I’d love to try to learn to ride this thing…
As the beginning of a school year approaches, I hear from many families whose children are not as eager as those shown in back-to-school advertisements. So many young people are downright dreading it. When asked for a reason, they’ll say it’s stressful, or boring, or both.
A common response from adults is: “You can do it!”
We say this with the best of encouraging intentions. What we mean is “You’re great, and strong, and we believe in you.”
While that is likely true, it’s an answer to a question they may or may not be asking. (Not to mention that it neglects the question of at what cost.) If a young person says “I don’t know if I’m smart enough,” then some version of “you can do it” is appropriate and plenty.
But as a response to “I don’t want to go to school because it’s boring/stressful/ boring and stressful,” it misses the mark. Mostly, I think we use “You can do it” because we don’t really have time to address what these young people are actually expressing, and even if we did have time, it would be hard to know where to begin. (I say this not to suggest laziness on the part of adults but rather as a reflection of experience, after more than two decades at work on the problem!) But it’s also possible that we’re just mis-hearing what young people are actually saying; that we think this expression of satisfaction or unhappiness is actually a lack of confidence.
Either way, it’s a good idea to try to move beyond cheering kids on, to look more closely at what they’re saying and why they’re saying it. I think that in our role as caretakers and guides for young people we don’t like to get into this kind of territory unless we have solutions at the ready. And sure, they wouldn’t mind a solution, but to have their communications actually received can go a long way, even in the absence of solution. A longer way than we probably realize.
Especially if we want young people to keep talking to us, to keep telling us what’s not working for them, to keep honing the ability to express what they’re experiencing and use it to navigate what’s ahead.
“Educability, humanity’s species characteristic, is not simply a matter of learning the answers to old questions, but, more importantly, the increasing ability to ask new questions that may lead to new answers. There is always the danger that old answers will discourage the raising of new and appropriate questions, with the result that the error becomes institutionalized, often as a way of life.”
I’m working my way through all of Dan Roam’s books about how simple drawings, alongside a few words, can bring ideas to life. I’ve finished The Back of the Napkin and Blah Blah Blah, and now I’m reading Unfolding the Napkin.
Dan points out that in school we are trained to communicate almost exclusively in words – drawing is relegated to art or free time. Yet pictures are much closer relatives to experience than words, and as young children are attempting to make sense of and assimilate what’s happening and what they’re being told, their first impulse is often to draw. We’ll grant them that, but not for long before we want them to focus their attention on reading and writing, shoving the drawing to the periphery (at best). I’ve been wondering what would happen if we let them draw as much as and for as long as they are compelled to. How would it influence their development? What effect would it have on how they communicate? Would some processes speed up and some slow down?
It’s been interesting, in the course of my exploration of Dan’s visual thinking work, for me to try to train myself to expand the way I think about communicating, to try to incorporate images into the way I share something I’m trying to say. It feels very difficult, but also as though if I figure it out, it’ll be a relief not to be quite so dependent on one mode.
This is sort of another plug for Ed Zaccaro, but also an observation about language and dignity in the context of math.
I posted a while back about Ed Zaccaro’s Challenge Math series, which I think was written for kids who needed more than the classroom could provide, but also seems to work well with kids with all sorts of different relationships with math.
This week I was surprised when one of the eight year-olds I work with asked specifically if we could work in the Zaccaro book. I’d done a quick bit of one page with her once before, and she was OK with it, but tends to balk at anything she has to stop and think about, anything that requires reading as the Zaccaro problems do. This is not because she doesn’t like to read or isn’t a good reader. She is. But as a math student, she tends to balk at reading. We’d mostly been working on quick little problems I’d chosen for the purpose of letting her see that she is more capable when it comes to math than she has learned to believe.
She leaned right in as soon as I opened the book in front of her. She remarked on the illustration of the large sweating ants and then started reading the first problem on the page. She sped through three in a row, understanding exactly what the problems were asking for and doing much of the computation in her head. This is exactly what she doesn’t do when she’s interacting with her Pearson pages from school (which, as far as I can tell, were written and issued very quickly after the Common Core standards went into effect). She’s constantly choosing operations that don’t fit the situations in the word problems.
I’ve been frustrated with the language of many of these problems ever since the materials were issued, but in watching this child with the Zaccaro problems, I realized something new about how they are tripping kids up. The Pearson word problem language is often ambiguous, which is terribly troublesome in the context of math, but it’s also just plain dull. For kids who are readers, accustomed to sentences written with care and intention, poorly written problems are not just potentially confusing. They’re an insult to the sensibilities of the literate child. The literate person.
I realized that what this student has been doing with her classroom math work is to scan each word problem and attempt to match it with a procedure. If it looks like the kind of problem for which one should divide, she’ll divide. If it looks like you have to trace your finger across the table shown and fill in a number according to a pattern, she’ll do that. No matter that often the problem is asking for something slightly different. In order to notice that, she’d have to subject herself to the agony of reading the dull text slowly. As a result, her actual ability and number sense is obscured. In a situation in which the reading is in and of itself engaging, she is freed up to think fluidly and flexibly about what there is to do with the numbers.
What the Zaccaro book does for her (that the Pearson book does not) is offer something. That sounds too simple to matter, but I don’t think it is. An offering concerns itself with presentation and connection, free of attachment to result. It is the fundamental unit of authentic human exchange. It says “Here. This is for you to have and use if you choose.” It grants dignity, agency, autonomy. In the course of our deep but desperate commitment to educate, we’ve moved away from offering toward mandate and decree, often undermining our ability to pass on what there is of useful knowledge and skill to our young.
The good news is we can resume a culture of offering any time we want.
from Manish Jain’s plenary, Western-style Schooling, Unemployment, and Cultural Breakdown, at the 2015 Economics of Happiness conference:
“Spending so much time in the four walls of the classroom and extra tutoring classes does not leave much time to develop deep emotional and spiritual relationships with the fields, the trees, the rivers, and the animals. So these slowly shift from being family members to being commodities.”
From Dan Baum’s recent Harper’s piece about drug legalization: “After telling the BBC in December that ‘if you fight a war for forty years and don’t win, you have to sit down and think about other things to do that might be more effective,’ Columbian president Juan Manuel Santos legalized medical marijuana by decree.” (I recommend reading the whole piece and I will likely mention it again in the next few days; here I just have this small thing to say about the Santos quotation.)
This reminded me of an old story in The New Yorker about artificial leaf technology. Harvard professor Daniel Nocera is quoted: “For the past two hundred years, we’ve run this other experiment, with fossil fuels, and it’s not working out so well.”
We forget that the things we try are experiments. They become truths, or mandates, part of the fabric of life and society. So if and when they are not working, it can be hard to abandon them and try new ones. It feels like we have no choice but to keep trying variations on whatever approach we’ve grown accustomed to, without rethinking the basis of the experiment.
I cannot think of many realms in which this is more true than it is in education.
The other day I thought maybe it might be time for me to try calculus again. I didn’t take it in high school the way I might’ve if I’d been born a bit more recently, because there wasn’t a year left for it after 9th grade algebra, 10th grade geometry, etc. And then I didn’t take it in college because, I think, I was tired. Or didn’t get along well with the teacher? I can’t really remember.
But there it is, out there, this un-learned mass with the fancy name. One of the young people I know, with whom I have been doing math for several years because she likes it and doesn’t “need” a tutor but likes having one, is nearing the end of pre-cal. She and I are really more like math buddies than tutor and tutee. I help her when she needs help, but a lot of the time we find interesting problems to try to solve together. Now, there she is, about to start calculus, and not only will I not be able to help anymore, she’ll likely be too busy with her calculus to do math with me much anymore.
So I’ve been brushing up on my pre-cal, looking for gaps and rusty spots, and considering calculus texts. I’m a Martin Gardner fan, and my library had a copy of Calculus Made Easy, the Silvanus Thompson text with revisions by Gardner, so I tracked it down in the 515s and opened to the table of contents. Thompson’s first chapter is called “To Deliver You from the Preliminary Terrors.” I immediately texted the words to my mom, who is still terrified by most math and went to all sorts of lengths to avoid passing her fear on to her female child.
I didn’t have terrors, per se, but I can’t resist this sort of language. In this chapter Thompson delivers us from our preliminary terrors by explaining that to learn the two principle symbols d, meaning a little bit of, and ∫, meaning the sum of all the little bits. (He mentions the fancy language as well, but uses the plain to explain.) The second chapter is called On Relative Degrees of Smallness. I will admit that I was so enamored of this title that I had to stop reading for awhile. But then I resumed. Here’s how the chapter begins:
We shall find that in our processes of calculation we have to deal with small quantities of various degrees of smallness. We shall also have to learn under what circumstances we may consider quantities to be so minute that we may omit them from consideration. Everything depends on relative minuteness.
Here I had to stop reading again and stare out the window. Who knew this was going to be a philosophy book?
I recently had occasion to look up the word pico. I have always been partial to words that mean lots of different things and pico is, among other things, the Spanish word for peak (or beak), an island in the Portuguese Azores, an acronym for a method of locating relevant clinical literature, and a prefix denoting one trillionth. 10−12. 0.000000000001. Very, very little.
The other night I heard about Erika Christakis’ new book The Importance of Being Little. This book is about very young children, and the way the world view of such people could inform the way we older bigger people interact with them.
This is an awful lot about smallness in one week, I’ve been thinking. A little hard to ignore. Also, my father, who is recovering from a massive stroke, cannot remember things I have just told him. To find the patience and presence to dial back a lifetime of conversational habit in order to sustain an exchange with someone who can cast backward and forward only a few moments is at once an enormous thing and a very very small thing.
I’m not sure how far I’ll get with the calculus, but I can’t help feeling that it’s a terrific thing every time we consider smallness in great depth.
Once a week, we have an eighteen month-old friend at our house for the day. She is, as most her age are, quite excellent at calling our attention to sources of delight we might otherwise miss. For the past several weeks, she has been most enraptured by two things – cats and round objects. She communicates mostly in sign language at this point, and so the signs for cat and ball are well-used.
It’s not hard to understand what might be so enjoyable about a cat, or any other four-legged creature, but we’ve been speculating about what makes a ball so much fun. It doesn’t seem to be the throwing, in the case of this young person, at least not entirely. Plus, you can throw all sorts of other things too and they don’t get nearly as much attention as the ball gets.
Maybe it’s how the ball behaves. Nothing else moves like a ball does. If you set it down on a surface that isn’t entirely level, it’ll find its own momentum and start wandering all over the place if there’s enough variation in terrain. Nothing else will do this but a thing with at least a round edge to help it along. In our living room the floor is not even close to level, so if you set a ball down pretty much anywhere it’ll set off on an apparently drunken journey and end up, inevitably, in a corner. If you didn’t know better (“better”), it’d be easy to think that it was alive, or whatever classification you’d give to things that seem to have character and creativity before you knew the world alive.
Oliver Sacks used to carry a ball around with him in his briefcase: “My main neurological tool is the ball,” he says. “You can learn a lot from how the patients play – and may patients who will do nothing else will open up to a gently tossed ball.”
My sense is that he chose the ball because it’s such simple access to play – tossing a thing back and forth. But the more we’ve been thinking and talking about this love and fascination and we watch it unfold for such a young child, the more I wonder about it as a thing that links us up with the physical world, the physics of the world, and invites us to engage with it as no other object could.