I feel that my level of mathematics has become like a pool of stagnant water, what should I do next to improve

Question

I feel that my level of mathematics has become like a pool of stagnant water, what should I do next to improve other than listening to my teachers in class?

I thought of reading further. But...My teacher said that I would suffer from conceptual misunderstandings if I read books beyond my level and die eventually.

can't allow the mosquitoes to breed there

currently at around pre-university level

Answer 1

I disagree with your teacher. In the words of my former linear algebra professor, "Mathematical definitions are written in such a way that they are impossible to misunderstand; this is not the same as saying that they are easy to understand." In other words, if you don't understand something in math, you'll know that you don't understand it. Misunderstandings can only arise if you make assumptions and are not careful.

So if you know what area of math you want to study next, look at an introductory textbook on that subject. If the first few pages make sense, go for it.

EDIT: Okay so you've added that you're at pre-university level. To me that says you either have taken some calculus or are about to start calculus. Calculus is so fundamental to so many topics that the best thing you can do for yourself is to understand the first year of calculus inside and out. After calculus, for the first time in your math education, you have a wide branching of potential topics. Look at the required and non-required math courses at the university level. Do a little research on some of them and see if they're interesting to you. A non-required course with few prerequisite courses is generally a good bet for independent study. Then you can take the course later just for the credits and get a free A!

I almost overlooked the definite topic to know: proofs. Most school don't teach you how to write proofs in calculus, and then as soon as you get out of calculus, they put you in classes where writing proofs is required. This might be a great thing to study now if you haven't. Find a book or online resource that discusses proofs. Know the difference between direct proof, proof by contrapositive, and proof by contradiction. Prove some simple arithmetic facts (the sum of even integers is even). The classic proof that everyone does in number theory is to prove by contradiction that there are infinitely many primes. Find that proof online and read it. Read as many proofs as you can understand. That will get the language of proofs into your brain.

Answer 2

There are a number of excellent books which you should be able to read at pre-university level-- the Mathematical Association of America has a series of books called the "New Mathematical Library" for this purpose (see link below). I've been reading "The Heart of Mathematics" recently, which is pre-calculus but has a lot of good material and will really make you think. University-level calculus is very important too, but you will get to it eventually anyway. There's a lot of other good stuff out there.

Answer 3

It's your teacher that's the pool of stagnant water breeding pests and other public menaces. By ALL MEANS read way over your head, there's tons of stuff on the internet you can look up for free. Even if you didn't understand most of the stuff, at least you can gain an overall view of what the field of mathematics look like and pick up a lot of good ideas, grist for your creative mill. The other answerers above have good suggestions. Get that swamp drained! You die in mathematics only if you've lost the interest and joy in it.

Answer 4

Amusing metaphor. It's true that you can't, say, jump right into calculus without knowing anything about algebra. But there are still lots of different things out there you could learn. There's a LOT more to math than what they teach in public schools. Cryptography, topology, knot theory all come to mind. I even remember flipping towards the back of my math books when I was in grammar school and middle school, seeing all of these fascinating looking things that we never ended up covering in class (pi, probability, etc.). So whatever level of schooling you're at (and what is that by the way?), you might find something in the book you already have.

I think if you try exploring more of what's out there, you might find something that looks interesting and want to look at a little more deeply. I'm always surfing around the math pages on mathworld.wolfram.com and coming across things I hadn't heard of. Also, one great author I would suggest is Theoni Pappas. A number of her books like "Joy of Mathematics" consist of short summaries of different places math shows up.

Answer 5

Your teacher has their opinion and it is wrong. Most of what you truly come to understand about mathematics will never come from a classroom. Rather, it will be a discovery you will make when you connect what you study with what you already now. The best way to learn anything is through the process that sometimes involves formulation ( and reformulation) of concepts that can be connected to what you have in the bank......ie: the things you know and know well. Just be very careful not to make false connections or narrow your thinking as you uncover the links that make all math the same.

Finally, you must remember that the way we percieve the world strongly influences how we learn and what we learn. No one person, including your teacher, has a catchall method that provides for optimum learning in all students. Good luck and have fun.

Answer 6

Go to a hot tub store and get some water treatment. That will keep the alge and bugs down. Don't worry about a little dirt. When it comes time to drain the pool use your garden hose as a siphon. That will get 90% of the water out with no effort.

Answer 7

tats not true if you read furter youd get confused
im a sophmore in highschool bout 2 be a junior
my freshman year i was placed in alg1 and didnt even knew so you could say calculus was not my level but i read books and everything uptill calculus3 in the same year
right now im tryin 2 take precalculus over vacation at college so i could take calculus my junior year but they say i've 2 be a senior to take a course at college

i wasnt good at math either i used get like 50s on all my test now im honors math only started it this year and i get all A+

and im trying 2 get ahead of honors class now if i can
so dont give up

Answer 8

I dont agree with your teacher. I always learnt more from the books than from lesson/lectures in the classroom. so pick up a book of suitable standard and read/understand the material given in the bookand do some exercises,you will know how much text material you assimmilated.

Answer 9

Study what your teacher says like:multiplying. You study that. OR if you dont know how to do it ask your mom. Trust me I am very good at math.

Answer 10

You can break out a compass and straight edge and start doing some geometric constructions.