Just kidding

Andrea* looks down at the algebra problem she’s working through and notices that she’s assigned a value of five, rather than six, to three twos. As she erases the five and replaces it with a six, she says “Just kidding.” We both smile. Then she continues with the rest of the problem.

This is a simple but brilliant little practice of hers.  Math can be so charged, and the prospect of making a mistake in math inspires fear and trepidation throughout the land.  If a young person can relate to miscalculation as an opportunity to pretend they’ve made a little joke, they’ve got at least one way to keep perspective.

So many of the kids I work with have learned to tense up and start defending themselves when they can’t remember something or when they mix things up.  Their eyes dart up to see how I’ll react, and before I even have a chance to, they start spinning their talking wheels – “Oh, I thought we were supposed to do plus, not times… My teacher said… When we did it in class… This is so confusing…” Or they just give up all together and tell me they can’t do it.  Usually over something as small as five, instead of six, for two times three.  These kids have received the message that if you don’t get every bit of it right every time, especially the single-digit stuff, then you might as well hang up your math cleats and plan on a route that doesn’t include any numbers.  They expect to be judged on their ability to achieve computational perfection.

Andrea figured out, in time, that it’s possible to miscalculate, even often, and still excel as a math student.  And that if she keeps her sense of humor about her, she can keep her head in the game.

I’ve started telling the younger kids I know, especially those who get skittish when they mix up six and five (or write a seven open to the right instead of left), about Andrea’s just kiddings.  I’ll say something like “One of the teenagers I know, when she makes a little mistake like that, always says ‘Just kidding.’ She’s not saying that to really pretend she meant to do it, she’s saying it because it’s funny to pretend she meant to do it.  I think she does it to remind herself that making a little mistake is no big deal and if she makes a little joke about it, the mistake doesn’t distract her from the real thinking she’s trying to do.”

A couple of them have tried it, and with noticeable results.  It interrupts the habit of panic and doubt, creates a space for relaxation and ease.  And there’s nothing like a little calm to free up the mind for math.

*Not her actual name.

Tools for a fraction renaissance

Many a parent has told me that if only they’d had a set of fraction tiles when they were young, math would have gone very differently for them. That may even be understating things.  It’s hard to imagine a handful of plastic pieces could significantly change the course of a life, but then again, things are in a bit of a state, math-wise.

If math can go differently from how it often goes (ie Not Well), the course of a person’s whole life, not just math success, can be altered substantially.  This is not to say that you can’t have a perfectly good life if math doesn’t go well for you (nor that fraction tiles are necessary).  It’s just that math is held as such a staunch indicator of intelligence and promise that if you get the impression that you’re not one of the ones who’s good at it, it’s likely to get in your way to some degree. And that degree is not usually small.

All of this is to say that in my opinion there’s no purchase (including fancy curriculum, fancy enrollment, fancy tutoring) that is likely to make quite the difference that a set of fraction tiles can make.  Fractions are often the turning point for young learners of math; all the adding and subtracting of whole numbers made sense, came easily, and then suddenly those whole numbers were stacked on top of each other, separated by little platforms, and they got new names.  Maybe, kids think, I’m not so good at math after all.  The fraction tiles can help.

And you don’t even really need to do much with them.  The tiles pictured above are available with magnets (or can be easily equipped with magnets), so they can be… stored… on the refrigerator, just like those trusty Fisher-Price alphabets of yore.  Anyone who goes near the refrigerator sees them, sees that the fourths are twice as big as the eighths, that four twelfths fit in a third, sees how they all relate to the whole.  And then they’re there for reference too.  If you’re baking and you want to halve a recipe you can ask someone to check the fridge to see how much half a fourth is, or just go over and do it yourself (out loud: “Let’s see.  A fourth is when it’s broken into four pieces.  If the fourth got broken in half again, it’d be the same as… (sift around until you find the right-sized piece)  the eighth.  So I need an eighth of a cup.”

There are languages, apparently, in which fractions have names that make sense and reflect their conceptual basis (I’m told that in Chinese, 3/5 is “out of five parts, three”).  In English, not so much.  Without the linguistic support in place, the least we can do is let kids learn the concept first, let them see the fracturing and make sense of the notation with their eyes and hands before we expect them to make sense of it abstractly.

If you can get your hands on a set of tiles and get them up on the fridge when your children are still toddlers, great.  They’ll get familiar with them the way kids get familiar with anything they see a lot from the time they’re very young – without even trying.  But no matter how old your kids are, no matter how old you are, it’s not too late to let the tiles make a difference!  And you may even find that your teenager, or your neighbor, or your high-achieving college graduate daughter will walk by one day, wonder why you now have fractions on the fridge, and then suddenly exclaim “Oh!  NOW I get it!”

Because most of us, still, don’t. It’s not just you.

Friends with fractions

I know lots of kids who can tell you that the top number in a fraction is called the numerator and the bottom number is called the denominator. But they don’t understand how the two numbers function or relate to each other.  The words numerator and denominator do technically describe the functions of each number, but only if you happen to recognize all the Latin roots.  So in the absence of Latin fluency, this might help. Continue reading

Exercise for the brain…

Solitaire has acquired the reputation for being a popular way to waste time in an office job.  It certainly can be that, but it’s also an opportunity for building mental agility and acuity.  It can also be very meditative, fun, and otherwise great, for some.  For others, it’s terrifically boring.

If you happen to know a young person who might fall into that some category, here’s a book I came across today. It looks good – the explanations appear to be clear, and the illustrations, sharp and fun to look at…

Shaking it off

Getting determined plays a big part in building your kid’s life around who she actually is, with some of it matching up with what we traditionally think kids should be up to and some not.  There will be things that work famously and easily, and things that don’t.

‘Til we’re blue in the face we can say we believe that if at first you don’t succeed, try, try, etc., meanwhile (understandably) hoping things that are meant to be will work instantly.  That they’re won’t actually have to be too much try, try.  But it often does take a lot of try, try, and it really can be the difference between getting somewhere and staying nowhere.  Which is probably why it can feel excruciating even though it sounds so simple!  I’m writing about it today because it keeps smacking me in the face with various attempts I’m in the process of.

That first phone call to a possible mentor didn’t work out?  The woman was downright mean?  There’s someone else out there who’s not, and it’ll be worth making the second call (unless it takes three, or four, or more). I promise.

Like Reading?

Kids often tell me they don’t like reading, except for things they like.

What the heck?  I can’t tell you how many zillions of times I’ve heard this.  Somehow we’re giving them the impression that  these People Who Like Reading that they’ve heard of and know about like reading everything.  When I encounter this, I assure whomever it is, up one side and down the other, that this is not the case. I know because I’d make a good Exhibit A.  I love reading things I like and want to read, and I detest reading anything I don’t like and don’t want to read.  It sounds ridiculous.

One way we could probably curb this confusion is to stop saying simply that we love to read.  It’s usually not true, anyway, without the rest of the sentence.  It’s like I was saying here about finishing the sentence to make it true.  Unless you really just plain love to read anything that’s put in front of you – love it for the reading of it and not anything to do with the content – you could do many kids a great service by saying something like “I love to read when the writing’s really good,” or “I love to read books that are about people like me,” or “I love to read road signs,” or “I love to read magazines.”  Then they’d start to get a more accurate picture of this reading world of ours, in which we all have taste and rarely read just because there are words in front of us and we want to spend time reading them because we don’t have anything better to do.

Let them know there’s something in it for you, and then they’ll have the freedom to find out whether or not there might be anything in it for them.

You Just Have To!

One thing adults love to say to kids is “Well, too bad; there are some things you just have to do.”  If you watch a kid’s face when someone’s delivering that line, you’ll know right away how many times they’ve heard this before.  In most cases, LOTS.  You’ll also get a sense of how inspired they are to act as a result of it.  In most cases, NOT PARTICULARLY.

It’s something we say to each other, as adults too, and it’s implied in much of what we do.  Because, of course, we heard it all the time back when we, the present-day adults, were kids.  So we take it as truth, and in good conscience, we pass it on.  We want kids to be ready for the real world.  And it helps us feel as though life is supposed to be as much of a drag as it can feel like when our days are full of things we’re doing because we think we just have to.

But it’s TRUE isn’t it?  There are things we just have to do.  Don’t worry; I’m not going to argue that it’s not true.  I’m going to argue that it’s incomplete.  On its own, the statement is in fact not true.  You don’t actually have to do anything.  You have to do some things if you want a specific outcome or you want to avoid a specific outcome. For example, nobody actually has to do the dishes. You might have to do the dishes if you don’t want to throw away all the ones you’ve used and buy new ones. Or you don’t want to cause a rift between yourself and a loved one.  Or you have a job as a dishwasher and you want to get paid at the end of the week.  So it would be more accurate to say “There are some things you just have to do if…” Or “There are some things you just have to do unless…”

What’s tough is that as soon as you decide you’re going to make it a point to complete the sentence, you start to see how much you’re insisting upon (from yourself and others, kids included) that demands deeper consideration of how the sentence should end.  Don’t worry, though.  There’s gold at the other end; if you commit to inquiring into why/if you have to do things, and why you actually insist on what you insist on for others, you’ll find that a lot of the fight falls away. Kids, in particular, will perk right up.  They can hear the difference between things we say on auto pilot and things we say because we’ve considered them and determined that they have some value.