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.