hibiscus is. Somehow she'd feel entitled to ask about hibiscuses, but she assumes that she's not entitled to enquire what closed and recursive formulas are. Either you know already, or something is wrong with you.

"When we don't know what the exercise is talking about, a good method is to browse through the previous pages and look for what we are missing." I'm gonna give her a fish today, but I'm also gonna teach her to fish. I flip literally one page back, and there is an exercise that looks exactly the same, except with odd numbers (1, 3, 5, 7). It takes her a while to agree that indeed, it looks quite similar in structure. 95% of math textbooks are shit and I'm in no business of figuring out whether this one belongs to the lucky 5%, so I just put it to the side and use that exercise as trampoline for our own explorations and my own explanations. I think back of Feynman receiving a pallet of physics textbooks to evaluate and, when presenting his findings to the commission, saying "I could open any of these books at random and show you that there's no science in any of these" (and then went ahead to do it, live). I think of how, in half a century, the largest change in textbooks has been the adjunct CD-ROM that comes with animations that my blind cousin could have animated better, my illiterate grandpa could have scripted more engagingly, and my mute aunt could have narrated less monotone. Teachers arguing we need more multimedia in the classroom are like tech companies arguing we need more standups. They both deserve their special place in hell – let's just hope the multimedia Standup that would emerge would never break free from that hell or we'll really be doomed.

We go back to her homework. I teach her the lexycon, which either she knows or she doesn't, and then dismiss any request for solutions. We just unwrap and unwrap what each word means. "Closed formula means how we can find a way to transform the list of whole numbers, the integers, into the list they give us, one by one. We have 1, 2, 3, 4 on the left and 2, 4, 6, 8 on the right, and we need to find a law that matches them. So how we can turn 1 into 2, 2 into 4, 3 into 6, 4 into 8, and so on. We must find a way that works for all those numbers. So how would you go about turning 1 into 2?" She still hesitates. She knows she doesn't know math, so surely she can't be thinking of the right answer. She looks at me with a face of incompetence, although I've asked a question that any neurotypical 8-year-old could answer.
She says: "I can add 1. 1+1 gives 2."
"It does. Now we need to check if it would also work for the other numbers."
"The next number is 2. 2+1 gives 3. But that's not 4, so it's wrong. I was wrong."
"That was an interesting exploration, but it didn't lead us where we wanted to get."
I'm astonished. How did that sentence come out of my mouth? I have no idea.
I continue: "Is there any other way you can think of that could turn 1 into 2?"
"I could double it. 1 times 2 gives 2."
"Yes, and would that work for the other numbers?"
She needs to verify each element of the sequence, but eventually she surprises herself in noticing that yes, doubling works. She may have discovered the first numerical pattern of her life. She's still looking for the right answer though – she looks at me and her face wonders "Ok, and what do I do with this now?"
"If we now call all the numbers on the left with n, so that n becomes a placeholder that can be filled with any of those numbers, how can we write down the action we've done to n, as we did to the individual numbers?" She's seen n in previous examples, and on the whiteboard, but it's always just been a sign. It may be the first time she grapples with generalizations and giving a name to a flurry of numbers. I know her brain is absolutely capable of that generalization though, because she does similar ones every day. The fact that she has the notion of bottle, a symbol that stands for the unending variety of shapes that can contain liquids, shows that she is capable of generalizations.
"Is that 2n?"
"What do you think? Does it make sense to you?"
"I think it does.", and flips to the end of the book to compare with The Solution. The most impactful innovation in school textbooks would be to strip away the solution pages (both from the students' and the teachers' copies) and just set them on fire during the intervals. But okay, one revolution per day.
"Yes, it's right", she says.
And I rephrase: "Yes, they agree with us."

I'm stunned at what I have done: I have turned all her sentences of incompetence upside down into neutral or positive remarks. I'm making her feel that she can do it. That she is competent, and master of herself. More questions start popping up. Unrelated questions, as it happens with genuine explorations. She's sometimes unsure how to treat fractions -- I tell her to make herself an example; she does and then say "no, it doesn't work the way I thought". She's slowly learning to fish. I leave her grappling with a problem and I turn to the boy.

He starts off giggling again. I ask "What's so funny?" "Nothing, I'm just tired.", and immediately stops giggling for good. He points at his exercise: he has a tougher one: -1, 3, -5, 7, -9. "Fascinating! An alternating one!", I cheer. And yes, I cheer for things that normal people don't cheer about; but no, I wouldn't cheer to my partner for an alternating number sequence, but hey you've gotta bring some life to the dry land they think math is. I invite him to start working with the simpler 1, 3, 5, 7, 9 and avoid the alternation for now. And it's a fascinating task: he's learning to generate odd numbers. He's not been able to start so far because the task was not clear to him. So I phrase it for him as well:

Take the list of numbers 0, 1, 2, 3, 4, and 1, 3, 5, 7, 9.
Can you find a consistent law that will match each of them, in order?

He surely can, he's just never done it. As soon as he can materialize these numbers in his mind, he will see that each on the right is double the one on the left, plus one. David Bessis explained that we can't understand anything that's not evident to us, and that when we are ready to understand something, it's impossible not to see it nor to unsee it after. So my role is to create the conditions that make this double + 1 law so evident that it feels impossible not to see it.

Again I restrain myself from giving answers that would give him a fish, but not give him the space to learn how to fish. It's such a delicate balance. You want people to figure things out on their own, but you always want them to be in a place where they can feel competent. Leaving a 6 year old with a knife in the forest for a few days, saying he should figure it out, is not teaching, is killing. But also taking the knife away from a 16 year old is killing, just in a different way. The 6 year old is killed because hey, he will starve; the 16 year old is killed in his soul because he's distrusted with something he could do. His creativity and independence are destroyed; he dies inside.

When the boy figures how to generate odd numbers, I point him to the next problem: to generate alternating signs. But the structure of the problem is again the same: how do you map the list 0, 1, 2, 3, 4 to 1, -1, 1, -1, 1? And then he's gonna have to put them together. I'm tyring to give him one of the key teachings of math: when you have a problem you can't handle, break it down in pieces you can manage. You can break it in chunks as small as counting on your fingers. You also have to learn to put the pieces back together. And maybe then you can bring this teaching into your life?

So I go on for an hour, back and forth between boy and girl, struggling with my instinct of showing them and the awareness that learning to fish takes an astounding amount of dead ducks and nobody is doing us a service in saving us from those. I learnt proper backups when I accidentally overwrote a disk image on the wrong partition. At the end of the hour they have both done one single exercise, but they both turn to me and, maybe for the first time in their life during a math class, their eyes glitter. He asks me: "You really like math, don't you? Are you a teacher here?".
Both their faces look competent. If you feel incompetent in math, and maybe science, and maybe computers, how much does it take for you to feel incompetent at life? If you feel competent in math, that competence can expand into your life.

I leave recommending them to treat numerical progressions as people. When you meet a new person, you don't start off with "Do you want kids?" (except in this Tinder era, but okay). You ask their name, where they are from, you comment on the beauty of the autumn colors, you learn what flavor of coffee they like most. You have no goal in mind: you just explore each other. I suggest they ditch the goal-driven attitude they have and switch to an exploration mindset – to getting a feeling for the progression they have at hand, getting to know it as they would do with a person. Then they will be able to answer any question about it.

---

After a year, I had finally managed to give these two students a new perspective on math. They may have had the first positive math experience of their life, at 16. And where has all this come from? How is it possible that I've failed at that for months, and now, one afternoon, I could with no preparation?

It is Feldenkrais.

Friends around me have listened to me telling them how the Feldenkrais teacher training I enrolled into has accelerated my breakup, sparked a wish to dance, made me a better friend and listener, allowed me to find comfort. And now the list lengthens with made me my best math teacher. Feldenkrais, especially in its 1:1 private lessons, is a lot about making the person feel comfortable, competent, and the master of herself. And what have I done today, if not give these two teenagers a Feldenkrais lesson, with a mathematical content?