Thursday, May 8, 2014

Isolating The Radical

My math students, past and present, are pretty darn awesome. 

They come to class week after week, full of good cheer and ready to work.
They complete boatloads of homework.
And every month or so, when test time rolls around, they sharpen their pencils and dig in. I'm so impressed with how well they do.

But most of all, my students are awesome because they put up with my whack-a-doodle explanations of mathematical concepts.

Here's an example of what I mean.


Recently, I taught a lesson on radical equations. In order to solve these intimidating beasts, one must first complete a step called "isolating the radical."

Well, even if you have no idea of what that means - especially if you have no idea what that means - those words just sound scary and difficult, don't they? 

And in my opinion, the first and foremost job of an algebra teacher is to break down the scary and difficult words, so that the students can get on with their learning. 

So whenever I present good old Lesson 108, I first share my story of free association with this frightening phrase, when I first heard it back in my algebra class.

When I was a little girl, our daily errands often took us around and through the campus at the University of Michigan. At most colleges in those days, anti-war protesters and peace activists were all the rage, and it wasn't unusual to see them out and about in Ann Arbor, expounding on their views and rallying the passersby. Often they looked very much the part of the classic counter-cultural political dissidents, brandishing their placards on the steps of the law school building and looking all bearded and hippie-like. They made quite an impression on four-year-old me. I had heard the expression, "radicals" used by disapproving adults to describe these zealots, and I logged that information away in my child-sized brain.

Years later, as a high schooler, when I first heard of this algebraic operation called "isolating the radical," my mind conjured up an image of one of those nonconforming dudes atop a steep flight of stone steps, classic columns behind him, anti-war slogan signboard in hand. In my mind's eye, I watch from afar as the police enter the scene to confront the dude, and the gathered crowd quickly shrinks back to distance themselves from the situation.

Thus, the radical is isolated. 


^ And if the verbal version of that wonky story isn't enough to cement the concept in my students' minds forever, I punctuate the telling with a hastily-drawn but fairly effective sketch of - you guessed it - an isolated radical.


^ Then I quickly demonstrate the mathematical process of isolating the radical, which in comparison to that outlandish preamble, is simple and straightforward.

My students, who certainly had every right to question my sanity during the big build-up, now quickly connect the dots. Forever they will remember this process, and the elaborate tale that preceded it.


^ And let's be honest. As nutty as my narrative may be, it's one heck of a lot more interesting than the dry description offered in the text. 


So I offer a big round of thanks to my awesome students, who patiently listen to my ramblings about

ice cream sundae and peanut problems, 
magic numbers,
flying trapezes,
schools of fish,
the fricken formula,
children who need to go home for supper,
the Hannah Cranny rule,
and of course, the man-eating dragon.

You listen to me because you trust me to make sense in the end, and I hope I will always hold up my end of the bargain.

P.S. Just two more lessons left to teach and then we are done for the year. Woo hoo! Summer, here we come!


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Other stories about my work:

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