This week I have developed a new appreciation for those who are learning to write or draw for the first time, thanks to a foray into ambidextrosity.  As I have mentioned here recently, my right shoulder has been giving me trouble, and so I was distressed to think that I couldn’t participate in a 100-day art-making challenge I heard about.  I realized that while my right hand works considerably better than my left, I do have two hands, and if I really wanted to participate without over-straining my right shoulder, I could use my left hand. It might even make an interesting creative challenge/constraint/improvisational score.

It is hard.  I often want to switch back to my right hand for things I know it can do that the left cannot.  Straight lines, for example.  So many things my right hand does without any intentional thinking require planning and troubleshooting, if they can be done at all (and many can’t).  Then there’s the challenge of writing against the flow of traffic, as it were.  My father and brother are both left-handed and so I have watched plenty of left-handed writing-utensil-wielding but not ever given thought to the degree of difficulty involved.

I’ve also been thinking about what it’s like for kids to sort these things out, and how much practice they need, and how much easier it would be without someone breathing down your neck about how neat it is, or how to do it “right.”

While we’re on the subject, here’s a little thing I posted on the subject a few years back:

I know several kids who write very, very slowly. I know others who like to decorate their letters as they write, many who form their letters starting at the bottom rather than the top, and lots who despise the task of holding a writing utensil at all, complaining of tired and weak muscles.

I watched one of these slow writers doing some math the other day.  The speed of her math performance has been a point of concern and discussion in school lately. It occurred to me as I was watching that part of the reason she takes a long time getting through math problems is that she wants the numbers to look nice.  For her, writing numbers (and anything else) is an opportunity to make art.

Artistry is often at work with the letter-decorators I mentioned too, though I’ve also seen letter-decorating used primarily to combat boredom.  Here are two other interesting coincidings: those writers who work from the bottom of the letter also tend to be the ones who would rather be designing and building things than sitting bent over a piece of paper, and the messiest and most apparently tormented or resistant are often the ones to whom the words are the most important.  The writers.

I’ve been observing young writers for a long time, and I was also one myself once.  The year I was eight was significant for me. I spoke in front of a large group of people for the first time, among other things. But the thing that got the most attention that year was my handwriting.  It wasn’t very good. I was in too much of a hurry, the adults told me.  I could do better.

Fortunately, that flurry of concern over my sub-par penmanship didn’t leave much of a mark on me, as far as I can tell.  I know that the parents and teachers who harped on my letter formation back then had my interests at heart and in mind.  I’m pretty sure that if they had realized I was just trying to keep up with my thoughts, they’d have handled it differently. The teachers I know now aren’t as hard on kids about handwriting as the ones I had when I was young, but we still tend to miss the opportunity to learn from what goes on with kids when they sit down to write – not just how the letters look but how kids are about it and what communication there may be for us to receive in the course of watching.

We miss this opportunity for noble reasons; we believe we know how to tell when writing’s going well and when it’s not.  The sight of neat legible letters soothes us, makes us feel as though things will be OK for the child forming those letters.  But too much haste, too little haste, unusual pathways, and general resistance worry us.  The task of writing feels important, so we get rigid and frightened about it and push for the results we know to push for.

But being rigid and frightened makes it hard to see what more there is to see, and it tends to undermine access to the very proficiency we’re after.

Here’s the thing.  The word is penmanship.  As with craftsmanship or sportsmanship, there’s grace and individuality suggested by and allowed for in the word.  Penmanship has come to refer only to how tidily we write, but it didn’t start there and we don’t have to settle for that.  We can ask ourselves more interesting questions about the emerging penmanship(s) of those newest to the tool – the way each one wields his or her pen.  What is there to see in a child’s resistance to writing?  What might it lead to?  Why would a person spend as much time drawing spiraling tails on every letter as choosing the words the letters make up?  Why is the messy writer in such a hurry?

If we ask questions like these, we’ll get insights into the behaviors themselves and also, most likely, surprising causes for further curiosity and even celebration.  And we’ll make lots more room for young people to come to own the work of writing, and to call on it to serve and support them in whatever paths and pursuits they choose.

a boost from the buddy bench

This Saskatoon news report is making the rounds, about a school in Vancouver that set up a buddy bench.  The first student interviewed explains it this way: “It’s where if you don’t – if you can’t find your best friends, and you don’t know where to go play, you sit on a buddy bench and someone will come find you and include you in their game.”

In this clip, the emphasis is on the momentary need for connection – a kid who just then can’t find his friends or isn’t otherwise engaged with a group and wants to be. In some of the other coverage I found of buddy bench implementation, the language leans more in the direction of “for kids who have trouble making friends.”

I can see the bench helping with either thing, but I think the framing matters.  The former suggests that we all may need a boost from a buddy bench from time to time, and having it there takes the pressure off.  The latter makes it sound as though while some  of us know what we’re doing when it comes to social engagement, others are flawed and need remediation.

I’d bet that most adults, introverts and extraverts alike, would agree that the former is a more accurate assessment of human experience in the social realm.

full moon

The moon was almost full last night, and sitting right up in the sky outside my living room window in a clear sky, so I had a good view. When this happens I get amazed that I can see variation in the moon’s surface.  I was trying to think this thought: “Amazing.  It’s ______ miles away and I can see all the _______.” But I didn’t know how far away it was or what the variations I could see actually are.  This is the sort of thing I think I am supposed to know but don’t.  Then I remembered that if you don’t know something you would like to know, you can find it out.  This is an obvious thing, an advantage of the brain plus books plus other people plus the internet, but I am constantly not bothering to do anything about it.

So I looked this one up.  (On the computer.) First up was Google’s answer – the moon is 238,900 miles from earth. I started thinking about how to really get how far that is, but then I spotted another search result three items down in the form of a question: How far away is the moon? I liked the sound of that, linguistically speaking, so I followed the link to the NASA SpacePlace page, which appears to be set up for younger people than myself.  Such pages can be excellent for learning information that one thinks one is already expected to know, because it’s (sometimes) offered in clear and plain terms, though one might also have to read around some condescension, which is too bad.

NASA’s explanation, not surprisingly, is a little more detailed and nuanced (accurate) than Google’s.  The distance between the earth and the moon changes, so it can be expressed as an average or as a measurement at a particular moment in its orbit (which is not a perfect circle, hence the variation in distance).  According to NASA SpacePlace, the moon is 238,855 miles on average.  At its closest, 225,623, and at its farthest, 252,088.

I had to stop myself from reading much more just then because when it comes to the moon, several very cool words come into play (apogee, perigee, penumbra, et. al.) and as a result I knew myself to be at risk for spending the rest of the day becoming a moon expert (relative to how I’d been night before) and I had other things people were counting on me to do.

All of that is to say I was glad to be reminded that a few seconds spent asking a question and looking for an answer is enough to put things in perspective, and when things are in perspective, universe-wise, it’s hard not to be amazed and inspired and re-energized for whatever earthly toil one has assigned one’s self, even in a terribly tumultuous time.

a few things about smallness

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.


I went to a concert yesterday in a church sanctuary. The concert was unrelated to the business of the church, but the materials (bibles, hymnals, etc.) remain in place no matter what is happening in the space (services or otherwise).  A stack of cards in a box on the back of each pew read “Welcome.  This card may help you communicate a need or provide information.”

I had this thought: What if we gave cards like these to children in school? What if young people had an ongoing opportunity to communicate, on paper? When I read the card, I got the impression that my experience mattered, that I was being invited to participate.

I thought about the young people I know and wondered what each of them might write on such a card.  The first person who came to mind is in sixth grade. He might write “Most of the time I’m confused when we’re doing math.”  Another would likely say something like “I’m really interested in invasive species; can we learn more about that?”  Two high school students I know might say “Is there any way you could punch holes in our handouts before you give them to us, or keep a hole punch in the room so we could punch them ourselves? That would help me keep my binder from getting so messy.”  Another might say “I’m really not trying to be a brat, but I’m bored, and it’s so frustrating when we spend so much time going over the homework that is exactly what we just did in class the day before.”  Given the chance, I think they’d tell us all sorts of things that would be helpful to know.  Things that would help us understand their behavior, things that would help us provide the best possible support for them, things that would help us know them better.

My guess is that there are some teachers and schools who have something like this in place, some way for students to communicate with teachers and administrators that does not require trying to get an adult’s attention verbally, or reveal his or her need or information to all those within earshot.   But in general, I think we expect that young people will speak up if there’s something they need to say, and I think mostly they don’t.

Some might abuse an “opportunity to communicate a need or provide information” in an anonymous fashion, as one quick look at the internet will tell us.  It might be worth the sifting and sorting it would take to manage that, though, if it would make it possible for us to hear more from  young people who are sitting quietly not communicating with us, and, too, many of the ones who aren’t sitting quietly but aren’t going to say theirs out loud either.

Even if none of them wrote anything down, I think they’d get that message that I got when I read the card sitting there in the pew of a church I don’t even attend – that if I was there, I was invited to communicate and thus to participate.


On Saturday we had a visit from four friends – my college roommate, her husband, and their two sons, who are six and three.

The three year-old and I found, in a box of old games, a cribbage board.  He was enamored of the board when he saw the hidden compartment which houses the little pegs.  He also liked the surface, with a track corresponding to each of the three peg colors in the compartment.  He decided that we would each choose a color and then move the pegs around the board according to what we each rolled on a  six-sided die.

He is mostly confident at counting up to six, but has trouble distinguishing between the four and the five on a die.  I was reminded, when I noticed this, of how much math learning will take care of itself in the course of dice games played with young children.

I didn’t have to do any instructing about this four and five thing, though I’d have been willing to if I’d been asked. I just counted out four each time I rolled a four, and counted out five each time I rolled a five.  When he wasn’t sure which he’d rolled, he’d say one or the other, lifting his tone slightly at the end, just enough of a question for me to confirm or correct whichever he’d chose. After a few rounds of this he stopped getting the two confused, and stopped reading the numbers as questions, because he knew he had figured it out.


On Thursday last week, I spoke with the mom of a child who had asked her to find out if someone could help him control his behavior in school.  (I’ll call him Owen.) He has a tendency to interrupt his teacher, to speak up without being called on first, and to have difficulty staying in his seat long enough to finish assignments.  Owen’s nine.

In our first conversation, his mom and I talked about how it’s easy to confuse and confound the symptoms of attention deficit disorder and profound intellectual strength.  The two can look quite similar in the context of a classroom in which children are expected to perform repetitive, stationary, lower-level cognitive tasks.  Owen, his mother told me, has tons of physical energy, and is very curious and interested in learning. He can’t always stand to wait for other students to catch up with where his brain is. He was recently diagnosed with attention deficit disorder/executive function. I told her that what I’d be able to provide for him is support in building strategies for managing his school work and that this work would most likely be successful if combined with intellectual (in the form of logic puzzles, creative problem-solving activities, and other tasks that involve higher-order thinking) that would meet his craving for intellectual engagement.

In our second conversation, after she had spoken with Owen’s teacher, his mom told me that there didn’t seem to be any evidence of the executive function difficulty in the classroom, and what the teacher was more concerned about was impulsivity – the interrupting, the speaking up without being called on, the scooting around the classroom when he was supposed to be in his seat.

This mom originally called me at the recommendation of the neuropsychologist who evaluated her son.  This evaluator has referred several children to me and I have worked with some of them.  I think it’s expected that I will be able to help children with their executive function difficulties.  It’s true that I have been able to help some children (as well as some adults) with executive function difficulty.  But as often as I help with that (which is only when the person him or herself experiences the executive function difficulty as an impairment), I end up helping with something else that makes a different kind of difference.

Helping children with executive function is usually a matter of helping them comply with environmental demands in which they don’t have much intrinsic investment.  It’s not that they don’t notice or feel the effects of not being able to comply with the demands; it’s that if given the choice, they would rather not be required to.  If you offered them the chance to exist in an environment that didn’t make those demands, and they could exist there without being ostracized for it, they would choose that.

If this is the case with a child, helping with the executive function tends to be a losing battle.  Kids who fit this description tend to undermine their own efforts to improve their ability to stay on task in school, get their homework done, and generally keep track of their assignments.

So executive function is for most children a matter of adaptation.  They’ve been assigned an environment, and in order to succeed there, to be deemed successful according to the measures of the environment, they must alter their tendencies and habits.

Owen’s teacher doesn’t think that he needed help with executive function, but the concerns she does have are also about his adaptive performance.  A typical classroom is not a natural fit for a person with a lot of physical energy, who needs motion and activity in order to keep calm, to think clearly, to feel at ease.

In my second conversation with Owen’s mom, she asked if I might be able to help with the impulsivity. Now that the executive function concern was out of the way, the focus would be staying seated and not interrupting or speaking without being called on by the teacher.

It’s at this point that my job becomes a little weird.  Weird is probably not the right word.  Agonizing is a better word, if you want one that describes my experience of it.  Here’s why: I could do what this mom is asking.  I could help her son get himself to stay in his seat.  I could help him build and use strategies for keeping quiet when he was expected to in the classroom.   And if I did, some things would be better for him than they are now.  He would feel less self-conscious.  He would be embarrassed by his behavior less often.  He might finish more of his work. His parents and teachers would stop worrying about his behavior and about his future.

Is there a cost, though, to staying in your seat when you have the impulse to move?  Or to completing a page of problems you already know how to do rather than thinking about something that intrigues or otherwise engages you?  Or to slowing your own thinking to meet that of a group of age-peers simply because they’re the same age as you are, and thus the only classmates you are entitled to?

In some ways, I wish there weren’t.  I wish I could sit down with a child and coach him or her to adapt to the environment that is the current reality for most children and believe that it would only help.  The push for adaptation, and quick, is tremendous.  I hear so many times a week that children need to be prepared for the way the world is.  They need to learn to do things they don’t want to do, to learn to be told what to do, to find out that life is hard, to get used to not getting their way. I do know that some adaptation is crucial to survival, and not just in the wilderness.  There are ways that the world is, and to be able to navigate them helps.  But to only adapt is not necessarily, in my opinion, to optimize the potential of the human organism.  And sometimes, to become accustomed to adapting without advocating for one’s needs and strengths is to shortchange the species, to deny it the potential for growth and progress.

A few years ago I was working with a fourth grader whose mom was concerned about his math skills.  One week he came into my office and sighed a great, heavy sigh as he settled into a chair across from me.

“What happened?” I asked him.
“I need you to show me the second way of subtracting,” he said.
I asked him to tell me more.
“Well, last week my teacher showed us how to subtract, where you cross out the one number and then add the one to the number next to it…” he looked up at me to confirm that I knew what he was talking about. I nodded, and he continued.  “So then today at math time she wrote another problem like the ones we were doing last week up on the board and started talking.  I thought she was just showing us that same way of subtracting again so… I… stopped… listening.”  He said this quietly.
“It’s OK,” I said.
He sighed. I waited for a moment to see if there was more.
“Is that the end of the story?
“Yeah,” he said. “That’s all.  I mean, I found out later that we were supposed to be learning a second way of subtracting that we have to do for homework and now I don’t know how to do it because I wasn’t listening.”
“OK.  I have a question.”
“Uh-huh,” he said.
“OK if I ask it?”
“You don’t have to answer me unless you want to, but I’m wondering what you were doing with your mind instead of listening to the teacher about the second way of subtracting.”
He took a deep breath.  “Well, my brother and I got a Lego Millenium Falcon for Christmas, and after we built it with the instructions, we took it apart and started building another one with our own design, but we’ve been having trouble getting it to support its own weight.  I had an idea about adding these struts in the back like this (he demonstrated the angle he had in mind) and I was trying to imagine how they could attach.”

I’ve asked kids this question, about what they were thinking about when the classroom environment demanded they be thinking about something else, attending to something chosen by the adult in charge, and it’s not always a complicated engineering problem as it was this time for this child, but it’s rarely frivolous. I suppose that frivolity is a matter of opinion, so I should add that it’s rarely frivolous in my opinion.  A wise friend of mine told me once that his primary reason for considering the possibility of not sending his children to school as soon as they turned five was that it was important to him that they have access to their own thoughts – that they have a chance to figure out what they were interested in, what mattered to them, and he thought that if they were hurried off to school, where they would much of the time be told what to think about and when, that they might not have the chance to get acquainted with the contents of their own minds and imaginations.

This fourth grader, once he thought he was all set with subtraction, turned his attention to a fairly complicated problem of engineering.

From a very young age, humans go looking for good uses to put their minds to.

From a very young age, humans go looking for good uses to put their minds to. There’s an extent to which we sometimes undermine and interrupt that process in the name of adaptation and presumed survival.  We imagine that if we just force a kid like this one to comply with our curricular plans for him, that later, once he’s been taught (and re-taught) everything we consider basic, he can turn his attention to contribution and participation.

There are a few problems with this model.  One is that the curiosities of a young person don’t necessarily hang in there in the face of being ignored, suppressed, or otherwise dishonored.  A child who is fascinated by technical problems as a five and six and seven year-old but is not free to explore such problems and is told that the most important thing is to do well in his schoolwork, his spelling and his multiplication, will often not remain loyal to his earlier curiosities.  (In fact, a child who does remain loyal is often considered a behavior problem, or difficult, or resistant, at risk for failure as a student.)

Also, we know that the brain is most elastic when it’s young. The flexibility and openness to new ways of thinking is not confined to language learning. If we spend all that elasticity on predetermined and prescribed content, we leave little room for the thoughts and unique creative potentials of the individual.  (And I don’t mean creative in an artistic sense, though I include the artistic – I mean creative in its basic sense, making things up, thinking of things that haven’t been thought of or haven’t been thought of in a particular way.)

This is all to say, I suppose, in many many paragraphs, that I think there’s a balance to be struck, to be sought, between adaptation and actualization.  Between supporting an individual in finding his or her way among the obstacles erected around him over time and supporting him or her in exploring and realizing the fullest possible extent of her capacities and curiosities. A balance which, if struck or even aspired to, could save a lot of frustration for a lot of students (and teachers) and offer all of us better access to the extent of potential contained in our human selves.

the sorter is broken

I asked a high-school aged friend if she’s thought about what she might want to study in college (she’d already told me she wants to go) or what she might want to do after college.  She hesitated, and then said that she really likes science but she’s terrible at memorizing things, so probably she’ll do something with history instead. She said she’s especially interested in environmental science and issues related to climate change.

You could think of this as a teaching or curriculum problem, but I don’t think it really is.  I think it’s a sorting problem.  Or a problem with how we’ve taught ourselves to imagine we should be sorted when it comes to ability and suited-ness to particular tasks and professions.  And also a problem with how we think about what our brains are best used for.

This young person thinks that her difficulty with memorizing will exclude her (or should exclude her) from a career in science.  She has classmates who memorize easily, and they are the ones with high scores on tests and in courses. So on paper, on transcripts, if it’s good grades that tell us about someone’s aptitude for a particular area of study, we can see that her quick-memorizing classmates are the ones destined for careers in science.  Yes, many a good teacher will tell you that if you don’t emphasize the memorization you can show something different with how you grade, but for most students in most schools, information recall is a big factor in grade determination and a teacher who makes it otherwise is swimming upstream and trying to pull her students along with her against a strong current.

What would we have to do to make it otherwise?  First we’d have to decide whether we believe that a scientist must be able to keep on hand a multitude of data.  Must one?  I’d guess not, at a time when it’s possible to put a handheld device with endless data in the hand of any professional anything.  Wouldn’t it make sense for the first qualifying characteristic for a career in science (or any participation in science) be an interest in participating, and then perhaps the second an interest in and capacity for problem solving and analytical thought?  Science once required extensive memorization, but it doesn’t any more, and we’ve got big enough problems, and many enough problems, that the more solvers we can get on them the better, it seems to me.  To exclude the ones who can’t memorize stuff as well as some others can memorize stuff seems unwise.  Not to mention that the good memorizers might be put to better use elsewhere especially if they’re not interested in the careers and occupations that their memorizing might qualify them for and point them in the direction of.