The most fundamental rule about studying maths regardless of learning styles or personal preferences is that you learn maths by doing maths. Just reading the textbook isn't enough, you have to solve problems - sometimes more problems than your teacher sets as homework! For many students, maths study can take up more time than study for other subjects, this is not uncommon.
Also, if you're falling behind, seek help! Friends, your teacher, maybe even family members. Maths is cumulative, this means that each section builds on the last. So you need to keep up. If you're struggling, talk to your teacher - a good teacher will be happy to talk about your problems with study and offer advice.
So let's talk about studying maths.
Paper and notebooks:
One thing you're going to have to come to terms with, is that unless you have access to a good quality writing tablet PC (no, not just a desktop or laptop computer or iphone) you are going to have to use lots and lots of paper. If this bothers you, invest in recycled note paper and recycle your old scrappy notes at the end of the year. One thing you can do to cut down on the paper use, is to get a whiteboard, I prefer the A4 size ones, you can carry them around with you, or you can be really cool and use your bedroom window. Then you can work through questions, rub bits out etc. If it turns out to be a really good problem, then you can copy it into your book for revision before exams.
Speaking of books, I suggest you have two exercise books for maths classes, one just for methods, notes, proofs, definitions, theorems and pertinent examples and another for homework and study questions that you have worked through. This means that all your methods for solving problems are in the one place and you don't have to search for ages through practice questions to find the information when writing your cheat sheets or just revising for exams. Since the "methods" book will be tidier, you may wish to hold onto it for a few years, since you will need those methods to help solve maths problems in later years (OMG yes you will use this stuff again!). The problems book can be recycled at the end of the year.
One mistake students (and some teachers) make is to try to squish as many problems onto one page as possible. Students often try to squash fractions onto one ruled line. Big mistake! It is much more difficult to see how to solve the problem when you squish everything up really tiny. If your question contains a fraction, use at least 2 lines. If your question involves an integral, again use at least two lines.
Some people were taught at school to rule a line down the middle of the page to fit more problems on the page. For high school maths and higher, I suggest this is also a big mistake. If you're just doing questions like 8-3=?, 9-5=? then that old method is fine, anything more than that and you're doing yourself a disservice. Besides training students to try to squish as much on one page as possible, the other half of the page can be used for something much more useful!
I suggest ruling a line down the page, leaving about 5cm (2 inches) from the right hand side of the page. This section is for writing what you have done. Divided the equation by 2? then write "divide by 2", need to list the factors of 96 when factorising a quadratic? Use that right hand side of the page to explain your steps.
Speaking of explanations, if you explain your steps, your teacher will love you to itty bitty bits! Seriously! If you've ever wanted to get on the good side of your maths teacher that is how to do it, and it is cheaper than buying them an apple (who does that anyway?!?).
Reading maths textbooks:
Maths just isn't like a lot of other subjects, you can't learn it just by reading about it, but also, when you are reading about it, you can't expect to read it as fast as you're used to reading a novel. Each sentence of a maths textbook is packed with information that you need to think about and carefully consider. - Unlike this post, which you could skim read and get the general gist. Here is an example, in a maths textbook you might see something like:
Small bit of text right? But when you put it into words, it actually says: The derivative of a function f of x plus a function g of x all with respect to x is equal to the derivative of f of x with respect to x plus the derivative of g of x with respect to x. And that is just the equation explained in "maths-speak", to explain the equation in human terms I would have to explain what a derivative is, explain the two systems of notation used to denote a derivative, explain a function, I'd have to explain the use of the names f and g and explain what it means for these functions to be functions of x. Can you see now how much information is packed into that short line?
To read a maths textbook correctly you need to stop frequently and think about what you have just read, what does it mean? Can you explain it in more human terms? Could you put it in terms that an underclassman could understand, or even a fellow classmate?
Thats a big ask isn't it? You already have lots of reading to do for other classes, not to mention assignments and study for exams. So what can you do, especially if the textbook is really difficult to read. You'll need to look for other sources of information. Try these:
- YouTube
- Khan Academy
- Try Wolfram Alpha Just enter a question and it will endeavor to find the answer!
- Any of the free textbooks being published on the web (google search examples: free year 10 maths textbooks, free calculus textbooks ebook)
- Other textbooks at your school / university library
- Maths forums (either google your maths problem directly or try searching for maths forums in general)
- Wikipedia
- Simple Wikipedia
http://mathcs.slu.edu/undergrad-math/success-in-mathematics - Saint Louis University (USA)
http://www.math.osu.edu/old-students/how_to_study.html - Ohio State University (USA)
http://tutorial.math.lamar.edu/Extras/StudyMath/HowToStudyMath.aspx - Lamar University (USA)
Links to some other how to study guides:
http://www.clemson.edu/collegeskills/sec3pg1.htm - Clemson University (USA)
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