Best Way To Teach Oneself Math? 609
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?"
College Bookstore (Score:4, Interesting)
Repetition of simple problems (Score:4, Interesting)
The thing is, when you're learning math you want to focus your efforts on the subject at hand - not the other simple math that accompanies it. For example, when a prof is going over a question on the board you don't want to waste time with the simple stuff. It takes away from what you should really be learning.
So I guess my suggestion is this - make sure you know the basic stuff really well. You will always have to use it and without it you will always be at a disadvantage.
Willy
Re:backwards (Score:1, Interesting)
That's how I taught myself math as a kid. Start with the last chapter. If you don't know it, go back a chapter. Once you've seen the later chapters, you'll know how the earlier stuff applies, so you'll learn it much, much faster.
maximize your curiousity (Score:5, Interesting)
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!
Re:well (Score:5, Interesting)
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 (Score:2, Interesting)
Re:College Bookstore (Score:5, Interesting)
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.
Internet-Age Approach (Score:4, Interesting)
Buy the same textbooks that the students at those universities use. For the pre-calculus mathematics, UC-Berkeley would be your best bet. MIT caters to only students who have already taken calculus in high school.
My best advice is to try a two-track approach: non-discrete mathematics and discrete mathematics. Traditionally high schools teach only non-discrete mathematics: e.g., trigonometry and calculus. Since you are studying the material on your own, you could improve upon the standard curriculum. Read a good book on discrete mathematics first. It will build your intuition of mathematics. Then, study the standard topics in non-discrete mathematics.
Discrete mathematics and non-discrete mathematics are quite different, but the reasoning in discrete mathematics will hone your skill in handling mathematical proofs, which are central to both branches of mathematics.
For a real challenge, after you finish your studies, try to determine whether P = NP.
Make it fun (Score:2, Interesting)
Re:College Bookstore (Score:1, Interesting)
1.)I started practicing simple math problems online in games.
2.)I started reading about math in dummies books.
3.)I often print out exercises and review my basics(addition,subtraction, multiplication, and division)
4.)I do this everyday during the weekdays for 30 minutes twice a day.
Remember not to be too hard on yourself! Since this doesn't come easy; you'll have to compensate through regular practice(that's what most things take anyways). Remember to start off slow and build yourself up. Sometimes success takes time so make the investment and you should be set! I wish you the best of luck and a wonderful adventure in learning. God Bless!
Re:3 ideas (Score:2, Interesting)
I hear this a lot, and as it is somewhat true, it completely depends on both the person and the math you're studying. I had no problem just watching through advanced calculus, but found out that I couldn't do that in real/complex analysis. It completely depends on where your strengths are, when you feel comfortable, go ahead and move on, but when you need to never hesitate to keep working on something until you fully understand it.
Guarnateed math learning! (Score:3, Interesting)
OK, Arithmetic: "The Trachtenberg Speed System of Basic Mathematics" by Ann Cutler and Rudolph McShane. This will teach you to do Addition, Subtraction, Multiplication, Division and Square Roots, much of it in your head. Learn to use an Abacus/Soroban. It helps to bring arithmetic into focus. there are a couple of computer-based practice utilities on the net to help you memorize the rules and gain quickness in TSS.
Algebra: "Programmed Reviews of Mathematics" by Flexer and Flexer. Six small books with a good introduction to the basics of many Math concepts.
"Algebra", "Functions and Relations", and "Trigonometry and Analytic Geometry": "Pre-calculus Mathematics" Vols I, II, III by Vernon Howe.
Calculus: "Quick Calculus" (Wiley Self-Study Guide) by Kleppner and Ramsey, and also "Calculator Calculus" by McCarty.
Most of these books are older and you will need to look for them. Most of them are "programmed instruction books", which is not a popular Thing to publish these days. Programmed Instruction was developed by B. F. Skinner and Norman Crowder and has been used to teach almost any subject imaginable. The information is presented in "frames" with questions and answers, on the principle that people learn faster in short, successful segments than they do with larger difficult presentations. Programmed Instruction seems to have fallen out of favor about the time that B. F. Skinner was castigated and demonized for his rigid behavioral views. I have never known anyone to NOT learn from good programmed instruction, if they could read the material and understand it. You might want to check with your physician to make sure you don't have an issue like dyscalcula (similar to dyslexia) or some other learning disorder that needs to be overcome first. If so, that could explain much of your frustration and can be handled.
Good programmed instruction takes a long time to develop and test. Each frame should lead to 96%+ success for people taking the course. Many older books simply broke up their information in short segments and asked a question without actually testing the goal and result. I am least satisfied with the Wiley Self-Study guides, but they are usually adequate for learning.
Good luck!
Algebra for The Practical Man (Score:2, Interesting)
Algebra for The Practical Man.
Geometry for The Practical Man.
Trigonometry for The Practical Man.
and Calculus for The Practical Man.
They're old self study guides and they're the best I've seen. I've seed the Idiots and Dummys guides, they're horrible. The Practical Man series really explain how it all works, not just memorizing formulas. I found them on Amazon.
Re:Internet-Age Approach (Score:5, Interesting)
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.
I wanted to learn math -- so I started a blog (Score:3, Interesting)
To regain my mastery of mathematics, I decided to take a single math problem very seriously. I figured that I would try to
understand the solution by grounding all ideas down to postulates.
I figured that this was a great way to learn mathematics anew and really get advanced. I soon learned that there were wonderful
math resources on the web. Wikipedia is really great. There's also MathWorld.com [wolfram.com].,
PlanetMath [planetmath.org], MathForum.org, and
Cut-The-Knot.org [cut-the-knot.org].
Being pretty ambitious, I chose Fermat's Last Theorem and Andrew Wiles's solution as my jump off point. I started this adventure
in 2004. Since then, because the problem is so tough, I started blogging through the different threads of the problem and I find
myself recreating the history of mathematics from the perspective of number theory.
I am not sure that this approach would work for everyone but if you are a solid problem solver, it can really make advanced
mathematics more fun. If you are interested to see what I came up with, you can check out my blog a My math blog [blogspot.com].
I also started a general math blog [blogspot.com].
Best of luck in learning mathematics.
-Larry
Math is a mess. (Score:3, Interesting)
1.) Don't be intimidated.
2.) Stay curious. Find ways to get curious about certain fields of math.
These are from different posts, but I think they go good together.
The truth is, math is a mess. It's a historically grown mumbo-jumbo of countless variations in notation. The problem is that with programming languages - no matter how crazy they may be - they allways come with a reference manual to explain their syntax. In fact, that is the main element by which we judge the viability of a PL. With math on the other hand academia kind of expects us to understand what the Professor is writing on the blackboard without even addressing the issue of a solid reference in which I can look up the meaning of the sum-symbol or what a limes means and how it looks like. It's like music-notation. Somewhere back in the day - often a few hundred years ago - someone came up with a certain notation and since then that's the rule of thumb by which everybody sticks to sorta-kinda 50% of the time. If he feels like it. These notations are mostly literally bolted on to terms and expressions in the most chaotic and hideous way one can imagine. It's like trying to understand a Perl obfuscation contest without the manual.
This is IMHO the single biggest problem in grasping math. Especially for Computer Geeks who are used to strict syntax constraints.
I' currently studying the first semester of BS-CompSci and am glad for having finished my German GED just this summer, with all the accelerated math (barely made it with a D+ due to the time-constrained tests) still in my head. I can just about keep up with the lectures. We allready have quite a few students bickering about the lack of a symbol and notation reference.
Bottom line:
Math is a mess. It is a non-trivial science and takes work to understand, but it's a mess none-the-less. If one keeps that in mind without using it as a cheap excuse not to fully work out and understand the details then learning math is much less frustrating. That's how I feel about it anyway.
city college (Score:3, Interesting)
SAT prep (Score:3, Interesting)
Re:3 ideas (Score:5, Interesting)
You know, I wince when people say that. Yes, math is hard, but then, music is hard. Creative writing is hard. Any subject is hard if you don't get it, and even if you do get it, any subject needs hard work to get good at it. Yes, math needs abstract thinking, and some folks are better at that than others, but then, some people are better at pitch and rhythm than others. Picking on math in this way is sowing the seeds of defeat.
One of the math books I have (I can't remember which one) starts with a riff about how most folks want to drop math as soon as they can, but then it lists a whole list of subjects (things like "how to avoid getting ripped off", "how to play the stock market", "how to save time and effort by taking shortcuts on common problems", "having fun with games and puzzles" and so on) and speculates that pretty much everyone would want to take a few of those options. The trick is, of course, that they're all math. I'm convinced that the reason most people hate math is because it's taught in an almost completely abstract way (because the teachers have to get through the syllabus in a limited number of class hours). Teach it the other way -- take real problems and show how math can solve them or generalise them, and I reckon a lot more of the students would go along for the ride.
A friend of mine used to teach remedial physics to a college class. He wasn't much older than the students, so he started the first class by pretending to be another student and mixing with the others as they came in. In the process he discovered that most of them were bikers who had to get the physics qualification to support a motor mechanics apprenticeship they were doing. After some consternation when they discovered he was really the teacher, he started by asking them how they would tune a 2-stroke engine; what effect the things they were doing would have on the engine, and how they would measure the effects. This led them through all sorts of physics, from friction and levers to gas laws and fluid flow. He got every student through the exam, because he made it relevant. The same can be done with math, and it makes it a whole lot easier.