It’s been some 20 years since I last messed with PreCalculus and I was apprehensive as the quarter started. I mean, do you remember how to factor a quadratic equation?
Most of the last six days I’ve spent pouring over my online textbook, doing the requisite problems and watching the requisite videos, trying to get back into the hang of things, mathematically. Part of the problem is that the first time I took this in school it was to satisfy a separate need: as a Marine Biologist, how often was I really going to need to use trigonometry? Or create mathematical formulae to describe something? You never saw Jacques Cousteau whip out a Texas Instruments graphing calculator, so I spent four or five quarters of advanced math thinking, “yeah, yeah, but this doesn’t really apply to me”. I studied long enough to get the grade and not one moment longer.
Here we are 20 years later, I’m in the same class (in the same school – although not with the same teacher) doing the same work, and have discovered two things:
- It’s a lot easier to do the work if you understand the theory and are studying to that rather than the formula itself – if you get the “concept” you can back into the “formula”, it doesn’t work so well the other way around, and
- The newer textbooks have pretty much accepted you’re going to rote-memorize some things and probably don’t care about the formula.
Yep, you read that right. For example, one of the things I find now in my text are handy “tables” that tell you the “standard answers” for common mathematical functions. Twenty years ago, we had to demonstrate mathematically WHY, for example, the sin(pi/6 aka 30o)=1/2. You got out your quadrille paper, you graphed a unit circle, you labeled stuff, drew your arc, and did the math. Now, you have a table. This helps, right?
Not really. Sure, you have a handy table, and you go and apply that to all of the problems in the homework. Or you leverage your graphing calculator to tell you that sin(30)=0.5, no problem. But when it comes time to use what you have learned so far to apply it to a new concept, or to solve a problem where there is more than one missing value, you’re hosed until you get another table or some set of instructions on what to plug into your TI83.
As I’m actually going to USE this math in Economics – first quarter Microeconomics shows you enough graphs and charts that you immediately understand the significance of Understanding What The Graph Is Actually Telling You and How To Derive a Formula For It – I wish the textbooks actually worked to have you get the theory as much as they do the application. This is like when you’re at work and your boss asks you to provide a presentation and then hands you the template and tells you exactly what to write – that’s great, but I’d really like to participate, please.