Algebra v. Basic Math

As I was listening to NPR this morning, a story came up about algebra. Now, when I was in school, I remember many of my fellow students having difficulty with algebra, but I always found it incredibly easy. I always got tripped up on the simple math: adding together two two-digit numbers to this day still requires a calculator.

This story on NPR suddenly made it all make sense. The segment’s focus was why so many students struggle with algebra and the subject’s practical application in the real world.

The segment’s host asked the expert asked their on-air math-expert why, if the letters in algebraic equations represent actual numbers, is it such a stretch from basic arithmetic?

Their expert explained that it’s not the same thought process: which basic arithmetic, the student is dealing with valued quantities; e.g., in 2 + 3 = 5, the student is mentally combining a quantity of two with a quantity of three which results in the sum quantity of five; whereas in an algebraic example, 2 + x = 5, the student has to switch to a logical thought process to come up with the answer x = 3.

The expert went on to respond to the typical student nagging “when am I ever going to use this in the real world?” with a simple answer: spreadsheets. He said that spreadsheets are used for nearly everything these days, from finances, to sports scores, to even video games (he used some Warcraft example here that I still don’t get). The point is, though, that spreadsheets do the arithmetic for us, all we need to do is understand the logic to create what we need.

Now while I’m sure this is very useful to that 6th grade teacher listening on his way to work as a way to help his students connect with the material; or to that student finishing his algebra homework in his parents’ car as he’s driven to school as a new way to look at that equation that frustrated him all last night. For me, however, a different lightbulb came on: I had never consciously thought of numbers as having value.

To me, basic math had always been memorization, not quantitative equations. So when I got to algebra, there was no new thought process for me; the letters in the equations were just as valueless as the numbers had always been. I spent my whole schooling unaware that math was anything more than logical theory… which perfectly explains why I always found it both easy and incredibly dull: it was only meaningless puzzles.