Wednesday, September 12, 2007


I have always thought that one of the best, scariest costume anyone could ever dress up as is something right out of a math textbook--A FRACTION!!!! (Horrible screams now invariably follow.) It's like these fractions were actually screaming "BOO!" at the students, while the students were throwing it right back at them, "Boooooo fractions, Boooooo!" These seemingly innocuous numbers have undeservedly earned a bad reputation among math students, at least since the proliferation of what I believe to be the culprit--Graphing Calculators.

Sure, the fact that every kid owns one now and that they are used in every math class all the way down to some elementary classes is good for the calculator companies, but not necessarily for the student. Students have developed a calculator "reflex," grabbing for it when asked to do mind numbing calculations like "five plus seven" or "three take away two." Many students use the calculator like a crutch. Some students use it as a stretcher!!

The consequence is that many a student's ability to work with numbers in his head has atrophied. Students lack number sense and the mental agility required to quickly determine the solution to a problem such as 1/2 + 2/3. They don't even know if the solution is greater than one, less than one, or equal to one. When they have this much difficulty working with concrete numbers, imagine how difficult it is for them to do similar calculations or procedures on a more abstract level involving variables (or even complex/compound fractions!!)

As students enter into my precalculus class, the weening period officially begins. Initially, students are only allowed to use their calculators as a straight-edge. They groan. They whine. They want nothing more than to cuddle in the safe arms of their TI-83s. I slowly introduce the proper way to use a calculator, as a graphical tool to confirm and verify answers and to explore the behavior of equations that would be too tedious to do by hand.

"Are we going to get to use are calculators on the quiz?" they inquire.
*GULP* "Are we going to get to use them on the test?"
"Absolutely not"
**Double GULP**
"Are we ever going to use them?"
"Eventually. I'll let you know this summer." *Ha, Ha, Ha. Evil Math teacher strikes again*

Here's a quick example that came up in class the other day when we were completing the square.
"What is half of five?" I asked
"2.5" a sharp student quickly replied as he stared down at his calculator screen.
"OK, what is 2.5 squared?" I asked as I ran over an covered his screen. I thought he was going to cry. He didn't know the answer was 6.25 (actually a very easy calculation for someone with number sense.) His calculator buddy next to him fortunately bailed him out.

So I instructed them the advantage of thinking in pure rational form.
"Half of five is simply five halves, written 5/2. Now 5/2 squared is 5 squared over 2 squared or simply 25/4."

You would have thought that I was a Mathemagician. The students who were not shrieking in terror were enthralled at the simplicity of this new, equivalent approach. There might be something to these fraction thingamajiggers after all. Maybe they are not so terrifying after all!

Now those compound/complex fractions . . . those sound REAAAAALY scary.

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