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

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

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: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: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.

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.