The Comma

If [this], then [that].  We talk a lot about [this] and [that] in the math classroom. Teacher supplies [this], student responds with [that]. They even have names:  hypothesis and conclusion.  But, what about the comma?   All the power of the entire process is summed up with a tiny little "," that is all too often ignored.

No more.  It's time to give the comma a voice.

We were getting ready to add rational expressions and I wanted my students do have a workable rule for adding fractions with like and unlike denominators.  My goal was to develop the idea that when adding fractions with unlike denominators:

A lot of students don't see this very clearly.  They do what they do to jump from [this] to [that].  And most of the problems end up looking a lot like

with no real understanding of what's taken place between the hypothesis and conclusion.  And up to this point, no one has really cared because Johnny was able to find the correct answer on multiple choice scavenger hunts with a great deal of accuracy added fractions like a champ in 6th and 7th grade. However, when Johnny gets to algebra, and sees

for the first time, you'd think he's never worked with fractions before.


Time to talk about the comma.  It was actually a pretty simple adjustment to a simple question, but the conversations it generated made all the difference in the world.

This quickly became

See, the beauty here is that the process became the outcome.  The numbers become the variables and we get a good grip on how one-third plus two-sevenths becomes thirteen-twentyfirsts.  The abstract isn't so abstract and the easy part is swapping out the 1, 2, 3, and 7 for a, b, c, and d.

Mission accomplished.  Now, lets hope they remember it tomorrow.