Seriously, you algebra/college wizards are some smart folk. Every one of you better be pulling in at least 70 grand a year (gross) with all those high falutin' noggins. BTW now that I found out calculating a tip percentage is algebra (huh?) I'm going to be gun-shy. I was able to do it, now I'll have to research what formula I was using all along, other than multiplication with a decimal point.
I used algebra at work and it confused the hell out of a coworker. Because of a complicated return, the drawer would be $48 short from the day's earnings, so I said "150 + X-48 = total" (150 is our daily starting amount, X was actual cash earned). Took the guy a full 2 minutes to realize what I did. I just did it to remind myself that $150 had to be there the next morning to open.
Why would I even use that formula? Just multiply the total bill by .2 (if you want to leave a 20 percent tip of course). X and Y don't have a dog in this fight.
X = the tip Y = the bill total Get it? You've been using that formula all along without even realizing it.
But the point is that you actually are using the formula. What you call "the total," I called Y, and what you called the "tip," I called X. So what you wrote, is just the natural language equivalent of the formula.
And if it were actually taught that way, that extra lamina of "Oooo, today we're going to learn about a mysterious thing called 'X'" wouldn't be so daunting to some of us. In any case, it's still not necessary to the understanding of the process.
There must be some very bad teachers around (hey Dayton!) if they're managing to confuse people about what a simple variable is.
As opposed to this: As I say, X is usually understandable. But then there's Y and Z and all those cute little Greek squiggles. Maybe a good teacher can present them in a way that doesn't make them "Oooo, algebra! Mysterious!" but apparently I had three bad ones.
I think I see your problem now. You are treating the symbol that happens to look like the Roman letter "X" a special meaning, when the reality is you can put anything you want in its place. It could be a Greek letter, a Kanji sign, even a drawing of a smiley face. It doesn't matter. It's just a placeholder, nothing more.
A lot of it comes down to not wanting to take the time to understand. I was like that till around 9th grade. Then I sucked it up, took the time, and figured it out.
Tip calculation is a fairly simple example, but there is beauty in algebra in that it provides a systematic way of understanding problems, with tools to determine the answer. You can get in to some far more complex questions and still frame them in the form of an equation. I really like algebra, but I'm sure it only takes one bad experience early in exposure to turn a kid off from it for good.
The students I have tutored in various math courses, I've found that almost all of them understand at least part of what they're trying to learn. And that a good amount of the time they only need to be shown in a way that makes sense to them. But finding what makes sense to them is something teachers/professors often don't care to do, or won't take the time to do. When I tutor someone what I'll do is have them show me what they know by working some problems. I'll pay attention to what they're doing right and what they're doing wrong. Most of the time the students will have at least some grasp of what they're doing and it often comes down to where they know what to do. Or they at least know what smaller steps need to be taken. I can then show them where they used the right steps and where they are actually doing the step right, but in the wrong place. What really helps me is that I can look at a problem and see different ways to solve it. And from there I can see the pattern from the problem to the solution and I can then know the answer by just looking at it. And can fill in what's needed (if the prof/teach requires it). And once the student knows how to solve each step, I'll show the pattern so they can see the answer and make sure that their steps do result in the right answer. So I would say that it's more the teachers than a bad student. Most of the students I've tutored end up at least learning how to get at the answers and do improve a good amount. I've some that were so lost that they bombed their first test and still end up getting a B in the class or even an A. Teachers need to see that not everyone thinks the same way and that the method they use may not make sense or confuse the student(s). If the teacher really was a good teacher, they would realize that and have different methods that make sense to different people.
So since I can use this formula without realizing it, I actually cut to the chase and not call it a god damn thing, just solve the fucking problem. I like cutting links out of a chain - isn't algebra the art of "reduction" anyway? Here's my point: when my son was in college/studying for the ASVAB (military aptitude test) they had these long assed work problems where Steve leaves town heading East at 30 MPH...etc. etc. I was helping him thru these problems and giving him practice tests. I didn't give a shit about pigeon-holing problems into named formulas, I just draw them out quickly and solved them. I could "show my work" but fuck a bunch of formulas and properties. Luckily the ASVAB was multiple choice. I showed my son my method of solving math problems fast using common sense, estimation, etc. My methods may or may not fit into a certain method.....but they work for real world situations...and he got a very high ASVAB score BTW.
Here's the thing you were working with someone who cared or had someone who cared enough to hire a tutor. We are seeing the percentage of these kids and guardians decline. I agree the sign of a good teacher is saying and doing something in multiple ways but if they aren't open to it, it won't sink in.
Sad thing is over the last eight years as a teacher I can't explain something one time I have to explain something from three different view points. Lol I've been recording and posting all of my lessons starting this semester so when they watch them in class I hear myself teach the same lesson twice a day, it's funny the stuff I do unconsciously to get the lesson across.
And going out to get pizza and beer, I also saw the opposite side of the spectrum. I was supposed to get 17 cents back in coins, I gave the girl a dime to I would have a quarter and two pennies instead of a nickel, dime, and two pennies. SHE. COULD. NOT. Figure out the change... she asked the manager and he pulled out his phone to use the calculator. So yes, there are truly stupid people out there that cannot do even the simplest of math.
Agreed - I was an electronics/equipment instructor for a few years in The Army. You (as an instructor/teacher) will be challenged daily trying to find examples from daily life, experience, nature, science, etc. that can explain what you are trying to convey. I hated teaching "smart" kids. All they did was show off and kill time until they took the test. I enjoyed pulling teeth trying to get the struggling kids to get it together and function as well as their more gifted cohorts. The instructors that just "put out information" were coasting. Some of them had attitudes of "I can learn this shit. Why can't you?". But because I have trouble learning, I understand what it's like to be at the bottom of the class...which made me an awesome instructor in the long run. When you teach to smart kids you are just "preaching to the converted" IMO.
