Earlier this year I posted a link to an excerpt from a 60 Minutes show featuring Jacob Barnett. When Jake was two, and was diagnosed with autism, he seemed to be retreating into an internal world where his parents felt they couldn’t reach him. He’s now a graduate student in theoretical physics.  In his mother’s new book, she tells the detailed version of the story that aired on 60 Minutes.  As the popular summary of Jake’s story goes, his parents refused to believe that he’d never learn to walk or read. They followed many of the prescribed therapy regimens, but they also let him explore the things that seemed to fascinate him, though they didn’t exactly understand what those things were or what they would come to.  His mom, Kristine, writes in the book:

One morning when I walked into the kitchen to refill my coffee cup, the scene before me took my breath away.  Jake had run different-colored yarn all around the kitchen – crisscrossing through the refrigerator handle and around the garbage pail, the table and chair legs, the cabinet pulls, and the knobs of the stove.  The result was a series of brilliantly colored, intricate, overlapping webs.  Using yards of yarn, he had created not a terrible, tangled mess, but a design of complexity, beauty, and sophistication. …It must have seemed a little crazy to let him take over the house in this way.  Some days it was even impossible to get into my kitchen.  But his intricate designs were spectacular to look at, and when the sun streamed through the windows, the shadows they threw moved and changed as the day progressed, involving the whole room in a complex play of light and dark.  These creations were evidence to me that my little boy was in there, busy working on something magnificent.  They gave me a way in, a glimpse into his private world and his extraordinary mind.

The Spark

Jake’s parents could have ignored his fascination with light and shadows as a passing attraction or whim – they could have shut down his access to yarn and insisted that he instead spend all of his time working on his therapies – but they didn’t.  Of the many parts to the Barnetts’ story that can offer inspiration and insight to families with children who are struggling, I think this one may be the most compelling.  Their child was enthralled with things (like this work he was doing with the yarn) that they didn’t at all understand, things that could easily be deemed superfluous, a waste of time, an obsession, little more than a mess.  (And in fact such things often are, by parents and other adults.) The Barnetts were tempted to believe what professionals were telling them about their child – that they couldn’t hope for much from him. But what they decided to believe instead was that whatever Jake was up to in his mind could be the key to reconnecting with him and to helping him find a way to be with them in the social world.

We tend to dismiss many child-chosen pursuits as frivolous, cute, or passing. What if instead we took these things seriously the way the Barnetts did, even when kids aren’t retreating the way Jake was?  We wouldn’t all end up with pint-sized physicists as this family did, but we’d make it possible for a much wider range of potential to emerge and for more kids to feel as though they’ve got something worthwhile to offer, from the very beginning.

Lines less traveled

If you haven’t seen it, I encourage you to check out Logan Laplante’s TEDx talk about how he’s taken charge of his education, organizing his life around a commitment to being happy, healthy, and fostering creativity.

There’s just one small thing I wish Logan had taken a step further. He says that to follow a traditional educational trajectory is like skiing one well-worn line down a mountain, while designing a program for yourself is like heading off into the powder to blaze your own trail.  I’m with him up to the part where he says that the shared line is probably safer.  In the snow it may be, but when you’re building a life, I’m not so sure.

I think it may once have been, but it’s getting less and less safe to traverse the common route.  The competition is so great for the handful of spots there are to fill along the way (in the “best” colleges, “best” graduate schools, the “best” jobs) that it’s no longer a fail-safe way to build a life.  We just keep saying it is because the powder makes us nervous.  The powder’s unknown.  We’d rather take our chances on the thing that will almost certainly work out for some people, even if it’s only a very, very small percentage, than head off into the powder where everyone probably has an approximately equal chance of making it, because there are so many more routes possible and winning spots doesn’t matter so much, if it matters at all.

We’re not safer on the route we know.  We’re just more comfortable there.

I’m so grateful to Logan for the framework he offers, simply and frankly, in this talk. Logan lives in the kind of world I think we could build for everyone, where vitality is of the utmost value and importance and can, in fact, be the best possible guide.

…what you wish for

I got a delightfully practical and irreverent little book about landscaping and gardening for my birthday.  (Here’s a link in case you’re in need or want of such a book.) In the section about hardiness, and which plants will grow in which zones, I came across this note of caution and wisdom from the author:

“Zone envy is natural, but each of us has good things that no one else can have.  And I wouldn’t have it any other way.”

This could be said of many things, including us people, with our various proclivities and struggles.  Those children, for example, who frustrate their caretakers with what seems like excessive sensitivity often say and do astonishingly insightful, compassionate things that less sensitive children don’t.

If you could change that thing about your child (or yourself) that you wish were different, you might also have to give up something you couldn’t bear to live without.

Math resources, one new and one remembered…

I’ve added two resources to the math section of my recommended book list on amazon.

The first is two volumes’ worth of compiled Math Olympiad problems.  I’d forgotten about these, but I like them because there’s usually more than one way to solve each problem and the solver doesn’t know what kind of problem to expect at the outset.  You can see sample problems here; they come in “elementary” and “middle school” levels. (It may look as though I’ve botched the links, but I haven’t.  If you order any, be careful to examine the covers before choosing.  Volume 1 is called “Contest Problems for Elementary and Middle School” but it only contains elementary level problems.  Volume 2 is called “Contest Problems” but has some of each level. I think it’s just because when the first volume came out there was no second volume, and the title was describing the program, not the contents of the book.)

The other is a series of beautifully designed books from Thunder Bay Press called Doodle Yourself Smart. There’s a math volume, a geometry volume, and a physics volume.  Each book has 100 or so puzzles, one per page with lots of room for figuring (and doodling, ostensibly).  They’re refreshingly well-designed, for math books. The pages are actually pleasant to look at.  I’ve only interacted directly with the math volume (the puzzle I did was about finding pairs of primes that added up to various target numbers), but I’m looking forward to the other two.  I’d recommend these especially for math-likers with aesthetic sensibilities.


Jake’s example

I just watched this 60 Minutes story on Jacob Barnett, the 14 year-old student at Purdue University who’s been attracting attention for his exceptional abilities in math and science, particularly physics. It’s just generally inspiring and delightful to watch Jake in action, but the part of this story that got my attention begins about six minutes in:

Morley Safer: Just before his second birthday, Jake began to regress; stopped speaking and making eye contact.  After consulting with several doctors, the diagnosis was autism.

Michael Barnett, Jacob’s dad: We went through speech therapy, physical therapy, developmental therapy, occupational therapy; therapists came to the home…

Kristine Barnett, Jacob’s mom: He was going further and further from our world into a world of his own and I really was just baffled as to how we were going to get him back out of that world.

Morley Safer: And how did you get him back, out of that world?

Kristine Barnett: We realized that Jacob was not happy unless he was doing something he loved.

Morley Safer: Which even as a three year-old was math and science.  His parents say the more he focused on the subjects he loved, the more he began to communicate. 

Kristine Barnett: You could just see him just relax.  You could just see him feel like ‘Thank goodness we’re not working on something that I can’t do today.”

I’m inspired by the way Jacob’s mom talks about what happened when he was two.  She says that her son was “going further and further into a world of his own,” and that they wanted to get him back.  It seems like it would have been easy to worry that supporting Jake’s ventures into the depths of abstract mathematical thought would have pushed him further into the “world” they sought to bring him back from.  But the Barnetts trusted that those things that brought Jake the most peace and contentment were the key to maintaining connection with him. They reorganized his life around what was already engaging and fascinating to him, and eased up on pushing him to do the things that seemed to be shutting him down.

As it turned out, having permission to give his attention to the pursuits that called to him seems to have made it possible for Jake to find (or regain) avenues for communication and other social interaction.  From the sound of it, the family continued to work with him on speaking and engaging with others, but those things were no longer the center of attention.  Communication skills were reassigned – instead of taking center stage, they were given the chance to support the complex intellectual work Jake craved.

The Barnetts are quick to acknowledge that Jake is one person and it doesn’t work to generalize their experience to all or even any other children with autism diagnoses.  But they do encourage parents of any child who appears to be struggling to do just what they did – to look for the spark of contentment and delight in the child – and build around that spark.  Not every child makes it as obvious as Jake did where that spark lies, but I haven’t met a child yet who didn’t have one.

Analogy crosswords, for struggling spellers and others…

I remembered the other day that Mindware makes a book of analogy crosswords (several books, actually, at different levels of complexity).

Like anything else, these crosswords are no good when forced on unwilling doers, but for kids who have asked for help with spelling or those who enjoy tasks that bend the mind, inviting the formation of new neural connections, they’re quite effective and even enjoyable. (What makes them a relatively fun way to work on spelling is that they offer the hint of how many letters the word has, and occasional letters from other words.  For struggling spellers with agile minds (which is most of them, I find), the job of figuring out which letters are involved is rendered less arduous by that of figuring out which word it is in the first place.  Then the hint offered by the number of spaces and intersecting words acts as a bit of scaffolding.  It’s a little interim boost  – makes the task more manageable in the short term so it isn’t abandoned all together for being too much to handle.)

Here they are on amazon.  Sample pages at

Because they’re crosswords, you’ll have to forgive the makers for (what I would consider) an occasional… stretch… in the name of fitting an answer into both an analogy and a particular configuration of letters. It’s worth it, though.  Even the ones that seem slightly off invite useful mental gymnastics, in my opinion…

Fun with circles and teeth

A friend handed me one of these the other day and said “Like Spirographs, remember?”

I didn’t remember, but if I ever used one I’m sure I loved it (and apparently it’s possible to find similar products now but Hasbro doesn’t make the original anymore; if I’m wrong please let me know!). This thing is great fun if you like shapes or patterns or color or the unexpected.

And it’s one of those things that the mathematicians like to play with and calculate about that blurs the boundaries between math and art. I’m pretty sure this is the kind of thing Paul Lockhart is talking about all the time; the math that tickles, and wrinkles the brow with amazement.

I mentioned a talk by Conrad Wolfram a while ago, which I remembered in the midst of playing with the hypotrochoid set because I went looking to find out how the thing works and found this animation on his MathWorld of a point rolling around inside a circle in a fixed way which is what goes on with hypotrochoids.  No numbers required in the marveling at it…