This Algebra II is killing me (1 Viewer)

[BrianB]

That's kind of my point, Scott. By cutting off subjects & knowledge early on, you're limiting your choices later in life. And noone knows what their longterm path in life is.

 

[Mike Voigt]

Let's go to another part of this.

We've pretty clearly defined the potential uses of Algebra, and how widely it gets used. There are a number of careers that do not use it, but almost any technical field, including vocational fields, use algebra. At my facility, it is a requirement for anyone who wants to move into higher-paid spots, whether hourly or salaried. I don't think that one would want to do without it, not unless willing to severely limit one's options. So the question is, what is it about Algebra that does not make sense? Is there some part with which people are having particular difficulty? Is there something we, as a community, can do to support mastering this skill?

 

[D. Scott MacDonald]

When I was in high school, I had three problems learning Algebra:

1. It wasn't very clear to me why I'd ever need it so I didn't try too hard. It seemed more like busy work than something that I'd actually need.

2. The teachers didn't teach it in a very interesting way. I'm not sure how you'd make algebra really interesting, but they were pretty bad.

3. My biggest problem was that you'd take a year of Algebra 1, a year of Geometry, and then a year of Algebra 2. The problem was that I forgot everything that I'd learned during Algebra 1 by the time I got to Algebra 2. I eventually had to drop out of Algebra 2 and go back to Algebra 1. Had they somehow worked algebra into geometry, or had they started algebra 2 with a few weeks refresher course of algebra 1, I would have been fine in algebra 2.

 

[Colin Dunn]

Lots of interesting stuff in this thread. I particularly liked that article about why "imaginary"/complex numbers really exist. I, too, went through doing all those calculations with complex numbers in Algebra II, not knowing exactly why anyone would need a seemingly 'arbitrary' number system, seemingly built just to allow you to take the square root of -1.

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Now a concept I really have problems comprehending, to this day, is one I was taught in high school physics: Light is BOTH a wave and a particle. This always seemed like a cop-out. If it isn't strictly one or the other, then is it some other form that possesses properties both of waves and particles, and yet isn't either one? Surely it can't be BOTH a wave and a particle at the same time. A wave is energy; a particle is matter. Is light both energy and matter at the same time?

As far as I know, that question has never been answered. Whoever finds an answer to this question could well win a Nobel Prize in physics.

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The most recent time I had to fall back on algebra was when I was interviewing for a job as a client/server network consultant. That job does not require the use of algebra on a daily basis, but part of the screening process I encountered when interviewing an on-line psychological and aptitude test.

The aptitude section was entirely based on solving arithmetic and algebraic problems. Not only that, but the computer was running a clock while I worked through the questions. These math problems were used as a proxy to estimate my problem-solving abilities - especially eliminating irrelevant options quickly and coming up with a solution under time constraints.

So quite literally, knowing a little algebra got me back to work sooner than if I had dispensed with it entirely...

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What is wrong with math education right now? I can think of a few things...

1) It is often taught as a complete abstraction. Even the "word problems" are often contrivances, not actual problems a savvy consumer, engineer, scientist, etc. would need to solve.

2) There is a battle between teaching "problem-solving ability" and "accuracy" in math. The result is that some math teachers are extremely strict in grading and will flunk students who are perfectly capable of learning/doing the material, because every little homework assignment (and frequent unannounced tests) is harshly graded. At the other extreme are math teachers who just let students coast through class without learning anything. There has to be some sort of middle ground.

3) Wedging geometry in between Algebra I and II can't help, either ... especially if students get rusty with their algebra over the course of a year. I think a better sequence would be: Algebra 1, Algebra 2, geometry/trig (combining trig with geometry would reinforce some concepts and prevent students from losing their algebra skills), then on to algebra 3, then start with calculus.

 

[Jeff Kleist]

Mind you, I KNOW that these maths are important, I just can't do them

I've been trying to learn to program for 10 years

I still can only write programs that are basically "IF INPUT=1 THEN PRINT "You're a butthead" "

I cannot do proper 3-D modelling. I can move the camera, but making models? Making FX work properly? Forget it! I stick to the 2-D world and my life is simpler

It's been a great regret that I have this disability, but I keep trying. I doubt I'll ever succeed, but hey, who knows

 

[Morgan Jolley]

Since I love math so much, I'm taking an Intro to Programming (Pascal) class this year and I'm taking C++ next year.

The sad thing is, I will sometimes do math homework or extra credit for fun....

 

[Dome Vongvises]

DaveF said:

Memorizing something or anything should come as a function of repetition and use in the workplace.

Spelling words and memorizing equations are two totally different things. Spelling merely requires the proper ordering of letters, and you've been learning to spell all your life, hence the memorization that comes from repetition. There's a lot more critical thinking involved with equations. You have to understand how they were derived and what they're used for. You can't expect to have them memorized for a test, let alone the rest of your life, when you've only used them for three weeks!!!
I guess it's also partly my fault that I didn't fully develop my explanation, and the point I was trying to make. I was trying to make the point that it was more useful to remember the "how's" and "why's" of an equation. This is vastly different from just flat out memorizing an equation. Only through repeated use can somebody remember complex equations, and I'm not talking about sissy shit like y=mx+b either. I'm talking about memorizing data analysis equations students have never used in their lives and expecting them to have it as rock solid memory for a test in three weeks.
The argument for using computers and calculators comes from the fact that they simplify the work for you, and even then you still have to punch in the numbers at the right places.
Again, I making the point that it's important to know how and where to use an equation, not having to blatantly memorize each little thing in a short time span.
Let's say you wanna do linear regression analysis on a set of data. I think it's fairly reasonable to have a list of equations like this (this is only skimming the surface here)
Sxx = sigmaXi^2 - [(sigmaXi)^2/N]
Syy = sigmaYi^2 - [(sigmaXi)^2/N]
Sxy = sigmaXiYi - [sigmaXisigmaYi/N]
m = Sxy/Sxx
Sr = |-------------
|Syy-m^2Sxx
| N-2
Sm = |-------------
| Sr^2
| Sxx
and expect students to at least know how to use these equations. But I think it's extremely unreasonable for students to memorize something of this nature they've only used for three weeks. That's why I think it's good to use a computer or calculator to figure this out. Let's say you can't use a computer or calculator. Wouldn't you agree that it was more reasonable to have such convoluted equations somewhere in writing so that a student can use them? Memorizing it is great and all, but if somebody can't, it really shouldn't be held against them, particularly on a test.
Of course memorization is useful, and more power to the people that keep these things in their brain. I just don't see the point in forcing it upon somebody.
Hope that clears things up.
Repeatedly edited for mistakes and other thoughts.

 

[Artur Meinild]

Complex numbers help us gain a grasp of AC power (3-phase power, as well as single phase power), which in turns helps every one of us surfing on the internet.

So true, I'm having electromagnetism this year, and suddenly complex numbers and vector diagrams show up in the Alternating Current section...

 

[Frank Zimkas]

As 39year old geezer I feel obligated to comment! It may be a pain to learn but yes you will use it in the future. I'm in the heating and air conditioning bussiness and I sure do. I do a lot of work with roofing contractors that use trig on a daily basis. See...everybody from Rocket scientists to roofers use higher math evey day, but some folks just don't realize it.
When I was in HS I hated it!!! It just did not make any sense to me at all. Years later I took a few math classes at a community college (Algebra & Trig). My teacher wrote this on the Board
PMDAS (Paranthesis, Multiply, Divide, Add, Subtract)
She told us that if we did every problem in that order we would always get the correct answer. I tried it and I'll be damned if it didn't work. At first I didnot trust the results so I double checked every problem with my calculator.....HMMM.....yep it worked. I went from ZERO understanding (F in HS) to enlightenment(A+) in a very short time. No one had ever taken the time to show me this little gem when I was in HS, That really pissed me off! I could have had much better grades. Give it a shot and I think you might actually find Algebra bearable.

 

[Julie K]

The sad thing is, I will sometimes do math homework or extra credit for fun....

That's not "sad"!

What is sad are comments like this where the writer feels that liking math or doing math for fun is something to be pitied. It is not! If you like and enjoy math then revel in that fact. If you have a talent for it, then enjoy it for all it's worth. You have the ability to easily glimpse the inner workings of the universe. That is breathtaking - not sad.

A real sad thing is that I wish I could offer help and suggestions to others in their struggles in math. All I can really say is to find a good tutor. I am not one, however, in that math has always made enormous sense to me.

 

[MikeF]

OK those are all true examples but who REALLY uses it??? I'm sure I could think of somehow I could use it in every thing I do such as "the angle at which I pour my OJ in the mornings to make it flow the best" or something to that effect. And also, other than being a building block, is it REALLY useful?? I mean in some of your jobs you're not going to say, "Well, Bob, I gotta quit man because I don't know how to do rational expressions." Hot damn.

In my chosen field of study & work -- corporate law -- strong math skills are a massive asset. Indeed, I think they're a necessary (though not sufficient) condition for success. Complex calculations are required constantly, in respect of everything from takeover bid exemptions to calculation of profits legally available for dividends, to tax-focussed restructurings. Colleagues who have math "issues" err in take over bid calculations consistently. Indeed, they can't even seem to conceptualize the calculation required.

I bring up this example because law is not something that people typically associate with math. It goes to demonstrate that besides the inherent value of learning advanced algebra or whatever is troubling you, that learning may be useful in the places you least expect.

 

[BrianB]

Since I love math so much, I'm taking an Intro to Programming (Pascal) class this year and I'm taking C++ next year.

The sad thing is, I will sometimes do math homework or extra credit for fun....

What's sad is that you're made to think it's sad. :-/

And good luck with the programming class. Pascal rocks as a introductory language.

 

[Morgan Jolley]

Pascal is fun, but we're going kinda slow and most of it is more like busy work than learning stuff.

Actually, I have been able to turn my math skills for the better and help people with their homework. I sometimes will charge people for homework if its due in a period or two and they had a long time to do it (to teach them a lesson) but I usually just help them with one or two questions and let them do the rest.

I also sometimes will find better ways to explain things to the class when my teacher has a brain fart. One time, this girl didn't get how

3-(x+2)

turned into

3-x-2

so I had to explain that she should look at it as

3+ -1(x+2)

and then she got it.

 

[Steve Tannehill]

OK some of you are taking the stereotypical approach to life. Read Rich Dad Poor Dad by Robert Kiyosaki or some of his other books and you'll see that the approach to get good grades, go to a good college, and get a good high paying job with good security won't get u anywhere in life.

Van, as someone who is at least twice your age, I'll cut you some slack. I think you are looking for excuses to justify a bad grade. I also think you are looking in the wrong places.
I am not saying that you are going to understand Algebra II, or go on to higher math. I do think, however, with the right combination of teachers, tutors, and math books, you could at least get through high school with a foundation in math that will be useful to you in life.
Here is a problem that you should be able to solve:
Let's say that you like the classic television shows of the 70's and 80's and you want to buy a new television that will give you the largest possible 4x3 image so you can view these shows in their proper aspect ratio. There are plenty of affordable 4x3 televisions. But you also want to consider a widescreen 16x9 television, because you want to want to watch all your anamorphic widescreen DVD's with enhanced resolution.
Keep in mind that 4x3 material on a 16x9 television will appear "windowboxed" with bars on the side of the image (for this problem, we will not consider zoom modes, as they are contrary to the OAR principle). Thus, 4x3 content will be presented and preserved in the middle of the 16x9 frame.
You narrow down your television choices to a 50-inch 4x3 television or a 65-inch 16x9 television. (Both screen measurements are diagonal.)
Which television will deliver the larger 4x3 image?
What are the heights and widths of both television screens?

- Steve

 

[Morgan Jolley]

Thats an easy one.

The 4:3 one is 30x40 with a diagonal of 50. It has a total area of 1200 square inches for the screen.

The 16:9 one is 31.86x56.64 with a diagonal of 65. It has a total area of 1804.55 square inches.

The 16:9 can produce a 4:3 image that is 31.86x42.48 and has a diagonal of 53.1 inches. It has an area of 1353.41 square inches.

So the 16:9 set can produce a larger 4:3 image than the 4:3 set. Booya!

How about this (actual question we had for extra credit):

There are 3 circles, each with a 10 in. radius, touching eachother but not intersecting. There is a blank space in between them. What is its area?

 

[Darren Davis]

My teacher wrote this on the Board

PMDAS (Paranthesis, Multiply, Divide, Add, Subtract)

Frank, your HS or previous teachers never told you about the order of operations? That's pretty bad teaching. I'll believe it, though. I've seen a few teachers that just have no idea how to make someone else understand. They know the material so they figure everyone else does or forget that the students are just...students. My math teacher is pretty good, though. He makes sure to make any lesson as visual as possible for us. It can really help in understanding why something is the way it is.

 

[Darren Davis]

There are 3 circles, each with a 10 in. radius, touching eachother but not intersecting. There is a blank space in between them. What is its area?

100rt3 - 50pi sqare inches?

Good question

 

[Mike Voigt]

16.125 sq. in.

 

[Bill Catherall]

There are 3 circles, each with a 10 in. radius, touching each other but not intersecting. There is a blank space in between them. What is its area?

Mike got it right. And here's how it's done:
Sketch out the three circles and sketch a line from the center of one to the center of another and so on until you have an equilateral triangle (it doesn't need to be exact, just for visualization). You'll notice that the lines will intersect exactly where the circles touch. Now we need to take the area of the triangle and just subtract the areas of the triangle that are shared with the circles.
The base of the triangle is 20 and the height would be (using Pythagorean theorem)
10^2 + h^2 = 20^2
h=17.321
So the area of the triangle is A=1/2*b*h=173.205
The area of the circle shared by the triangle is 1/6th the area of the circle (60 degrees in every angle of an equilateral triangle...60/360=1/6)
A=1/6*pi*r^2=1/6*3.1416*100=52.360
There are 3 of those areas so subtracting all 3 from the area of the triangle gives us 173.205-3*52.360=16.125.

 

[Morgan Jolley]

I think thats what it is. I don't have the sheet I did the work on, but I got it and I think I was right, so hopefully I will get that extra credit.