Yes, young people should learn to read and write and do long division, whether they want to or not. But there is no reason to force them to grasp vectorial angles and discontinuous functions. What is needed is not textbook formulas but greater understanding of where various numbers come from, and what they actually convey.
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.
- Algebra is the underpinning of symbolic logic.
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.
- Like all math, it's just a way to describe quantities and the very limited relationships between them
...and how is that not logic?
- 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.
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.
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."
- I hope you don't insist that your kid learn symbolic logic unless he's really fascinated by it.
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.
Well, the reason you
- Fucking
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.
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.
This article is garbage, plain and simple. All the arguments the author makes about math, one could easily make about every single academic subject. Vet techs never use algebra. You know what, they probably never write argumentative essays, either. Should we throw out rhetoric as a requirement, and just make sure that individuals can read technical instruction and fill out forms properly? Let's call it "applied language".
I'm all for vocational training. No one should have to go to college to get a career they enjoy. But then how about argue for more vocational training, instead of the lowering the bar at the academy? Algebra forms the basis for all problem solving. How can we teach statistics without calculus, as this guy argues? And without algebra there's certainly no calculus. The guy is attacking the wrong thing. Let kids decide in their late teens if they want an apprenticeship, and then don't encourage them to go to college if they don't want to. Don't buy into the idea that everyone should go to college, and then say college is too hard for most people.
Furthermore, the author's argument that taking out algebra would increase graduation rate is exactly the kind of statistically pleasing nonsense that sadly seems to be the norm and might appeal to the US government. It reminds me of the NY state testing change that happened a few years ago to some tests, where high scores would be curved down and low scores would be curved up, so that the state could claim- backed by statistics, of course- that they created a test that increased the percentage of students who passed without making it too easy for higher scoring students.
What do you expect from a political scientist?
My buddy recently moved to Denver and got a job as a biology teacher in a high school. I saw him last week and he was griping about how he's not really allowed to fail students. They have a standing policy that if an assignment is turned in, it must garner at least 50%. No Child Left Behind is destroying education under the guise of fixing it.
Some of the clauses in No Child Left Behind just seem to be poorly thought out and hidden from the public. A friend of mine who teaches at the local high school informed me that teachers are evaluated, partially, on the improvement that a student makes throughout the year. Teachers who lead AP or IB classes with higher-scoring students are, under this clause, going to get a lower evaluation simply because these students do not have much room for improvement that can be reflected score-wise. Which means there's now an incentive for teachers to create impossible tests at the beginning of the year and then give an easy final to get a good evaluation, regardless of how well they actually teach.
- The debate shouldn't be about whether algebra, history, literature, writing, etc. are the proper material to teach students, or whether material focuses too much on memorization, or whether schools kill creativity.
I agree that our schools are broken, but if the problem isn't the subject matter (algebra, for instance), and the problem also isn't the method (memorization, for instance), what do you think the problem is?
- I think that poverty, family life issues, lack of perceived upward mobility, and other factors can contribute to ... poor performance
I'm sure you're right, but the school system itself can only attempt to provide students with the tools they need to understand the world they live in and make creative and informed decisions about what can be done to improve their world. And I really don't think the school system is doing that.
My widgets are not passing qual because of one bottleneck spec. This article says I should get rid of that tough spec. As an engineer in the semiconductor industry, this article's line of reasoning would get me fired. The widgets must be improved, not the standards lowered.
"Of the 1.7 million bachelor’s degrees awarded in 2010, only 15,396 — less than 1 percent — were in mathematics."
While only that amount was in 'pure' mathematics, there are many other disciplines that require a good amount of mathematics. Engineering, statisticians, and many science, business, and economic oriented disciplines all require a good amount of math.
If we make algebra optional, then who is to stop people from doing the same to chemistry, or any other course really? I feel that eliminating one presents a slippery slope.
Third, if math is making people drop out then I feel that math isn't the true problem. It's students dealing with their failures, rising up to their shortcoming, and overcoming them as opposed to giving up.
This article was kind of weak sauce, in my opinion.
- It’s true that students in Finland, South Korea and Canada score better on mathematics tests. But it’s their perseverance, not their classroom algebra, that fits them for demanding jobs.
The author drops this in about halfway through, and then provides no citation to back up the assertion. It kind of reads "They're not lazy like we Americans are!"
There may be a compelling argument about how math and algebra is taught in schools, or what is emphasized. The author seems to agree when he says
- What is needed is not textbook formulas but greater understanding of where various numbers come from, and what they actually convey.
I'd respond that it's both- the formulas are meaningless without understanding of what they mean, but that doesn't mean that the formulas themselves are entirely meaningless.
- But there’s no evidence that being able to prove (x² + y²)² = (x² - y²)² + (2xy)² leads to more credible political opinions or social analysis.
And there's no evidence that taking philosophy made me a better engineer. That doesn't mean that it was a waste. I'd rather be well-rounded than pig-ignorant.
- It’s true that students in Finland, South Korea and Canada score better on mathematics tests. But it’s their perseverance, not their classroom algebra, that fits them for demanding jobs.
I believe you may have misread these sentences because they're terribly phrased. The author isn't claiming that the US scores lower than Finland, South Korea and Canada because they're less lazy. Rather, he's claiming that although these countries score better than the U.S. in math, their algebraic skills don't make a difference past graduation. Rather, their perseverance helps them in their career pursuits.
By extension, the author implies that US students can simply make up for a lack of algebraic knowledge with perseverance. Okay.
I can see why you thought I was confused; I agree the writing there is indeed awful. However, I was not confused at all. I had the same reading as you do on that paragraph.
I still stand by my statement that his statement reads as "Americans are lazy, amiright," since he declined to provide evidence that other nations have greater perseverance or that their algebra skills make no difference.
- Making mathematics mandatory prevents us from discovering and developing young talent. In the interest of maintaining rigor, we’re actually depleting our pool of brainpower.
- Community college students face an equally prohibitive mathematics wall. A study of two-year schools found that fewer than a quarter of their entrants passed the algebra classes they were required to take.
This is a failure of instruction in middle and high school. The kind of algebra on entrance exams are things I learned in elementary school and that most of my peers had no issues learning. This kind of failure to learn algebra hasn't existed for more than one, maybe two generations.
Lowering the standard does absolutely nothing in solving the education issues being faced in the U.S. today. If we have become more interested in fixing statistics than actually educating our children, the battle is already lost, and we should indeed think about investing stock in Brawndo.
- What of the claim that mathematics sharpens our minds and makes us more intellectually adept as individuals and a citizen body? It’s true that mathematics requires mental exertion. But there’s no evidence that being able to prove (x² + y²)² = (x² - y²)² + (2xy)² leads to more credible political opinions or social analysis.
Show me a true intellectual who doesn't understand basic algebra and I'll take that statement a little more seriously. It's true intellectual dishonesty on the author's part, dismissing the notion that medium-level math might provide more benefit than is immediately obvious.
Being able to solve for a variable is an essential skill for many managers even those in lowly workplaces. If you want to get off the bottom rung of the worst of work it's an absurdly useful skill to posses. The ability to calculate how many you have done, did, need, and have left ect is a basic workplace skill.
I have what most would consider a "blue collar" job fixing electronic things, I use algebra every day. I would say it is only necessary if you want to be able to compete in a difficult job market. If you know what career you are going to be in for the rest of your life AND you know that you can get into that career without having to compete against anybody else then I would ignore it. But you'd better be sure...