How do you learn? (memory techniques, etc)

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Hi,

This may not be the ordinary question you recieve on these forums, its more about the methods you use when learning algebra.

How do you learn Algebra (particularly Advanced Algebra)? Besides the usual "practice, practice, practice" which is vague and understood by everyone, what memory techniques, visuals, learning habits, etc do you utilize when you learn (or learned) algebra?

I was reading the latest article in Scientific American titled "The Expert Mind" by Philip E. Ross and I have to say it was extremely interesting. Although it used Chess as an example, it can be applied to any practice. What they said that usually the experts in many fields are not experts based on genetics but instead on effortful study. They mentioned the memory techniques that many experts in their field use which is "chunking," which is to group facts of information together. Also, they mentioned how experts know very well the structure of their area of study. For example, chess experts understand very well the structure of the chess boards and its many possible positions. The same for a computer programmer, who would know and be able to recall the structure of any blocks of code. And most importantly, the way they improve is by "continually tackling challenges that lie just beyond their competence."

I would like to know how can you guys relate this to Algebra and math, and what are the techniques for learning and remembering do you have?
 
Well practice practice practice works (even though you say besides this). To learn you just pay attention to the your teacher and ask (lots of) questions. To excel in algebra you must use logic and make sure your answer is correct by plugging it back in your equation/formula/expression. Check your answers and make sure everything is accurate/reasonable. That is really all there is to it.
 
What if you don't have a teacher - besides the author of whatever textbook you are using?

Using logic is a good suggestion, but what do you mean by logic?
 
Well read everything you can in your book, ponder about it and try what you interprete from it in your math problems and check your answers. If there is something you do not understand google it and see what you can find. If you are still lost then come here. :)

Logic is rationality. If you are solving the rate of two trains and the question says the faster train goes two times faster than the other than you know that one train is going to be faster. Also whenever using the Quadratic Formula for speeds, time, ect. you know that any root that is negative you will not use since time, speed, ect. is not negative. Just make sure the answers make since in the terms of the context. Check your answers by plugging them back in your equation. Make sure everything "fits".
 
Makes sense jonboy, thanks for the logic explanation and your tips. :)

Also tell me, is many of the basic rules of algebra natural to you? For example, the theorums that govern the way that formulas are structured, and equalized, etc like Distributive Property, Commutative Property, etc. Those are easy for me, but there are times when I am doing an equation, and I find myself asking whether something I did was right. I'm sure it would be rather automatic for you guys. That basically relates to what I read in the article regarding the "structure."

Anyone else have any tips, mnemonic tips, memory/learning tips, methodology, etc?
 
Amirsan said:
Makes sense jonboy, thanks for the logic explanation and your tips. :)

Also tell me, is many of the basic rules of algebra natural to you? For example, the theorums that govern the way that formulas are structured, and equalized, etc like Distributive Property, Commutative Property, etc. Those are easy for me, but there are times when I am doing an equation, and I find myself asking whether something I did was right. I'm sure it would be rather automatic for you guys. That basically relates to what I read in the article regarding the "structure."

Anyone else have any tips, mnemonic tips, memory/learning tips, methodology, etc?
Click to expand...

I would love to say the basic rules just come natural........but they do not. I worked to reach my plateau by practice and logic. I really do not have to many tips, you just gotta dive head-first into the books and discover!


Just remember whenever you see this: \(\displaystyle \L \;(x+3)^2\,\to\,(x+3)(x+3)\)


It is not \(\displaystyle x^2+9\) , it is a FOIL problem: \(\displaystyle \L \;x^2+3x+3x+9\,\to\,x^2+6x+9\)


That is the only real tip I can think of right now. One must unlock his math wisdom through action! Also with equations just think about what you are trying to do and what will lead you to your goal. Practice, practice! ;)


Some helpful tips can be found in our thread of Math Mnemonics: here


Math is fun and I hope you succeed. :D
 
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