Where to begin?
America is an innumerate nation. I can't even add a qualifier to that statement; it's too abysmally true. We are so innumerate that most people confuse simplistic number manipulation (addition, subtraction, division, and multiplication) with "math." Nothing could be farther from reality.
Here's the sad part. People will argue about your numeracy based on how efficient you are at these basic computational skills. Get over it, folks. This is not "math;" these are monkey skills. At best. Pigeons have been trained to do them, too, sometimes outperforming U. S. college students. Wanna do basic computation efficiently? Use a freaking calculator. And I say that as a guy who finished college when the slide rule was king and who is still not so comfortable with those newfangled electronic thingies.
So lemme anticipate your response. You figure a kid needs to understand *how* the answer is derived. He hasta grok the concept; it's not sufficient to simply get the answer. Ok. Actually, I personally agree with that to an extent; but let me ask you a question.
For whatever reason, your boss needs you to obtain a logarithm for him. Right now, of course, because this is cutthroat American corporate capitalism we're talking about and if you wait until tomorrow, your job'll be outsourced to a slave-labor company in China or Thailand or Canada and you'll be out on the street begging for spare change. Whatcha gonna do? Obviously, the simple (smart!) answer is that you're gonna look it up in a table or use your calculator.
Hypocrite. [VBG] No, make that a [snide grin]
Do you know and understand how to derive that log you just looked up? No? Base 10? Base e? Do you even know what e is? BTW, did you know that e is transcendental? Like, wow! Far out, man! Groovy, dude! You mean you're gonna be content with merely having the answer? Do you think that table of logs was delivered from on high by the Logarithm Fairy?
Whoa! I just got a vivid mental picture, kind of a combination of Arnold Schwarzenegger and Big Gay Al from South Park. Big, bulky guy with a half-chewed cigar in the corner of his mouth. 2-day beard. Very hairy forearms. Lovely blush pink tutu and gossamer wings. Pink toe-shoes and white tights. A halo populated with twinkling, spinning logarithms and a long, thick, oversized log log double decatrig slide rule sticking out the front of his… , errr, I mean, a slide rule as a wand. Yeah, that's it. A slide rule wand.
But back to the topic at hand, what's sauce for the goose is sauce for the gander. If you're content simply having the log "given" to you by your calculator, then it should be ok for your kid to be "given" the answer to his problem by his calculator. If you still insist that he must understand the concept first, then you put your calculator away and derive that log yourself with no help from the Logarithm Fairy.
He's probably busy right now anyway. I think he and the Universal Gravitational Constant Fairy, Big G, are out on a date. The Big G stands for something other than "goodness," I can tell you! Remember, F="BigG"(m1m2/r^2) and I'm pretty sure that F stands for "Big Fun" for big math fairies! It's the original, actual, scientific Law of Attraction. Well, it's the *equation* of attraction, anyway.
So, if you're gonna require your kid to memorize the "times tables" and learn at least one algorithm for doing basic calculations, why would you stop there? Those skills alone do NOT constitute numeracy. Monkey math. Monkey math. Monkey math. And I say again, MONKEY MATH! (Pigeon math?) Nothing more. Stop there if you want to, certainly; but don't kid yourself that you've now transcended your innumeracy. e is transcendental. I worked with e. I know e. You're no e. [With apologies to Senator Bentsen and President Kennedy, but never to Dan "potatoe" (sic) Quayle.]
Besides, consider this second question on this topic, do you actually think that memorizing the times tables and memorizing one or more algorithms to do simple calculations constitutes "understanding the concept?" As a counter-proof, I offer you the high school success stories who populate the cash register employee niche at our fast-food chains. How many of them can actually make change on their own without having the register give them a value? We're talking simple subtraction here. How many, huh? These are the products of a decade or more of American math instruction and they can't fucking subtract. I can't think of an adjective abject enough for this situation. "Pathetic" is pathetically inadequate.
So where does that leave us?
Well, I'm gonna stop for now and call this Part 1. Therefore, that leaves us at the end of Part 1. Stay tuned for Part 2 where the action really heats up.
[Go to part 2.]