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.

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Fraction ease

Fractions wouldn’t take as long to teach (take a look at local or state curriculum guidelines to see how many grades’ worth of math time are generally allotted) if young children got as much experience with other fractions as they get with halves.  I meet lots of kids who are “having a hard time with fractions” but can manipulate and handle halves with ease.  It’s usually the other fractions that present a problem.

Fractions only exist in language.  When we say fractions we’re actually referring to a bunch of words and ways of writing things that we use to communicate with each other about parts of things.  The reason kids understand halves so well is not that halves are easier than, for example, thirds.  Half and third are the same concept.  It’s just that kids become fluent in halves because they hear them spoken.  We could facilitate fluency in other fractions too.  When sharing among trios or quartets, for example.  I often hear myself say “split it in half” but I don’t hear myself say “split it in thirds.”  If there are three or more ways to split something, I’m more likely to say “split it up.”

The other interesting thing is that kids (these same ones who are comfortable with the concept of half) tend to have a hard time explaining what half means.  What they’re doing with halves is not so much understanding them as speaking them.   Their trouble explaining isn’t an indication that they don’t get what a half is.  It’s that they get it so well it hasn’t occurred to them that it’s something you should be able to explain.  There’s no reason that couldn’t be true for thirds and beyond.  And once it is, the rest of it – all the fussing about with denominators and so on – will become much, much easier.

Mathematician’s Lament…

I’m not sure how I didn’t know about this book already, but I’m glad I do now.  It’s called  A Mathematician’s Lament, and begins with the following quote from Antoine de Saint-Exupéry: “If you want to build a ship, don’t drum up people to collect wood and don’t assign them tasks and work, but rather teach them to long for the endless immensity of the sea.”

It’s not every day that a book about math, or anything about math for that matter, invokes… well, humanity.  That was my experience in reading through this excerpt.  If you’re someone who loves math, or dreads it, or worries how you’ll ever help your kids learn it, have a look at the excerpt and see if this one might be for 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

Why are they called numerators and denominators?

I’ve been doing fractions for several decades, and only yesterday did I find out how the numerator (the number on the top) and the denominator (the one on the bottom) got their names. I’m not sure that knowing why they’re called what they’re called will help too many folks who struggle with fractions, but I’m pretty sure it will help a few, so here goes. Continue reading

Math Practice for the Younger…

I hung on to a daily math practice book from my last classroom teaching job, and it’s proven a good keep.  It’s published by Great Source, and is set up as a quick review for a range of math concepts (place value, fractions and decimals, etc.).  It’s called Practice Counts, and comes in several different grade level versions.  (It can be tricky to find – it’s available on amazon but you have to check with the vendor to be sure you’re getting the level you want; you can also order it through a retail store.  The publisher only sells them several at a time.) Continue reading