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Noclevername
2011-Nov-25, 12:18 PM
Unfortunately I am a product of the US public school system, so my mathematical education was spotty and shoddy at best. I feel like I'm practically innumerate-- I have to whip out a calculator to do simple arithmetic and I don't even know what a cosine is (some type of vegetable?) Trigonometry and calculus, forget about it!

Are there any suggestions for online or home-based remedial math education? I'd like to at least be able to follow a few of the equations put up on this board. I really am missing out, not having a solid foundation in math. :(

AndreH
2011-Nov-25, 01:21 PM
Unfortunately I am a product of the US public school system, so my mathematical education was spotty and shoddy at best. I feel like I'm practically innumerate-- I have to whip out a calculator to do simple arithmetic and I don't even know what a cosine is (some type of vegetable?) Trigonometry and calculus, forget about it!

Are there any suggestions for online or home-based remedial math education? I'd like to at least be able to follow a few of the equations put up on this board. I really am missing out, not having a solid foundation in math. :(

Not thatI would know about good sources for self education in English, but I feel that we would need a better description of what ypur exact status of knowledge is.
Needing a claculator for simple operations does not exactly mean you are a math dummy, it can mean you have not enough practice.

So were does your knowledge stop?

Did you learn how to add, subtract, multiply and divide with paper and pencil?
(I mean like puttting 5 numbers in a colum and add them digit by digit)?
Did you learn how to solve simple equations like 5 - x = 1, what is x?
Did you learn a bit more complex equations like ax + b = c, what is x?
Did you learn to solve equations with 2 variables, two equations given like 5x + 3y = 4; x - 5 = 1?
Did you learn how to solve quadratic equations like ax² + bx + c = 0
Did you ever have basic calculus (like what is a function, how is it defined how to fin out about properties?

That is basicly the stuff from 4 to 8/9 grade here in Germany. I think giving a view answers to this may help others to recommend you a good book for self study.

Noclevername
2011-Nov-25, 01:33 PM
Did you learn how to add, subtract, multiply and divide with paper and pencil?
(I mean like puttting 5 numbers in a colum and add them digit by digit)?
Did you learn how to solve simple equations like 5 - x = 1, what is x?
Did you learn a bit more complex equations like ax + b = c, what is x?
Did you learn to solve equations with 2 variables, two equations given like 5x + 3y = 4; x - 5 = 1?

Given time, yes, I could muddle through about up to that point; y= negative 12, all in my head. It took me a minute or so.

ETA: And it's the wrong answer. Whee!

Did you learn how to solve quadratic equations like ax² + bx + c = 0
Did you ever have basic calculus (like what is a function, how is it defined how to fin out about properties?

No and no.

Argos
2011-Nov-25, 01:38 PM
With all due respect, Noclevername, the most important things I know in math were acquired out of school. With effort you can accomplish anything.

Best regards. :)

jokergirl
2011-Nov-25, 01:45 PM
With all due respect, Noclevername, the most important things I know in math were acquired out of school. With effort you can accomplish anything.

Best regards. :)

And this is the effort he expends. Let's help him with it, ok?

I have a book at home that is quite amazing to learn geometry and a lot of other basic math ideas. It's also quite old.
Look it up. (http://en.wikipedia.org/wiki/Euclid's_Elements)
(I have Heath's edition which also doesn't even use numbers for a lot of things - which is a Good Thing, in my mind. Math should be about ideas, not counting.)

;)

AndreH
2011-Nov-25, 01:56 PM
Given time, yes, I could muddle through about up to that point; y= negative 12, all in my head. It took me a minute or so.
No and no.
Ok the first thing we have clarified is you are not a math dummy!
Anyway, I was not so much pointing at if you can figure it out in your head, but if you can use the formalism. This is what you need if it is getting more complex.

What I mean is following:
5 - x = 1 is formally solve as follows:

first you right the equation down
5 - x = 1
formally we need to have x alone on one side of the equation. Hence we substract 5 on both sides of the equation
5 - x = 1 ; -5 yields
- x = -4 ; multiply both sides with (-1)
x = 4
This is the formalism you need when it gets more complex. For small numbers we usually "see" the results. But id the numbers get more complicated and the equations more complex you might get lost.
If you have learned how to that we have a good starting point I thing. It would be solving linear equations with 2 or more variables and quadratic functions. The next step would be basic calculus I think.

Like Argos I would also encourage you. Even though I learned a lot in school, during my University time we need to do a lot of self education, as lecturers are not always that good. You just need the right book.

swampyankee
2011-Nov-25, 02:01 PM
Noclevername, there are a lot of issues with the US public education system, including a severe over-abundance of less-than-mature students, who manage to ruin classes for everyone else in the room. As for sites to check? A number of universities, colleges, and community colleges are making videos and transcripts of their classes available for download, such as MIT's Open Courseware.

You could also try http://www.mathfoundation.com/, http://www.makingmathreal.org/, and any of Danica McKellar's books (although walking around with Hot for Math may be slightly embarrassing...)

Incidentally, a few years ago I taught an introductory physics class for liberal arts students. On the first day of class, I gave a math quiz identical to one my eighth-grade (13-14 year olds) daughter had in her public school. One of the students was unable to answer any of the questions. (I'm not evil...mwahaha...but it's impossible to teach physics without some math.)

Argos
2011-Nov-25, 02:08 PM
Math education is inadequate all over the world. Keith Devlin, in his "The Math Gene", suggests that children should start learning math with group theory instead of arithmetics, to put their extraordinary powers of abstraction to use at the right time [and I would agree with him].

AndreH
2011-Nov-25, 02:19 PM
Math education is inadequate all over the world. Keith Devlin, in his "The Math Gene", suggests that children should start learning math with group theory instead of arithmetics, to put their extraordinary powers of abstraction to use at the right time [and I would agree with him].

I don't buy such statements so easy. Right the year after I came to school in Germany "set theory" was introduced in the first grade (we do not refer too Kindergarten as school, so first grade is when you are about 6 or 7). With the same argument, the power of abstraction. It was a complete desaster, after about ten years it was abolished again and replaced by arithmetics. If done the right way, one can also understand the underlaying structure of math. But I guess we are hijacking the thread here.

Argos
2011-Nov-25, 02:36 PM
Group arithmetics is very intuitive, and I have a feeling that it could be taught to infants early in the school life. As for hijacking, the thread is about a) perceived inadequacy of math education and b) a call for help. I think we´re complying with the constraints. :)

Regards.

PraedSt
2011-Nov-25, 02:38 PM
Are there any suggestions for online or home-based remedial math education? I'd like to at least be able to follow a few of the equations put up on this board. I really am missing out, not having a solid foundation in math. :(There's a lot of emphasis on problem-solving in maths, so I wouldn't recommend that you just study on your own. Go for evening classes if you can manage it.

AndreH
2011-Nov-25, 02:52 PM
There's a lot of emphasis on problem-solving in maths, so I wouldn't recommend that you just study on your own. Go for evening classes if you can manage it.

It will help to go to an evening class, but there are great books with problems and solutions available, also. That is what you need. I jsut cannot recommend you any, because unfortunately I am speking the wrong native language.
The book I was using for calculus at University had problems for each step in each lessons. The solutions were in the same book in the back. You just need to take care not to cheat yourself. If the book is really good, the solution is not just the math, but also explaining in words the why and how.
If Noclevername has no time to visit an evening class, that is what he needs. Typically it is not the standard school book.

AndreH
2011-Nov-25, 02:56 PM
Group arithmetics is very intuitive, and I have a feeling that it could be taught to infants early in the school life. As for hijacking, the thread is about a) perceived inadequacy of math education and b) a call for help. I think we´re complying with the constraints. :)

Regards.
It was only I was feeling I was ready to start a discussion about didactics of math. I wanted to avoid that. ;)
Regards

Solfe
2011-Nov-25, 03:03 PM
Novlevername,

Go and check your high school's web page. They may have resources for students on line, such as whole books.

My high school adopted online books a few years back: http://highschool.shs.k12.ny.us/MathTexts (some of the picture links are dead, try the blue text instead). I used my high schools online texts to get myself ready for college math.

jokergirl
2011-Nov-25, 03:09 PM
A lot of the problem with introducing "new" math teaching standards is that they forget to re-train the teachers. And if the teachers don't understand the theory, how can they teach the children other than in a "Put in X, go through the formula, get out Y" way? Problem solving is a much more important part of math but is often left by the wayside.
</rant>

But seriously, check out Elements.

;)

Cougar
2011-Nov-25, 05:54 PM
Right the year after I came to school in Germany "set theory" was introduced in the first grade... It was a complete desaster...

I was a whiz in math in high school. 9th grade: algebra. 10th grade: geometry. 11th grade: trigonometry. In 12th grade, instead of a more in depth preparation for calculus, we were offered the "new math": set theory. While this has served me well in terms of logical consequence and information science, I barely scraped by in calculus and differential equations at university. Of course, my poor preparation in calculus was greatly exacerbated by the fact that my dorm was a short walk down the cliffs to one of the best private surfing beaches on the California coast. And there might have been a few other, uh, distractions. :rolleyes:

Then, third year at university, I took abstract algebra. Group theory. Matricies. Well, this I like. Not because it was particularly applicable to anything I was likely to run into. I was no engineer. I studied math like it was the history of art. The art of human thought. Now, abstract algebra is one of the crucial foundations upon which quantum theory is built, as well as general relativity. These fields are not particularly useful in "everyday life," but they do represent the current culmination of scientific investigation into the world and universe we live in. And I think that's certainly worth knowing something about.

AndreH
2011-Nov-25, 08:34 PM
I was a whiz in math in high school. 9th grade: algebra. 10th grade: geometry. 11th grade: trigonometry. In 12th grade, instead of a more in depth preparation for calculus, we were offered the "new math": set theory.

Just to clarify: I was not harmed by the introduction of set theory, as I happened to be that one year earlier in school to go on with the classic arithmetic. Only my friends who were/are one year younger than me where hit. I had it first time in 5th grade (10 years old). I found it interesting and logical. And there are some things you can even use in daily life.

While this has served me well in terms of logical consequence and information science, I barely scraped by in calculus and differential equations at university. Of course, my poor preparation in calculus was greatly exacerbated by the fact that my dorm was a short walk down the cliffs to one of the best private surfing beaches on the California coast. And there might have been a few other, uh, distractions. :rolleyes: Oh well - this distractions are present everywhere even if they do not weare Bikinis.

Then, third year at university, I took abstract algebra. Group theory. Matricies. Well, this I like. Not because it was particularly applicable to anything I was likely to run into. I was no engineer. I studied math like it was the history of art. The art of human thought. Now, abstract algebra is one of the crucial foundations upon which quantum theory is built, as well as general relativity. These fields are not particularly useful in "everyday life," but they do represent the current culmination of scientific investigation into the world and universe we live in. And I think that's certainly worth knowing something about.

I completely understand the awe of math. For me it was "vector spaces" and the algebra defined in them. But my point is: This does not belong into first grade! My doughter is 7th (13 years old) grade now. They started with classical arithmetic in the 1st grade. They had a very good book, explaining the tings in a way that 1st the kids learned how to do calculations, and second understood the underlaying structure.

BTW: Do you have a good book recommendation for Noclevername? As we found out above it should maybe start with solving equations and equation systems with 2 or more variables.

2011-Nov-25, 10:50 PM
Unfortunately I am a product of the US public school system, so my mathematical education was spotty and shoddy at best. I feel like I'm practically innumerate-- I have to whip out a calculator to do simple arithmetic and I don't even know what a cosine is (some type of vegetable?) Trigonometry and calculus, forget about it!

Are there any suggestions for online or home-based remedial math education? I'd like to at least be able to follow a few of the equations put up on this board. I really am missing out, not having a solid foundation in math. :(
First, I must commend you on your courage to post this. When you are teaching yourself math, just remember that the key is to focus on comprehension and practice as opposed to memorization. In other words, the combination of a pencil and scratch paper (lots of it) is more useful than a highlighter and flash cards. I know that this method works because I have used it to teach myself differential and integral calculus when I was in 10th grade.

As far as resources are concerned, I think that Paul's Online Math Notes (http://tutorial.math.lamar.edu/) are excellent. The website provides an easy to understand review of topics ranging from Algebra all the way through Calculus and Differential Equations.

Best of luck with your studies.

tlbs101
2011-Nov-26, 03:29 AM
I just finished 12 weeks of student-teaching high school algebra and geometry (switching careers from engineering to teaching).

I have a couple of sugestions based on experience:

1. My late wife was in much the same position you are. At 42 she started community college and took basic math and algebra courses. She did quite well.

2. http:/www.khanacademy.org Sal Khan has won numerous awards for his teaching videos. These videos are 5 to 15 minutes in length and cover all math subjects. You can watch them over and over until you "get it". I used some of them as part of my curriculum. Kids around the world who don't have any other access to math education are watching Khan videos.

Note to mods: I have no affiliation with khanacademy.org, I just find the site useful for what I described.

Jens
2011-Nov-26, 06:47 AM
I don't even know what a cosine is (some type of vegetable?)

If you're a Leo, then a cosine is someone who is also a Leo.

Noclevername
2011-Nov-26, 08:35 AM
I want to thank everyone for their advice and help, so I will: "Thank you!"

PraedSt
2011-Nov-26, 09:33 PM
However good books and videos can be, I still think a significant amount of interaction is essential for learning maths, especially at the stage Noclevername is.
Having said that, if you do decide to go the solo route, you can always ask us if you get stuck. Grapes and Coelacanth, for example, are exceptionally good mathematicians.