How do YOU do your math homework?

[GirlInDoubt]

How do YOU do your math homework? Do you read the pages of examples, proofs, theories, etc, in the textbook? Or do you learn it by taking notes in class? If you learn by taking notes in class, do you still read the textbook? Or do you just not read the textbook, and just skip to the problems?


I read every single word in the textbook, which gives me a good understanding of the material, but I feel like it is very time consuming. Is reading the textbook a good approach for learning math? What is your approach?

 

[The1337gamer]

Lectures are often pretty ineffective for teaching because they go at a fast pace, i make sure to copy all the notes. I usually go back over my notes and rewrite them, if i don't understand something i will refer to a textbook. Read over notes on a regularly basis so you don't just forget. Understanding is more important than memorising though.

When doing homework, i try to attempt most problems, i will usually use my notes if I'm stuck and if they don't help, refer to a book, the internet or a friend.

 

[bigfooted]

The theory of learning in general [sorry, no citation] says that you should expose yourself to the material in as many different ways possible, use your brain as 'actively' as possible and repeat it often. The idea is that in this way, more and stronger networks will be formed in your brain, and that stored information is better retrievable.

When I was at the university, I would go to the courses, but mainly listen, only occasionally writing down important statements or something that is not in the book. It is just too much input to listen and make detailed notes (i.e. write down every word he says, including the jokes) at the same time.
It helps if you read the corresponding chapter beforehand. Then later I would make a short summary of what I thought was important. Then, I would do a lot of exercises. If it involves proofs of theories, then you should derive the proof yourself.

Learning/understanding can be time consuming. Compare it with top-athletes or musicians. They practice every day for several hours.

 

[rktpro]

What I find with myself is that my math teacher is not interesting at all. He might crack jokes in between lecture, but he starts any chapter with exercise 1. He won't give a read to how the theorem originated. He won't even read the two extra chapters provided every year about 'Mathematical Modelling' and 'Proofs in Mathematics'. You can fairly well understand the importance of them. Reading book provides you the idea behind including that chapter, relation of that chapter with other chapters and relevance of studying that in daily life. If you want to be a mathematician, read the books; if you want to be a clerk, just solve it.
If you attend lecture with utmost sincerity, and read the material in book at home; you are going to be well in examination.

 

[chiro]

Hey GirlInDoubt and welcome to the forums.

If you are doing mathematics or a subject that is built on mathematics, I suggest you get the main ideas early and then fill in the details later.

The big ideas will help you fill in the actual details when you come to problems that require specifics in terms of specific calculations and applications of main ideas.

Getting the main ideas in the most concise manner without sacrificing details is pretty tough in any area of learning. Having a more experienced and enthusiastic lecturer will help immensely, but if you have a class where this is not emphasized early, I suggest you ask the lecturer what the class and subsequently the area of study and techniques are all about. This will put everything in perspective, and it will give you something to fall back on when you end up doing exercises, other assessments and exams.

Getting the best information to do this as stated before is not easy and it can take a lot of personal effort to do it right.

Also you should realize that even professionals are still building intuition with every new experience in their craft but as I stated before: chances are if you have an experienced lecturer, they should be able to give you something that you can start off with and build on with your further development and experience.

 

[nickadams]

in4 mathwonk's response

 

[homeomorphic]

I've done various things.

I try to develop my own version of the subject as I learn it. Often, rather than reading the proofs in the book, I will try to come up with my own proofs first. Kind of like Moore's method.

http://en.wikipedia.org/wiki/Moore_method

 

[I like Serena]

Welcome to PF, GirlInDoubt!

First I run over all definitions, cursive words, and new symbols.
In each case that a new word or symbol is introduced, I know I will need to know what it is.
Often I make a list of these words and symbols with a few catch phrases to remember them by.

If I am in a rush, that's all I do.
It means I will understand the questions and I will be able to follow a lecture.
(Otherwise it's like listening to someone talking in a foreign language, which is pretty useless! )

Then I check out the examples, see if I could do them myself, or if I at the very least understand what they are doing.

Then it is time to check out the problems.
The first couple of problems are usually to check whether you got the new words and symbols, and to improve your understanding of them.
Then there will be a couple of problems where you need to redo an example, just with different numbers.

If there is still time left, check out the proofs, and do the problems for which you need them.

 

[JHamm]

I usually try to skim a chapter before a class, mainly just focusing on new terms/notations so that I can focus on the ideas better. During the class I take no notes whatsoever and just listen and read, I find notes distracting and unnecessary especially with a textbook laying around. After that I give the few couple of problems a go, these are usually just to make sure you know what the new terms are. From there I skim through the problems to look for interesting or particularly hard ones, if I can't get them then I'll go back through the textbook.
It seems like a waste to me to meticulously pour over each word if you already know something.