I disagree. The second line is easily derived from the first through factoring. In the first, simply factor the difference of squares to get the result of (x+y)(x-y). Go ahead and simplify it, it works. Now for the right side of the equation, simply factor out a common multiple, y. Divide each term by the one you are factoring out and you get y(x-y). In fact, (x+y)(x-y) DOES equal y(x-y) in this specific example, because if both are FULLY simplified, 0=0.
(x-y)=0, you can prove this by replacing x with y or y with x. Replace (x-y) with zero and you get this:(x+y)0=0y
0=0.
I just wanted to chime in. You said your son wants to be a Chef. I am the General Manager of an upscale restaurant. One of the biggest differences between a good Chef and a bad Chef is that a good Chef can controll the NUMBERS. Creativity is needed, but if he can’t figure out the food cost, he won’t be working very long. I agree with you that he needs business math, but if he is stuggling with algebra, he’ll never get accounting.
I was a music major in college. I was sure I wanted a career in music. Friends of mine in music school had taken only the basic math requirements in high school, I took every thing that my school had to offer(music theory was easier for me and my math-abled friends than for those who did not understand basic math, they are closely related). After 3.5 years of college, I figured out that I was in the wrong career for me, but had no more time, money or energy to start over in a different major, so I finished the degree. I am now doing very well in a very different field than I every thought I would be in. The single most useful thing that I learned in any of my education is advanced mathematics. I use algebra every day.
I also agree with many posters that logic and reasoning skills are greatly improved by the study of math.
Encourage your son to learn anything and everything he can. You never knows where he might be exposed to thoughts and concepts that will alter and improve his life.
First off, as a 20-year old, I certainly know that Hamilton is on the $10 bill (also not clear on how that’s “history”). Moreover, I know lots about his policies as Secretary of the Treasury, his duel with Aaron Burr, and Burr’s short-lived conspiracy to break away from the Union. And I’m a Chemist…
As for algebra, not only do I use use it on a daily basis, I use it unconsciously. I don’t sit down and think “ok, let’s do some algebra”; it’s just an integral part to my thought. And I went into college as a prospective art major. Moreover, I know of very few places that require 4 years of algebra (although I’m not questioning the veracity of your statement)–that would seem a bit extreme. The standard for my school was 2 years in middle school or one in 8th grade and one in 9th, and then on to Geometry, Pre-Calc, and for a good bit of the school calculus (2 years, for some of us). This is all before college in a public school. From people I’ve talked to, this is fairly standard, perhaps a little bit more than usual, but not too much. Besides, devoting multiple years allows for more topics to be covered, and in greater depth. For example, I know single-variable calculus inside-out, because I spent 2 years doing it–even though my high school was a school for the arts. Multivariable and Diff EQ, which I know I will need, I don’t remember at all, because I didn’t spend 2 years on them.
Besides, the point of high school is to provide you with a well-rounded education, with an emphasis on your interests. Interestingly enough, this is a huge advantage no matter what field you end up in: software companies (particularly video game) and medical schools frequently look for people who attended liberal arts colleges and learned “useless” subjects like history and lit. Why? Because these people can think in multiple ways…and algebra is one of these ways. Well, nuff ranting.
Good post there Myrr21. In fact, in appreciation, I’m going to promise you flying cars by 2006. It’s a little late, but you understand we had to fight the vietnam war first. So, as an added bonus, I’m going to promise you disposable clothes by then, too.
Hell, I’m a photographer, and I need to use algebra occassionally to figure out the technical aspects of more tricky photographs. For example, an f-stop is based on powers of 2. f2.8 lets in twice as much light as the next f-stop (f4). f2.8 lets in four times the light of f5.6m eight times the light of f8, 16 times the light of f11, 32 times the light of f16, 64 times the light of f22, etc, etc, etc.
There are times when, for example, I need to perfectly expose something which has a lit candle. If I expose for the candle, everything else will be underexposed. If I expose for the main subject, than the candle will be overexposed. So the solution is a double exposure. I figure out the exposure for the main subject and the the exposure for the lit candle. I take one shot of the lit candle, then I blow it out, and figure out the difference of Exposure (main subject) - Exposure (lit candle) to get the proper exposure for the 2nd half of my double expo. It can get fairly tricky and complicated in certain situations, when you have to start using the powers of 2 to calculate everything.
It becomes frustrating when I try to explain simple technical concepts to students, and the logic just doesn’t click in their head because some basic mathematical ability is missing. Eventually, after drawing several diagrams, they seem to catch on, but is it that difficult to explain that each f-stop differs by a factor of 2 from the next one? And that each shutter speed (on a conventional camera) also differs by a factor of two. And hence, there is a straightforward relationship between them? To me, this seems painfully logical, but for a lot of people, it takes about a couple hours of explaining.
The very fact that your son is struggling with it means he needs to take it. There is very little point in presenting students with activities that are all fun, or that don’t present a challenge. Even if he learns no algebra at all, learning a subject that doesn’t come easily to him will serve him well. And, although I may be jaded on the side of math (I’m a physics and math major), there are certainly worse ways for him to spend his time. Particularly at the high school level, there are many reasons to be exposed to allthe subject areas, and preferably, extensively. Which is why, though I was certain I was going into physics and math, I had four years of english, history, and french as well. Being well rounded and generally culturally literate (and in a highly technological society, math is most decidedly a part of that) should be much closer to the focus of a high school education that preparation for any specific career.
Where did i say my kid was struggling with it?
He got an A- in it on his last report card. It’s boring the hell out of him is what it’s doing. Anyway, school is out. It’s over. It’s summer. He took and passed it. It’s over!
He just got a job as a cook (not a chef, but its a start).
When he has to use more algebra than one year of basic high school algebra would have given him, I’ll let you all know!
Beyond what has been already cited by other users, (Algebra being a foundation for logic, 4 years of algebra is doubtful, typical is Algebra I, Algebra II, Geometry, Trig/Pre-Calc) Algebra is neccesary for all higher math, such as Calculus and beyond. As an engineer, I use algebra almost daily, and it is implict in many of the standard equations that I use (ie, they were derived using calculus and algebra). Algebra and calculus are the foundations and tools for most of the sciences and engineering. To me, it is sad that a parent couldn’t answer this question on their own, and basically points to the poor fundamentals of education in this country.
Incidentally, if history is being presented as a collection of trivia, it is being presented wrong. One needs history to be able to figure out the historical backing of what’s going on now, not to gain success and fame at Trivial Pursuit.
At my high school, the track for Joe Average was Algebra, Geometry, Advanced Algebra (w/ Trig), Pre-Calc. The track for an above average kid was Geometry, Advanced Algebra (w/ Trig), Pre-calc, Calculus. However, the track for students who were not as mathematically gifted as Joe Average was, Fundamentals of Algebra 1, Fundamentals of Algebra 2, Fundamentals of Algebra 3, Fundamentals of Algebra 4. This track was basicly Algebra and Advanced Algebra (without Trig) spread over four years instead of two.
So, there is a reason why someone might have to take four years of algebra in high school. Because it takes some students four years to learn what others learn in two.
PK, the reason why your son was so bored would indicate to me that he didn’t belong in the slower track. My guess would be that he screwed around in junior high or freshman year and got tracked accordingly.
I’d kick his ass, take away privilages, etc., he’d straighten up for a long time, then drift. He always scored high on standardized test, but when it came to homework he got lazy. We always had to be on him. His grades didn’t always match his intelect or abilities. (But he never failed or even got below a c- in anything). This last year he excelled though.
