Also… from time to time I post something quickly on Facebook that I don’t post here – usually an article or video I want to share but don’t have time to comment on – so if you’re interested in seeing those, you can visit the page or add it to your Facebook feed.

Here’s the amazon link; enjoy, and send questions if you have ‘em.

…I am half way through the Mathematician’s Lament and am totally, utterly passionately sold. But…now what? I’m not a mathematician and fall into the “duh” populace of math paralysis. Who has a curriculum, a study guide, activities prepared to those of us who want to give this gift of wonder to our kids and allow the +,-, X,/ come later, and and naturally? I don’t know where to begin or what to show. I wouldn’t have known the triange in the rectangle thing if I hadn’t just read it in the book. So where do we find sources? (I intend to track down the author and ask him the same).:)

Here’s my response:

If you haven’t already, I’d recommend you have a look at Beyond Facts and Flashcards (read more about the book here); whether or not the mathematical content is right for your son where he’s at now, the book may be able you at some ease about your own ability to guide him through what he’ll need in the way of math.

The other thing I often recommend is that people who feel about all this as you do (“the duh populace”) start by looking around to find out what they’ve been using in the way of practical math all along, more or less without disaster, humiliation, or other unfortunate incident.  It’s there!  You’ll likely find out that you’re more savvy and capable than you’ve been led to believe, and that you have more to offer than you think when it comes to passing on useful stuff to your child.

Then when it comes to the other realm that Paul Lockhart’s talking about – the stuff that’s about finding beauty and wonder in shapes and relationships and numbers – you can go exploring.  The thing about mathematics as a pleasurable pursuit is that it didn’t exist until people started talking about what they noticed, and then started creating language for it so they could talk about it and share in the exploration and creation.  So the thing to do if you’re interested in finding out what’s in this realm of mathematical beauty is to go looking for the people who have found it fascinating and then see if there’s overlap of interest and intrigue.  You can Google things like “mathematics and beauty” and “interesting math discoveries.”

You don’t (nor does your child) have to love it, or even care at all about it in order to find your way quite effectively and peacefully through the world!  Sure, that thing about the triangle in the rectangle can be useful in the context of a math class, and can help facilitate the acquisition of subsequent knowledge, but unless it’s inherently interesting how shapes interact with each other, it’s likely to have at most cursory usefulness (and to try to get a kid to dig deep into math when it’s just plain not that intriguing to him or her is to make it more difficult to just learn it to the extent that it may be necessary in the context of preparing for a test or getting through a class; the more we let things be how they are the more smoothly things go).  Like anything else.  I’ve worked on problems like the triangle/rectangle one with kids who are fascinated by it and want to spend scads of time thinking about it, and others who shrug and say things like “Yeah, I guess that’s cool.” I don’t think that’s entirely the fault of the delivery.  I think it’s at least in part attributable to the spectrum of human preference.

The fact that we make a big production about math is not an indication that it’s any more important or essential (and I’m still talking about the big fascinating puzzle math, not the managing finances) as anything else, like art history or needlepoint, things that we’re perfectly fine with taking an interest in or not taking an interest in.  You can go after the interesting math the same way you would anything else, by asking people you know if they know things about it, or know anyone who does, and then asking those people what they read first, or where they started, what they’ve seen online about it that they like, etc.  Some of the stuff you come across will be over your head at first, but some of it won’t, and that’ll be where you start.  If you find it interesting.  If you don’t, then maybe, slowly, you realize that it doesn’t mean anything about you that it’s not interesting to you, just as it doesn’t mean anything about you that you’re not interested in needlepoint or engine repair. And you can choose to keep exploring, or stop!

Thanks for asking the question out loud, and for being willing to venture out beyond what you’ve been taught to believe about math!

“What are those?” he asked.

“Fraction cards for a math game,” I said.  ”Do you like math?”

He shrugged.  ”I don’t know. I don’t really get it.”

What he meant, actually, was that he doesn’t really know what the word refers to.  He’s at ease in conversation about money, cost, discount, tax, about measurement, rate, distance, speed, about logic, pattern, or other relationship.  It’s just not called math at his house. It only exists in the context of life, not as a separate entity.

Soon he’ll know what we mean when we talk about math, and that he’s been doing it all along without knowing it; he’ll realize there’s not actually anything he doesn’t get.

But I couldn’t help imagining a world without the word.  A world in which math isn’t a thing; just part of myriad other processes we go peaceably about in the course of our days.  The kind that some of us do for fun, the kind that’s just for the sake of itself (distinct from the daily use kind), could have some other name – number play, maybe. Anything that gives it some distance and breathing room from the word that’s come to strike such fear and confusion in the hearts of so many  What a world that would be.

The first post of Scott’s that I saw was this one on taking care with the words always and never where kids are concerned.  I found my way also to his interview with Home Education magazine in which he talks about, among other insightful things, the opportunity to replace domination with partnership: “Domination is exerting power over others and squelching their autonomy; partnership is sharing power with others to enhance each other’s autonomy” and the potential of that shift to transform the experience of parenting (not just the experience of being a kid).

I don’t often come across a resource I find this refreshing and potentially empowering and supportive for parents committed to navigating their family lives according to their actual values and intentions (rather than those that trickle down or poke in from outside).  I encourage you to have a look and see if Scott’s work has something to offer you.

So I get to work, and soon I have carpal tunnel from turning the screwdriver and I’ve thrown out my shoulder with the back and forth of the saw.  The work is going very very slowly.  ”Plenty of houses got built this way,” people tell me.  ”And it’s important to know the basics.”  Eventually, because I was more interested in the house than basic tool use, I stop.  The house is not realized.

And so it goes, too often, with young people and writing.  So intent are we on basic primitive tool usage that we forget to pay attention to what it actually takes to realize the proverbial house, and in so doing we run the risk of destroying the drive to do so.  If a child has an idea, a story, a thought of any kind to communicate, why wouldn’t we just get out of the way?  If she wants to use the computer, the spell check, the voice-to-text, why not?  These are tools of realization.

Generally the ‘why not,’ is in the worry that if we teach her to type too soon, or allow her to dictate before she can transcribe, she’ll never learn to use a pen, to write by hand. She’ll be hindered by skipping a critical first step.

But pens and pencils are to writing what screwdrivers are to building and fixing.  There was a time when they were the only tools available, and we needed them for big and small jobs alike.  We had no choice but to build houses with hand tools, and so learning to use them first was the only option. And there was a time when we had no choice but to do all our text-based communication by hand.  Now it’s not the only option, but we keep insisting kids wait to use the more efficient tools until they’ve learned to use the ones that are really only necessary for small jobs now.

We’re often insisting on it out of habit or nostalgia, which is too bad because it not only creates frustrated resistance in young people who don’t understand why we won’t let them use all the tools available but because it thwarts the realization of the house.  Or the poem or the novel, the thank-you note or the Valentine. It sends the message that kids are only welcome in the world of text once they’ve mastered a process that is now only peripherally necessary, which of course in turn makes them less enthusiastic about joining us in that world at all.

Does it?  The skeptic in me sneers and says the camera’s a machine, and does its own thing.  That someone else in that same moment could have captured that same image without any love for the subject.

But then I’ve seen photographers capture astonishing beauty and ugliness that were only evident in the photograph.  And so I have to say that I think the way a person looks at something can alter it, can bring out that which might otherwise remain invisible, silent, unrealized.

If so, we’re wise to recognize that our eyes work just like cameras this way.  When we’re looking at children with doubt or worry about their progress, we’ll likely draw out more cause for it, or at the very least drive up the same fear in them.  When we’re looking for brilliance, for kernels of promise and inspiration, that’s what we’ll see, because it’s always always there somewhere. And in so doing we’ll show kids what’s possible beyond what already is.

One group of words, that twist and hide truth and understanding, is “structured–unstructured.”  Almost everyone who talks or writes about learning situations that are open, free, non-coercive, learner-directed, calls these situations “unstructured,” and their traditional authoritarian, coercive, teacher-directed opposites “structured.”  People who support open learning use these words in this way as much as people who oppose it.  It is a serious error.  There are no such things as “unstructured” situations.  They are not possible.  Every human situation, however casual and unforced… has a structure.

I often hear that certain kids “need more structure.”  Generally people mean, as John suggests here, that these kids need more of being told what to do, to have more limits or boundaries or confinements set up around them.  And while I don’t always disagree that structural changes might benefit a particular child, we tend to undermine our intentions when we lunge for habitual structure before considering what kind of structural changes might actually serve a child who’s struggling in one way or another.  A child who’s expressing some sort of discontent or lack of compatibility with a situation may well not benefit from being more closely confined by rules and mandates.  He may instead need, for example, more clear communication, or better access to different materials or resources.  It’s possible to make this kind of structural change and it can be tremendously beneficial, but we’re often too busy with setting new schedules and requirements to explore a range of possible structural adjustments.

Quick descriptions of John Holt’s work tend to refer to his opinions and positions on opting out of traditional schooling, but to look more closely is to find a long, inspired series of unusually careful and clear observations and illuminations of how learning actually works.  This early section of Freedom and Beyond is one such pairing of observation and illumination.  If you have the chance, find a copy of the book and read through these seven pages on the structure of freedom.  Be warned, though, it may be difficult to stop there; there’s the rest of the book, and then all his others.

Why?  To check her credibility.  If her reviews were always positive, I’d have been a little suspicious.  Some were, and some weren’t, so at the very least I knew she didn’t only have good things to say.  (It’s of course more common to find that a person’s reviews are consistently negative, which is also helpful to know.) I just wanted to know whether she was someone who sometimes likes/approves of things, and says it, or whether she was just posting a bunch of positive reviews to improve her own morale, or plug the company, or whatever else might possess a person to do such a thing.

Kids give us opportunities to show credibility all the time.  They say things like “This homework is stupid.  Why do I have to do it?” and we very often pass up the opportunity, even though if you asked us we’d say we want to be seen by kids as trustworthy. We just don’t recognize it as an opportunity to gain credibility.

So we don’t tend to look over their shoulders and say things like “Huh.  I see why you feel that way.  I wonder why the teacher assigned that.  Do you think it’s because…” Instead, we’ll say things like “You don’t have to like it you just have to do it,” or “Can you just get your homework done so we can eat?” or “Your education is important, your education is your job, you’ll be glad later that you learned that.”

And every time we do that – every time we turn down the opportunity to weigh in honestly about something, to give kids a chance to see us  grappling with the complexity of things – we forfeit a little bit more credibility.  We’re like the reviewer who only says good or bad things.  We’ve merely chosen a position, and declined to engage in any kind of inquiry, analysis, or critique of it.  It’s an odd choice, when you think about it, because we want kids to become discerning about what they choose to opt into and out of (when it comes to what they’re asked or pressured to do by friends, partners, insurance salespeople, etc.)

It’s not as though we have to engage in a lengthy discussion every single time a child challenges something; it’s just that if we never do, it sends a message that’s inconsistent with how we say we want kids to turn out.  If from time to time we say things like “Huh.  I’ve never really thought about why kids have to do that.  Maybe it’s _____, or maybe it’s ______, or maybe the reason was once good but it’s time we rethink it,” then kids see that we’re willing to actually consider what’s in front of us.  So that when later we say “I’m concerned about your staying over at _____’s house because ______,” they’re less tempted to dismiss our concern out of hand as just another in a long series of thoughtless adult responses we’re delivering on auto-pilot.

If instead the language sounds more like this: “I’d like to talk with you about your iPod.  I don’t always understand how important some things are to you because we didn’t have them when I was a kid.  I know it’s easy for adults to just tell kids what to do without thinking about it. I’m trying not to do that with you.  But there are some things that I’m concerned about that I’d like for us to talk about.”

That kind of language is an opening for conversation and interaction, one that makes it possible to move out of the compliance vs. resistance zone.  It doesn’t mean the child will throw down her iPod and tell you she’s been dying for you to bring it up and from now on she’ll only use it on alternate Tuesdays. It’s just a first step.  The longer we’ve been stuck in a comply or resist dynamic with a child, or the more pronounced the dynamic is, the longer the journey out.  But that first step goes a long way.  It’s that step that makes it possible for things to begin to shift.  And especially if we want kids to figure out what kind of a role they want technology to play in their lives once they’re no longer in our care and charge, we’ll be wise to take it on.

I’m reading Clay Shirky’s Cognitive Surplus: Creativity and Generosity in a Connected Age.  It’s about how technology makes use of human talent and generosity in ways that haven’t been possible in the past.  It’s a pretty significant departure from the technology-is-ruining-us, especially-the-kids rhetoric.  Here’s an interesting passage, which reminded me of the piece I linked to a few weeks ago about how kids are reading more than before, even while we agonize about the screen time:

“…young populations with access to fast, interactive media are shifting their behavior away from media that presupposes pure consumption.  Even when they watch video online, seemingly pure analog to TV, they have opportunities to comment on the material, to share it with their friends, to label, rate, or rank it, and of course, to discuss it with other viewers around the world… Even when they are engaged in watching TV, in other words, many members of the networked population are engaged with one another, and this engagement correlates with behaviors other than passive consumption.”

And a few pages later:

“It’s also easy to assume that the world as it currently exists represents some sort of ideal expression of society, and that all deviations from this sacred tradition are both shocking and bad.”

It’s this assumption that has us tend to jump to conclusions about kids’ technology use.  We think that the way we’re used to doing things must be the way things should be done.  We don’t tend to think “Is it possible that there might be some benefit or use to what kids are doing that we never did?”  Shirky’s suggesting that we look a little more closely.  This is not to say that just by virtue of being looked at more closely what kids are up to with their technology will seem more worthwhile.  It’s only to say that we don’t have the foggiest notion what kids do and don’t get out of what they’re doing.  It isn’t necessarily bad for them just because we didn’t have it when we were young.  And as Shirky suggests, it’s possible that it’s leading us to a place of even more social engagement, connection, and potential contribution than was possible when we were growing up.  Maybe more than has ever been possible.

If you’re interested in more on this topic, I highly recommend the book.  It’s unusual in that the thinking is dense, deep, innovative, but the writing makes it very accessible. You can also get a taste for the content from Shirky’s TED talk on the topic.