Is Focusing on Textbooks the Key to Becoming a Better Mathlete?

[veronica1999]

Hi,

My name is Veronica and I am in middle school.
I love math and like doing random math problems.
(I think I am quite good and learned a lot from doing random problems
but I do have to admit there are huge gaps in what I know)
Now the teachers are advising my parents to have me stop doing the contest problems, and focus on the textbooks.
They are saying that the contest problems are slowing me down and creating serious gaps in what I know.
I am already three years ahead of my classmates. I think if I focused on finishing the textbooks, I could take the AP calculus exam next year.
But why do I have to finish so fast?
The teacher said that if I trust her and focus on the textbooks I can do statistics, multivariable calculus, and linear algebra all in high school and this should help me be a better mathlete.
I find this hard to believe because contest problems and textbook math is really different.
Contest problems are really exciting and I can sit for hours with one problem.
Can't I just keep on doing what I like?
If I focus on textbooks, would that really make me a better mathlete?

~Veronica

 

[Jameson]

Hi Veronica (Wave),

Cool thread and I'm glad to hear you're interested in math competitions. I did Math Counts in middle school and was part of the math club in high which had monthly competitions on the weekend with other schools from all over the place.

1) What competition/contest are you interested in? Math Counts, the IMO?

2) Without knowing quite a bit more about you and your level I think I see where your teacher is coming from, but not sure. Often math contests employ memorizing lots of "tricks" because the solutions are very difficult to derive on the spot so students just memorize them. It's possible to use these tricks to do problems at a high level without really understanding the theory behind them. What math are you taking now? Geometry?

3) At the pace you're going it would definitely be possible to do Calc I-III and more before graduating high school. If you really enjoy math then not everything has to be about competing better, as one day far from now you will be able to use your math skills to potentially have a very nice career. You're young and don't need to worry about that too much but just know that a college math degree or a science degree can very likely lead to a good job (not guaranteed but it's possible).

I'm looking forward to reading what others have to say and am glad you've found us. Hope we can be of help to you as you go through your math education. :)

Jameson

 

[caffeinemachine]

Hi,

My name is Veronica and I am in middle school.
I love math and like doing random math problems.
(I think I am quite good and learned a lot from doing random problems
but I do have to admit there are huge gaps in what I know)
Now the teachers are advising my parents to have me stop doing the contest problems, and focus on the textbooks.
They are saying that the contest problems are slowing me down and creating serious gaps in what I know.
I am already three years ahead of my classmates. I think if I focused on finishing the textbooks, I could take the AP calculus exam next year.
But why do I have to finish so fast?
The teacher said that if I trust her and focus on the textbooks I can do statistics, multivariable calculus, and linear algebra all in high school and this should help me be a better mathlete.
I find this hard to believe because contest problems and textbook math is really different.
Contest problems are really exciting and I can sit for hours with one problem.
Can't I just keep on doing what I like?
If I focus on textbooks, would that really make me a better mathlete?

~Veronica

Math is like a language. Its grammar would consist of techniques like contradiction method, extremal principle, pigeon hole principle, mathematical induction, exhaustion etc. Using this basic grammar huge literature has been written. That includes Algebra, Analysis, Topology, Geometry etc. Contest problems are just about the "grammar of math". Its a great thing you are doing contest problems. If you want to do good at math contests then practice High School Geometry, pigeon hole principle, Induction and extreme principle. But there's no harm in learning literature. When you go to university it will certainly help you. Find some time each day to learn them too if its not too much. Of course your teacher is there to help.
For contest problems I'd highly recommend "Mathematical Circles by Fomin,Genkin,Itenberg" and "Art and Craft of Problem Solving by Paul Zeitz". These two train you well on HOW to solve contest problems. For an advanced problem-book "Problem Solving Strategies by Arthur Engel" is very good.

 

[veronica1999]

Hi Veronica (Wave),

Cool thread and I'm glad to hear you're interested in math competitions. I did Math Counts in middle school and was part of the math club in high which had monthly competitions on the weekend with other schools from all over the place.

1) What competition/contest are you interested in? Math Counts, the IMO?

2) Without knowing quite a bit more about you and your level I think I see where your teacher is coming from, but not sure. Often math contests employ memorizing lots of "tricks" because the solutions are very difficult to derive on the spot so students just memorize them. It's possible to use these tricks to do problems at a high level without really understanding the theory behind them. What math are you taking now? Geometry?

3) At the pace you're going it would definitely be possible to do Calc I-III and more before graduating high school. If you really enjoy math then not everything has to be about competing better, as one day far from now you will be able to use your math skills to potentially have a very nice career. You're young and don't need to worry about that too much but just know that a college math degree or a science degree can very likely lead to a good job (not guaranteed but it's possible).

I'm looking forward to reading what others have to say and am glad you've found us. Hope we can be of help to you as you go through your math education. :)

Jameson

Hi Mr Jameson,

I do dream about competing in the IMO but I know this will not happen.
I am not a David Yang and never will be.
But it's okay. I never compare myself with others and sulk.
This is my strength. :)
If I did, I would have never come this far. Many of the kids solve the problems before I even understand them.
I feel this is why everyone is starting to discourage me. I guess input and output doesn't add up.
But I am going to keep on trying.(Until my mom really says stop(Worried))
I think my parents want me to settle for being the best at school and divert my time to other fun activities(violin practice, golf, swimming, sat prep...:()

Anyway, I am really grateful for all the great advice and awesome help that I get.

Veronica

P.S. I was able to persuade my dad to buy me all the books that Caffeinemachine recommended.;)

 

[caffeinemachine]

P.S. I was able to persuade my dad to buy me all the books that Caffeinemachine recommended.;)

That's a very good thing Veronica. I am sure those books will do wonders for you.

 

[Jameson]

Hi Mr Jameson,

I do dream about competing in the IMO but I know this will not happen.
I am not a David Yang and never will be.
But it's okay. I never compare myself with others and sulk.
This is my strength. :)
If I did, I would have never come this far. Many of the kids solve the problems before I even understand them.
I feel this is why everyone is starting to discourage me. I guess input and output doesn't add up.
But I am going to keep on trying.(Until my mom really says stop(Worried))
I think my parents want me to settle for being the best at school and divert my time to other fun activities(violin practice, golf, swimming, sat prep...:()

Anyway, I am really grateful for all the great advice and awesome help that I get.

Veronica

P.S. I was able to persuade my dad to buy me all the books that Caffeinemachine recommended.;)

It's great that you try to compete with yourself and not others. This is a very good attitude! About balance - there is something to be said when you are young to try different things, so I think your mom is doing the right thing for sure. :)

Anyway, the title of your thread is "need advice on study method" so the last piece of advice I'll give you is to make sure you understand the foundation of mathematics, the core ideas, extremely well before moving on the more complicated stuff. Many young people who take things like calculus lack any real understanding of what's going on and simply memorize formula after formula. If you take your time and focus hard on the details your understand will be truly on another level.

It's great you were able to get the books caffeinemachine recommended as well!

 

[issacnewton]

I recommend the following...

How to solve it by George Polya

and when you go to college , please read

How to Solve It: Modern Heuristics by Zbigniew Michalewicz and David Fogel

read their great amazon reviews

regards(Malthe)