Cross Multiplication.

Many of you, somewhere in middle school or high school learned how to cross multiply. From what I can gather, cross multiply is a way of solving when two fractions are equal, and you draw this X and the numbers move around magically. I was never taught to cross multiply.

I was, however, taught that if you have two fractions equal to each other, you should multiply both sides by both denominators, because the denominator will divide with the numerator you have just multiplied in, (preposition end, I know) and leave you with the same result as the cross multiplied answer, only with more mathematical relevance and a greater understanding of the functions of multiplication, division, and fractions.

Mr. Ebbert taught us never to say cross multiply, and now I know why. Because it's a cheap shortcut that cheats students out of mathematical understanding. It's a way for teachers to give students a formula in a few minutes rather than take 15 minutes to actually show them mathematics that they can always remember, even when they can't quite recall how to cross-multiply. If you teach students mathematics based on the fundamentals of math, rather than a bunch of odd rules and shortcuts, they won't forget. What's more is they'll be more able to synthesize the information when presented a new problem.

Mr. Ebbert also taught us to never say "plug in" the number. It does sound ridiculous. We substitute in numbers. I've always said that. Mr. Ebbert taught alot more about math, too, but my blogs are too long these are the two relevant topics of the day.

I'm now at college, a mathematics education major. Frequently I hear people saying they are plugging in numbers, and my mathematical soul cringes a little. I feel that they are wronging the mathematics of the proper terminoogy it deserves. However, knowing that I'm probably a very small minority that ever even was told not to say "plug in," I know that it's not of great importance.

A bigger deal is that today in class, a student was giving her presentation to our group of three. It's part of microteaching. She set up the proportions, then asked for one of us to come up and cross multiply the fractions on the bored. I stared, perplexed, knowing full well how to solve the proportion and having no idea how to follow her directions. I could very easily solve for x, but I had no clue how to perform or even properly show my work for cross multiplication, if such a thing existed. Luckily, she proceeded to demonstrate for the class, where I quickly realized what to do for further reference.

Thank you, high school, where I learned real mathematics, wihtout stupid rules and meaningless shortcuts. I learned how to actually solve for a number, not to just perform some weird pattern.

And yet, for some reason I still find myself in classrooms with no idea of how to follow the stupid directions.