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?"

3 ideas

[stoolpigeon (454276)]

There are plenty of self study guides [amazon.com] 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. [homeschoolmath.net]

Re:3 ideas

[stoolpigeon (454276)]

should have included math.com [math.com]

Homeschoolers secret: Saxon Math

[AntrygRevok.net (1150851)]

http://www.saxonpub.com/ [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/ [abebooks.com] for cheap.

Re:3 ideas

[Guido del Confuso (80037)]

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

[iron-kurton (891451)]

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

[Anthony (4077)]

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

[Tumbleweed (3706)]

No matter what you do, realise the Mathematics is not a spectator sport.

Not yet, but it sure would be more interesting than watching golf!

Re:3 ideas

[arth1 (260657)]

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.

And remember that being good at maths is part aptitude, part attitude, and part doing it. Just like you won't become a good musician without having a minimum of talent, liking music and lots and lots of voluntary exercise, you won't master math as long as you dislike it and don't do more than you have been asked to do.

If there's something in math you don't understand, take one step back and play with what precedes it, over and over again, until you truly master it, and it leads you into what you don't understand. Then you'll get the "a-ha!" experience, and everything will become much easier. In math, you must understand all the foundations before you can proceed to the next level. You can't pick that up later, or you'll end up just going through the motions with no understanding, and you will become lost and unable to apply your skills if a similar but not identical problem comes along.

Re:Internet-Age Approach

[bwt (68845)]

I went to graduate school at Cal in Math, and I couldn't agree more with the previous poster. I was the head TA for Calculus and a regular TA for discrete math. I think discrete math should be taught in high school along with probability and statistics. It's more fun and more useful to most people.

The materials mentioned are quite good, but never forget that math is learned by working problems. My advice: go to your nearest college bookstore and buy the text book for whatever course is appropriate for your level. Read it, in order and work the problems. I also recommend creating your own "lecture notes", with the book closed, for what you just learned. Do not ever skip move to the next section until you you absolutely understand it cold. Memorize nothing (other than defintions and terminology). Math is very natural to do self paced like this, and there's a good chance you'll enjoy it more this way. Just don't get impatient.

Practice

[Wonko the Sane (25252)]

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 (469723)]

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

well

[gadzook33 (740455)]

I don't have a great answer for your question. However, for me the key to learning math was to stop being intimidated by it. I don't think they do a great job of teaching it in school where they take a very linear approach. They tell you about a concept (e.g. integration) and show you how to do it in certain situations, etc. If someone from the beginning had told me how to visualize what integration was, I think I would have gotten it immediately. Instead I was worried about writing down every little thing the teacher said. Having now gone through six years or so of advanced math, it's somewhat difficult for me to completely empathize, but I guess I would start with the basics. Wolfram, wikipedia, whatever are all fine resources for math. Start reading the simple stuff and if it's confusing, don't be afraid to move backwards and get even simpler. We all forget that stuff now and then.

Re:well

[pz (113803)]

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.

Re:well

[nbetcher (973062)]

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.

ocw.mit.edu

[scum-e-bag (211846)]

http://ocw.mit.edu/ [mit.edu]

Nothing fancy.

[EinZweiDrei (955497)]

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.:

Community college

[PCM2 (4486)]

There's probably a community college in your area that teaches courses in all of the above and beyond. The fees are low (my local community college charges $20 per class credit) and there's usually no requirement that you formally enroll, declare a major, etc. The advantage is that you have an instructor who can answer your questions, plus who assigns you homework. In my experience, the only reliable way to learn math is to do it, and it's too easy to get lazy with self-directed study.

Math skills...

[Glove d'OJ (227281)]

Find a tutor. Seriously.

Any sort of advanced math is very easy in which to develop bad habits. Advanced math "build", unlike other subjects in those same grades. If you didn't "get" Death of a Salesman, you still have a shot at understanding Moby Dick. However, if you did not "get" fractions or percentages, then you really can't go a lot further.

If your math skills (or, rather, lack thereof) are holding you back, think of the tutor as an investment.

On a side note, you would be surprised at the proof of "bad math skills" that can be seen in the corporate world. People rarely / never stop to do a reality check. "Can it be that 105% of the people required to take the training have taken it?" Ugh.

maximize your curiousity

[Doviende (13523)]

In order to learn it on your own, you want to enhance your curiousity at any chance you get. If you get the feeling that you're forcing yourself through it, you might not continue. To maximize curiousity, i suggest you find several math books. Each day, you set aside some time to do something, anything, without a preconception of what it will be (unless there's something you're really keen on doing). When you sit down, you bring out your 3 or 4 books and you flip through until you see something interesting and work on that.

Sometimes you'll find something that requires previous concepts that you don't yet have. This is fine, because now you can go look up those concepts with a sense of purpose. This will help you to your larger goal of the more interesting thing that you flipped to in the book. I did this when i picked up a book on fractals...lots of bright pictures, it seemed interesting. In there, they talked about integrals, which i hadn't learned yet, so i set out to find out what those were.

As for practical tips when you're learning one particular concept, reading textbooks is sorta like reading manpages in unix. it takes a certain mindset, and you usually want to pick out the relevant pieces from the page the first time around and then go back for specifics later. Textbooks are usually written very precisely and they sometimes have a lot of formal jargon or formulae that aren't useful the first time you read it, but can be helpful when you go back to get more details. So read it with that in mind. The first time through, don't expect to understand everything there. Just skip past the parts that are too hard and continue on, trying to get the general idea.

Next, do some of the easiest questions at the end of that section or chapter. Sometimes those questions may seem too easy, like you can just look at them and you think you know how to do it already. I suggest doing some anyway rather than skipping them. There's a difference between knowing the concept enough to recognize it in the questions, and actually knowing it well enough to do the questions quickly and correctly. Doing more questions is always good practice even when they seem easy at first glance.

When you've done several of the easy questions, you start to get more of an intuitive feel for the concept. Go on to the medium questions, and now you'll probably better understand the parts of the text that were difficult to understand on the first time you read the section. I suggest that you try hard to really understand the concepts in one chapter before you go onto the next one. If you have a solid grounding in the beginning, then the later stuff will be much easier and it'll be easier to get that intuitive understanding that lets you see the direction to the answer right from the start.

If you have several textbooks to choose from each time, then as you work your way through bits of each of them, you'll start to see the connections between different areas of math. This is something that most people don't get in their normal classes because they tend to focus too closely on one topic. If you wander through several topics following your curiousity, i think you'll get a better broad understanding of the connections, and it'll help you personally keep your motivation up so that you can continue to do it. remember to have fun with it. if it turns into a chore, then you'll stop doing it before you reach your goals.

have fun!

Get a GMAT Test math prep book

[chuckfee (93392)]

I just finished taking the GMAT test. the quantitative (math) section covers almost all of the math you are looking to learn. A good book (like the official guide to the gmat) has problems arranged in order of difficulty and explains all of the answers in a step by step process.

GMAT math covers basic athrimetic, geometry, algebra, combinatorics, probability, word problems and data sufficiency. I haven't done long division
by hand in probably 15 years so I found the steps to be quite helpful.

One plus of using the gmat math as a stepping stone is that if you ever want to take the test yourself then you will be pretty well prepared for it.

Another plus is that there is a ton of free material out there for gmat math preparation - study guides, practice tests, quizzes, etc. that can all be downloaded for free.

If teaching yourself

[teh moges (875080)]

If you are going to teach yourself, I highly recommend firstly finding out how you learn. Knowing that you learn better by reading, or by hearing, or by drawing, modelling or however can save you a lot of time later on. A quick google search shows a few sites. As with all internet quizzes, never rely on one, but do a few. My girlfriend recently went back to Uni and after determining her learning sytle is doing much better now.

That said, I do maths at Uni and still occasionally forget some of the specifics about the basics. For that reason, I still have all of my high-school text books and even a few second-third-forth hand. One of them is particually good at one thing, another is concise at another. So, my suggestion is to go to second hand book stores and garage sales and pick up a couple of these. Few people want these after school and if the textbook was fazed out, they wouldn't of been able to sell it. As a result, you can often pick these up for $5-$10, especially if you aren't worried about it being brand new.

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

[Jonathan Walther (676089)]

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!

Re:Study ...

[corsec67 (627446)]

And the whole 3 = 1 thing...

Re:Study ...

[jcr (53032)]

The way I always heard that explained was Pi = 3, for sufficiently large values of 3.

-jcr

Re:College Bookstore

[TheCouchPotatoFamine (628797)]

There is a quandary here (in your reference to getting a book) that i've been confused about for a long time. Since every game console out there is essentially a mathematics imaging system, and given that they are pretty common and rugged, how come there isn't a sweeping line up of interactive educational math titles that let you play with the problems in realtime parameter tweaking, or in context, or visually, or what-have-you..

Seems like every math class in america should have a playstation 2 with "Calculus: The Beginning" stuck in it. Cheaper then the calculators and computers per student and the student can play it at home if they want. What's not to like?

In the larger case though, i would just like to have such a thing as an entertainment option to, like the submitter said, keep a sharp edge on the skills.