Best Way To Teach Oneself Math?

An anonymous reader writes "In high school I failed two out of three years of math classes and eventually dropped out of school completely. I earned my general equivalency diploma as soon as was legally possible and from there went on to college and beyond. That was many years ago and my most basic algebra, trigonometry, and geometry skills are slipping away at an alarming rate. I'm looking for a self-guided course covering the equivalent of 4 years of high school mathematics including calculus. My math skills are holding me back. How can I turn this around?"

Comments

3 ideas

[stoolpigeon]

There are plenty of self study guides that one can purchase.

Another option, if it fits into a persons schedule, would be to take classes through a community college. Costs are lower, classes are generally smaller than a university and schedules are often flexible for working adults.

Another thought I had is home schooling materials. I've never personally been involved in homeschooling, but as I understand it these kids can earn a highschool diploma at home. So why couldn't someone put themselves through such a program just to learn the information? I'm sure there are lots of resources out there for this, a quick google turned up this one.

Re:3 ideas

[Guido del Confuso]

I think that taking courses at a community college is the best idea. In fact, take it for a letter grade. Although the grade doesn't really matter, this will give you an incentive to do the work and stay with the class.

I think it's only too easy to just pick up a math book and tell yourself you're going to do the work, only to get frustrated and abandon it a few weeks later. By having an actual class that you have to make time to attend, you're making more of a commitment and are more likely to stay with it.

Re:3 ideas

[Anthony]

I concur, Good study guides and good courses will put you on the right track.

No matter what you do, realise the Mathematics is not a spectator sport. I continuously fall into the trap of reading about Mathematics than doing Mathematics. Do the exercises and do some more. One thing I did do which was invaluable was a bridging course that reviewed much of final year high school Mathematics with plenty of exercises and a great teacher. Recognise your wakness and go back and make sure you understand whatever is being assumed at the level you are having diffculty with and again, do those exercises. For example, if you are having trouble with trigonometry, review the ways of deducing angles for triangles and bisected parallel lines. Review Pythagoras's Theorem, fundamental algebra, etc.

Re:3 ideas

[iron-kurton]

Attending a class also allows you to ask questions for topics that you may not understand completely, even with studying the book. I know that most math books are written by math PhDs, and although the topic is covered, it may not make sense. That's why it's so important to have an interactive learning environment. Like the parent says, you are less likely to get frustrated and give up.

Re:3 ideas

[srhill]

Above all, practice (Math is a muscle). Find some problems that you think are interesting, and solve them. If something doesn't work out the right way, try it again. Try and explain the problem to someone else -- that almost always helps.

I highly recommend this book: The Square Root of Two by David Flannery. It's an excellent book which gives some real good insight into how to think about math problems, and is a pretty fun read.

http://mathforum.org/dr.math/ is a great web site for helping with homework.

Also, don't get discouraged, Math Is Hard.

Practice

[Wonko the Sane]

The way I kept my math skills fresh was to invent new problems to solve. Also I would derive every new formula instead of just memorizing it. Some random examples off the top of my head:

Derive newton's method.
Find the formula for the circle that passes through any three arbitrary points
Derive all the trigonometric identity functions

Re:Practice

[nautical9]

But remember kids, never mix calculus and alcohol. Don't drink and derive!

Nothing fancy.

[EinZweiDrei]

Get a math textbook. [Hungerford's 'Contemporary Pre-Calculus' worked for me. For Calculus, Larson's 'Calculus' is keen.]
Set aside 30 minutes a night.
Work the problems out with pen and paper.
Where necessary, remember formulas however best suits you.

Avoid technological fixes.

:My $0.02.:

Re:well

[pz]

I don't think they do a great job of teaching it in school where they take a very linear approach.

I'm not currently a professional teacher, but I have been one, at a Big Technical University that you have heard of, for four years. My skin crawls when I hear people demeaning a linear pedagogic approach because, frankly, and you can take this as an expert opinion by someone who has won awards for teaching, there is no better way. Period. People learn depth-first by cycling down from coarser details to finer ones. They learn in steps. To quote Prof. Patrick Winston of AI fame, you only learn that which you almost already know. Trying to teach in fuzzy alternate ways, teaching by trickery, emphasizing word problems or case study, teaching two or three paths at the same time, all of that stuff does not work for technical and mathematical subjects, pure and simple.

For the basic mathematics that the original post is inquiring about, the concepts are reasonably simple and straightforward. What they require, however, is what often appears to be mind-numbing repetition. It's work. While I applaud this fellow's current initiative, the effort should have been put in when he was a teenager because it's a lot easier then. It sounds like he's understood the mistake and is currently, as an adult, trying to correct that, which is definitely commendable. Unless he's the sort of person who developed phenomenal self-discipline later in life, however, the best bet is to get to a classroom. There are any of a large number of adult education services in every city I've been to. Often local high schools will have evening adult-ed classes as well. Or, as another poster suggested, the local community college can be a good resource. But basic mathematics requires a lot of rote work. It can be a joy to know that you've learned everything that was used to get mankind to the moon, a tremendous joy in fact, but it takes work.

Homeschoolers secret: Saxon Math

[AntrygRevok.net]

http://www.saxonpub.com/
they've changed their URL, but it redirects pronto, and the new one isn't rememberable. . .

Diff between these and the normal ones?

One concept, one lesson.

Big concept? broken into several components, and distributed over several lessons.

Syncopated plan: one gets the chance to get a knowing into long-term-memory/function before one hits the next lesson that relies on it.

having tried many, and lost my math in some brain-damage I got in my teens, this is THE required one.

Find the book you need,
by doing a placement-test,
then get the ISB# for that recommended book,
then find a second-hand copy on http://www.abebooks.com/ for cheap.

Re:well

[nbetcher]

Trying to teach in fuzzy alternate ways, teaching by trickery, emphasizing word problems or case study, teaching two or three paths at the same time, all of that stuff does not work for technical and mathematical subjects, pure and simple. Actually, I tend to disagree with that point. While it is my opinion - as well as the opinion of many other well-educated professors and other academic teachers - that everyone doesn't learn the same way. Myself in high school I often found it extremely difficult to learn in linear ways. While I agree that teaching 'fuzziness' or 'trickery' isn't the correct path, I do however believe that myself and many others alternates ways (taught at the time of the original lecture) can often be very helpful to people. Instead of teaching your students that this is the way that you do it, I believe it's equally more important to show how else the problem can be solves, or how it is incorrectly solved. Word problems, hmm. While I consider myself fairly good at English and other subjects, I've never found a good crossing between words and mathematical problems to form a word problem. Although, I have seen people outside of myself learn from those types of problems. In today's society everyone expects you to be in the norm (such as the professor indicated in the above quoted excerpt). In-fact I 'blame' (and I use the word lightly) these differences in education teaching to be the reason I was unable to successfully go to college straight out of high school. Additionally for me I found that college was basically a whole lot of homework and very little lecture. Sure, it may be a scientific 'fact' that most (99.99999%) people learn better from homework rather than lecture, or at least retain the knowledge better via homework after a lecture. However my situation is different, I've always learned from lecture. Again, in high school I found that I always learned the subject better by listening to the teacher and NOT taking notes. Often my grades were very bad because of the homework that was never done, however I made up for that lack from acing my tests. Point being: don't generalize, professor. While 99.99999% of the population seems like a good enough statistic for you, some of the brightest minds out there don't learn the same way as you.

The low-brow, DIRTY way to quickly learn the math

[Jonathan Walther]

I saw several people here recommending tutoring, college courses, and college text books. I don't recommend any of these to begin, although they are good if you want to continue.

What I recommend here is the "low-brow" way. The easy, the "dirty" way that purists and snobs will turn up their nose at. This is equivalent to the advice of those people who give children comic books to encourage them to read. The method works, right? This will work for you too, and you'll enjoy it as much as comic books.

The key, essential text, is a book written a long time ago, called "Mathematics for the Million". It is still in print, and is excellent. It takes you from early chapters on counting from one to five, and works up through simple geometry through to algebra, logarithms, trigonometry, spherical trigonometry, calculus, and ends off with combinators and linear algebra. It is written in a great style, easy to read, but packed with information. It has lots of interesting stories and applications of the math, but not any fluff. This is the key text. It is 800 pages long, and worth every page. The price is astoundingly cheap. A chap on a desert island could rebuild much of civilization if he had this book with him. If I was on a desert island, this book would come second on my list, right after the Bible. With each chapter, it puts the mathematical developement in historical context, showing how real people developed the math out of the math that went before it, which will be fresh in your mind from the chapters you already read.

After that, you may want to work through these books: "Algebra The Easy Way", "Trigonometry The Easy Way", and "Calculus The Easy Way". In the "Easy Way" series of books, each concept is introduced in the context of a story and a practical application, as a group of people "discover" these fields of mathematics for themselves, to solve their problems. It is set in a fantasy setting with kings, queens, dragons, etc.

Finally, for inspiration, and "fun", I recommend all of the mathematics books by Martin Gardner, Ian Stewart, and A.K. Dewdney. All three of these men ran a very successful mathematical amusements and puzzles column in Scientific American. Their books are compilations of their columns. They make math interesting, showing interesting relationships between the different bits of math that we are told are "important". And they show interesting applications, puzzles, and pictures resulting from the mathematics. One Martin Gardner column that really stuck with me was the one on the "super ellipse". It has the interesting property that it looks like it should tip over, but it actually keeps itself balanced, and resists being tipped over.

As an earlier commenter said, you can't just read about math. You have to do it. You have to practice. If you are willing to practice though, the books I listed above will get you where you want to be, with a minimum of head-scratching.

Good Luck!