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Author Topic: I need to re-learn some math....
Belle
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I'm a new teacher, but I always planned on continuing in school and getting additional certifications. I want a job closer to home and away from the environment I currently teach in.

I am getting my master's degree in English as a Second Language, and I've decided that I would like to have the option of teaching more than just the English content area.

So, I've decided to make myself even more marketable. I want to add a math certification to my resume. Luckily, I can certify by test so I don't need to take any classes. But, I have to re-familarize myself with math up through calculus in order to pass the test.

Now, I tend to do very well in math and I like numbers. I tease about being a liberal arts major and not able to handle a lot of math, but I was alwasy very successful in school in math classes and took two more math classes than my major required in college because I enjoyed it. So, I'm not a hopeless case. [Wink]

But, the area I am most concerned about is geometry. It's my least favorite math, and the one I "forgot" the most.

Anybody know of any good online resources? Or good books to use beyond just getting my hands on some textbooks? Fortunately my husband was a math/engineering major and he has a lot of his old textbooks (plus he is going to help me, which is awesome!)

I have plenty of time, I can't be certified by test until I have two years teaching experience which won't be until next May so I won't take the test until probably March or April of 2011.

If you know of any good resources, I'd certainly appreciate it!

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steven
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I have some excellent geometry advice. Never ask me about geometry. I SUCK at proofs, because I'm not good at logic.

Shocking, huh? LOL

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scholarette
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If you have a few thousand bucks sitting around, Sylvan has some excellent resources. [Smile] Just thought I would be completely unhelpful. I do tutor geometry but everything we use is proprietary and I don't actually teach (I think I am the only tutor at Sylvan without cert so I am a bit of an oddball).
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scholarette
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quote:
Originally posted by steven:
I have some excellent geometry advice. Never ask me about geometry. I SUCK at proofs, because I'm not good at logic.

Shocking, huh? LOL

Here in texas, they don't do proofs.
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King of Men
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When I studied geometry (age 13-15 or so, in Norwegian schools) all you had to remember was that in a triangle where the angles are 30, 60, and 90, the short side is one-half the hypotenuse. Plus maybe how to construct a right angle using your compass. If you knew those two things you could pass all the exams.

I bring this up because I've recently been doing some tests where a particular variable took the values 30, 60, 90, and 120, so as I submitted the runs I'd chant to myself "tretti-seksti-nitti-trekant" ("thirty-sixty-ninety-triangle") just as we used to do in junior high. Nostalgic!

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Icarus
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Hey Belle. I don't know how it is in Alabama, but in Florida, I was able to find a study guide for the certification exam, including a practice exam, in the library of my local university. (Not their general library, though--the college of education had its own library.) Actually, for some exams I found both the official study guide and a study guide by a third-party publisher.

I can't think of any other resources you haven't though of off the top of my head. Over the summer maybe I could look and see if I have an old geometry final floating around in my stack of ancient floppies.

Something you may want to consider: if you add a math certification, there is a good chance you will never be permitted to teach any other subject area. Your ESL specialization may buffer you from this, but I have a math certification and a language arts one, and I have never gotten to teach language arts at the pre-college level. Here, at least, math teachers are harder to find.

I see that you've got your husband helping you, but I'd be happy to help in any way that I can, if that would be useful to you. I don't tend to check Hatrack much, but there are people around who can give you my e-mail address if you need something and I can't be found. I'm sure we could figure something out.

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Belle
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Thanks Icarus! Yeah, around here the math certification is a lot more valued too.

I don't mind - there are SO many English teachers that jobs in English are hard to come by in any decent school systems. By "decent" I am referring to any school system that is less than 40 miles from my home. Finding jobs in English is extremely tough and I actually think I might enjoy teaching math.

My main reason for doing this is to hopefully land a position where I can teach sheltered content for ELL's in both math and English. But, if I wind up "just" teaching math I think I would be all right with it.

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theamazeeaz
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On the practical end of things many math teachers aren't up to actually teaching calculus (or psych themselves out if they were), so if you are more comfortable with that, you could use that as clout to not have to do geometry after you pass your test.
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King of Men
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quote:
Originally posted by steven:
I have some excellent geometry advice. Never ask me about geometry. I SUCK at proofs, because I'm not good at logic.

Proofs in geometry (and math in general), oddly enough, have very little to do with logic, as such. What's called for is much more of an intuition, a feel for what the next useful step is. It's a trainable skill to some extent, but I have never seen it taught well; most math teachers (IME) seem to assume that you either got it or you ain't.

Edit: On second thought, I'm not at all sure how I would instruct someone who wasn't getting it; perhaps it is an aptitude after all. The only thing I can think of is to do some example proofs in an area where the steps are fairly stereotyped - geometry is good for this - and see if they caught on; and then leave them to do lots of practice.

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Icarus
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quote:
Originally posted by King of Men:
On second thought, I'm not at all sure how I would instruct someone who wasn't getting it . . .

One approach that I found useful years ago, when I last taught Geometry, was suggesting that students work backward from what they were trying to prove, for more or less the same reason mazes are easier to complete when worked backward. There seem to be fewer theorems, etc., with a given endpoint than ones that can fit a given set of initial conditions. So I would think out loud something along these lines: "I would be able to conclude _____ if I knew what?"

We teach proofs in high school geometry not because proofs are more intrinsic to geometry, but because geometric proofs are easier than proofs in other fields, because of how codified a structure Euclid gave us. This may hinder the future math majors, who flounder when they first encounter paragraph proofs. (Other than proof by contradiction.)

I don't know that I agree that they have little to do with logic, though. I agree with you that there is an instinct that you can develop, but the steps in the end are deductive steps. Then again maybe the distinction you're drawing is between product and process. Maybe the difficulty some students have with proofs lies in the fact that they're concentrating too much on the deductive end product and not enough on the intuitive sense that would lead them to it.

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King of Men
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Well yes, each step is a deduction, but the essential skill is to be able to pick out the one deduction that's actually helpful in moving you closer to the goal.
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Glenn Arnold
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quote:
Originally posted by scholarette:
quote:
Originally posted by steven:
I have some excellent geometry advice. Never ask me about geometry. I SUCK at proofs, because I'm not good at logic.

Shocking, huh? LOL

Here in texas, they don't do proofs.
Whoa! That explains a lot.

quote:

Proofs in geometry (and math in general), oddly enough, have very little to do with logic, as such. What's called for is much more of an intuition, a feel for what the next useful step is.

Hmm. I sort of agree, if you're talking about algebraic geometrical proofs. It's not just a matter of applying the next logical step, but remembering the theorems needed to SEE the next logical step. But I always found proofs of geometrical diagrams (where a set of lines was given as parallel and you had to prove that two triangles were congruent, for example) to be very logical.

Belle: When I took my math certification test I went to the local community college, and they had a resource room where there was a computer program that led me through a sequence of online lessons from basic algebra up through calculus. I wish I could remember the name of the program, although it's probably outdated by now, but you could check with local college librarians and see if they know of similar resources.

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theCrowsWife
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I loved proofs in high school geometry so much that I went on to take an entire class in them in college. It basically introduced several different fields of number theory in order to provide fodder for our proofs. Man, that was my favorite class that I ever took. No one else was anywhere near as enthused, though.

I agree with KoM that the intuitive part of proofs is at least as important as the logical part. If you don't have an intuitive idea of where you are going, how can you find the right logical path to get there? With simpler proofs, trial and error can work, but that gets unwieldy pretty quickly.

--Mel

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rivka
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quote:
Originally posted by Glenn Arnold:
quote:
Originally posted by scholarette:
quote:
Originally posted by steven:
I have some excellent geometry advice. Never ask me about geometry. I SUCK at proofs, because I'm not good at logic.

Shocking, huh? LOL

Here in texas, they don't do proofs.
Whoa! That explains a lot.
Nationally, there is a trend in this direction. [Frown]

I think it is HORRIBLE, and my dad -- who has helped select math textbooks books for LAUSD's "approved" list, and who gets them as college students who never learned to do proofs -- entirely agrees.

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King of Men
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quote:
It's not just a matter of applying the next logical step, but remembering the theorems needed to SEE the next logical step. But I always found proofs of geometrical diagrams (where a set of lines was given as parallel and you had to prove that two triangles were congruent, for example) to be very logical.
I think there's an analogy to chess here. You can in some sense learn to play by memorising how the pieces move and then doing a brute-force search for "If I move this, he can do that, and then I would...". This is the equivalent of learning the theorems and running down the list "If I apply this, I get that." But you'll never play at anything beyond a beginner's level with this approach. (Although it does often work in geometry; that's because the list of theorems is pretty short and there are not many different kinds of proofs. As was pointed out, geometric proofs are taught first because they're simpler than other kinds.)
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andi330
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When I was taking my first math classes in over 10 years I used the Demystified Series. They are all by different writers, but I thought that they worked well and were understandable.
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Glenn Arnold
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quote:
Although it does often work in geometry; that's because the list of theorems is pretty short and there are not many different kinds of proofs. As was pointed out, geometric proofs are taught first because they're simpler than other kinds.
I think it goes beyond that. Geometric proofs are simpler because they're visual. We have an intrinsic ability to recognize similar shapes, and we can fall back on pattern recognition to make intuitive leaps, which are then reinforced by theorems.

In my undergraduate work I took two courses titled "Fundamentals of Mathematics" I and II. Also Axiomatic Geometry. All of the assignments in all of these classes were proofs. And in each case, I had a connection back to my 7th grade math teacher who taught us that mathematical proof is a prerequisite to understanding basic philosophy, because without understanding what "proof" really means, we can never understand what it means for something to be true.

If there's any one principle that I believe should be taught in every person's education, that's it.

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Belle
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My favorite maths are algebra and trig. My daughter was taking trig this semester and I enjoyed helping with her homework.

Next year she takes pre-cal, because they don't offer calculus at her school, which is disappointing. Honestly, I see myself staing in middle school, which means not teaching past algebra I. I suppose it's possible I could end up in a high school somewhere, but as it turns out the trend is to use ESL teachers more in the elementary and middle school grades and less in the high schools.

Of course, if as Icarus says I wind up teaching math...I could be anywhere. We'll see. I just want more options and a chance to get away from where I am. It's....bad. Not the students' fault, of course. But circumstances have made the job almost unbearable.

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Amanecer
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quote:
Here in texas, they don't do proofs.
We did many a proof in my Texas geometry class. Granted that would have been 10 years ago now, so maybe the standards have changed.
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mr_porteiro_head
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Yup. I had geometry in Texas, and it had proofs.
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Icarus
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Around here, what has become increasingly common is to do proofs at the honors level, and not at the regular level.

I'm not sure what I would do if I were in the position of teaching geometry at the regular level, if I would buck the system or not. My feeling is that without the proofs, there's not a lot left that isn't already covered in middle school. I think proofs are the reason for the existence of geometry as a high school class.

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The Rabbit
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quote:
Originally posted by Icarus:
Around here, what has become increasingly common is to do proofs at the honors level, and not at the regular level.

I'm not sure what I would do if I were in the position of teaching geometry at the regular level, if I would buck the system or not. My feeling is that without the proofs, there's not a lot left that isn't already covered in middle school. I think proofs are the reason for the existence of geometry as a high school class.

Agreed. I think one could reasonably argue that one should skip that proofs, but if you choose to go that route, you should choose to skip the geometry class altogether and devote more time to algebra and trig.
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katharina
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quote:
Originally posted by scholarette:
quote:
Originally posted by steven:
I have some excellent geometry advice. Never ask me about geometry. I SUCK at proofs, because I'm not good at logic.

Shocking, huh? LOL

Here in texas, they don't do proofs.
When did that start? I honestly wonder, because I went to high school in Texas and we definitely, definitely did proofs.
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Darth_Mauve
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I found this website thanks to NPR. The guy teaches basic math concepts via YouTube. I never took Trig, but now--I actually know what a Sine and Cosine are.

Khan Academy. KhhhhhhaaaaaaaannnnnnnnN!

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scholarette
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My husband taught geometry in 2003 in Houston. I don't know when the curriculum shifted. But Houston, which was kinda the basis for no child left behind, is the district that perfected the art of institutional cheating on the standardized testing (for ex, 10 grade is when you take the test- in order to move from 9th grade to 10th, you have to be able to pass the test, in order to move from 9th grade to 11th, you have to be a certain age and have taken 9th grade twice. So basically any kid far enough behind will never take the 10th grade and be tested).
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Tstorm
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I don't recall doing any proofs in geometry, either. But my geometry teacher sucked. Well, he was smart enough in the subject area, but he couldn't control the classroom. In that class, I saw a spitwad the size of a baseball.
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The Rabbit
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quote:
Originally posted by katharina:
quote:
Originally posted by scholarette:
quote:
Originally posted by steven:
I have some excellent geometry advice. Never ask me about geometry. I SUCK at proofs, because I'm not good at logic.

Shocking, huh? LOL

Here in texas, they don't do proofs.
When did that start? I honestly wonder, because I went to high school in Texas and we definitely, definitely did proofs.
I may be mistaken, but hasn't it been around 15 years since you took geometry in the Texas schools? A lot of stuff has changed in the public schools since that time. No child left behind has made forced a lot of curriculum changes, mostly for the worse.
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The Rabbit
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quote:
Originally posted by Tstorm:
I don't recall doing any proofs in geometry, either. But my geometry teacher sucked. Well, he was smart enough in the subject area, but he couldn't control the classroom. In that class, I saw a spitwad the size of a baseball.

May I ask how long ago you took geometry?

I'm just guessing here, but I'd bet that proofs don't appear on the standardized tests and so have been cut from a lot of curricula during the past decade.

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Icarus
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That seems like a good guess.
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scholarette
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I was talking to one of the kids I tutor and they complained that all they did the entire year was prepare for the test. He wondered why they never did anything that was not TAKs prep anymore.
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King of Men
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Embarrassingly, I just used the Google calculator to get cos(120 degrees). :oo
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Elizabeth
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Belle,
Check the Department of Ed. site in your class. Massachusetts always has free classes to prepare people for the math test.

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Belle
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My hubby has helped me find some online lectures offered free and he has some old college textbooks.

I've got the breakdown of what is tested. As I looked back over problems I realized I could do them...but just too slowly. I need to practice and do hundreds more problems to improve my speed.

I can't spend a lot of time on it right now because in addition to teaching, I'm taking two graduate classes in ESL. I want to work for a couple of hours a week until the summer when I can really buckle down.

The middle school certification test only goes through algebra...I know I could take that one and pass it now. But, I thought I may as well have some more flexibility and it's a personal challenge - I would like to prove I could do it, even if only to myself.

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rivka
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Good for you! [Smile]
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