Algebra is the underpinning of symbolic logic. Without algebra one is left as a victim to the relationships and systems created by others. It is only by taking the numbers out of math that math becomes a tool rather than a chore. The object of operating on math is to build proficiency with the tools. The object of operating with math is to illustrate what the tools are for. Learning algebra is to logical thinking what learning penmanship is to writing. No matter how well you can type if you do not have the mechanical ability to write letters by hand you will always be a slave to someone else's system. Simply learning to type will teach you to communicate but it will not teach you how to communicate on your own terms. The fact that so many people in the United States fail to learn algebra is not a failing of algebra - it is a failing of instruction. 2x=14 is not math, it is reasoning... and if we can't teach our children to reason, we might as well buy stock in Brawndo. I learned algebra in fifth fucking grade (and negative numbers in 2nd). It had the effect of turning all math from that point forth into calesthenics. There were no daunting concepts, only daunting exercises... and every scientific discovery ever made became an eventuality in my head, rather than magic. Go ahead and decide the kidz don't need algebra. My kid is going to know it backwards and forwards and I can guarantee you your kids will work for her.
You can argue that analytic geometry teaches a somewhat limited form of deduction, but, no, you can't reasonably say that algebra teaches logic. Like all math, it's just a way to describe quantities and the very limited relationships between them. Unlike the author, I do think algebra and geometry are a useful part of an education, which, unlike the author, I think should have nothing at all to do with job training. If we really want our kids to learn to think, then we're going to have to actually give classes on thought: induction, deduction, abduction, analogical reasoning, dialectical reasoning, and causal reasoning. We're also going to have to give them the information and ideas they need to reason with: history, literature, philosophy, and social studies. Finally, we'll need to ensure that they can express their thoughts: rhetoric, composition, and basic math. If we really want to educate, instead of just train, we're going to have to make room for a real education, and that means clearing out both shop and calculus. Just like auto mechanics, most higher maths are only useful for very particular jobs, and as such they're just job training, which employers should be doing, not education, which is what schools should be doing.Algebra is the underpinning of symbolic logic.
...and how is that not logic? It seems like a bit of a jump from "defending algebra" to "revamping the entire educational system." Not that I disagree with your assertions, just that I"m a bit more pragmatic.Like all math, it's just a way to describe quantities and the very limited relationships between them
If we really want our kids to learn to think, then we're going to have to actually give classes on thought: induction, deduction, abduction, analogical reasoning, dialectical reasoning, and causal reasoning.
This article describes logic. Don't be fooled by the title: it's hosted at a philosophy site, and philosophers distinguish between many different categories and forms of logic, but this is the general meaning of the term. It's what we mean when we say, for instance, that Mr. Spock is logical.
No, that article describes "informal logic." This article describes "symbolic logic."
The article I pointed to describes "logic." I had assumed that you didn't really mean to say "symbolic logic" in your original response. For one thing, it's unrelated to algebra except in the sense that it takes a mathematical form; for another, it's useless for anyone who isn't interested in following some of the dead-ends that the 20th-century analytic philosophers ran down. I hope you don't insist that your kid learn symbolic logic unless he's really fascinated by it. It certainly won't help him employ anyone. If you want him to learn formal deduction, try Aristotle's syllogisms. They're useful.
It does not. It describes "informal logic" which is a philosophical term. We're not having a philosophical discussion. We're having a mathematical one. I Fucking Said "Symbolic logic." No for every fucking reason in my original post. The fact that you think "symbolic logic" and "informal logic" are the same thing is a strong indicator that not only do you need to focus on your rhetoric, you need to retake algebra.I hope you don't insist that your kid learn symbolic logic unless he's really fascinated by it.
Well, the reason you Said "Symbolic logic." is because you don't know what you're talking about. Here's symbolic logic: [(p ⊃ q) ∧ (q ⊃ r)] ⊃ (p ⊃ r). And here's algebra: (x² + y²)² = (x² - y²)² + (2xy)² They are only vaguely related. You can't reasonably expect anyone to learn about one from being taught the other. And both are of limited utility if what you want is to learn to reason.Fucking
Let's stop tripping over the term "logic," shall we? IF it gets cold when it rains, AND it is raining, THEREFORE it will be cold. That's "logic." Technically it's "Boolean algebra" but FFS, it's also "logic." "Algebra" doesn't mean "symbols." It means "solve for the unknown." "Solving for the unknown" is a daily activity for people who think. Not only that, but the argument isn't "let's stop teaching reasoning" it's "let's stop teaching ALGEBRA" which, by your logic, we don't need. And, simply put, you're wrong. There aren't that many more ways I can illustrate the wrongness of your thinking because it requires a basic understanding of symbolic logic and I'm guessing you suck at algebra.