Practicing creative / improvising math skills

[Arcthor]

Hello, I am currently 18 years of age and I will be attending my last year of high school (well, "gymnasium" since I am from Sweden) and I have some questions.

I am completely in love with math and physics. I just find the idea that these two subjects can describe reality fascinating, to say at least. However, during the past two years I've been in high school, I've only gotten 1 B and 3 C's in the math courses (i've been acing physics and other natural-science / programming courses so I would not characterize myself as stupid). I don't really understand why, I believe I have a clear grasp of the theory behind the math and I usually study more than my peers. I want to say I'm good at math, but I've been kind of let down by my grades.

Before a test, I can complete every single hard question in our math-books with ease. But during the test, I just cannot perform on the hard questions. I think I have trouble being creative with math and applying the logic I've learned in new, difficult environments under pressure, cause when I review the tests some week after I understand what to do. I don't know if my problem solving skills are sh*t or that it's just that I'm nervous, cannot focus etc.

Has anyone else got this problem or know how to deal with it? It's so frustrating receiving a C when I've been explaining the hard problems of our material to my classmates. I feel like giving up on math and physics because of this, but my curiosity keeps me going which is why I would like to study math/physics on an university level but I am afraid my math skills are not enough.

Anyway, during the summerbreak I've brought home 2 math books and a physics book. Does anyone know how to train improvising/being creative skills with math? Right now I am just doing the exercises and reading the material, but that does not seem to cut it regarding math.

Thank you! Sorry for my possibly incoherent post and poor sentence structure, english is not my mother tounge.

 

[Mogarrr]

At a very basic level, you can use problems as templates and use different numbers.

If that becomes too easy, you can imagine scenarios where you can apply some of the concepts you've learned.

If you can imagine scenarios, then you should also be aware of the conditions where the method you want to use is correct. Quite often problems have assumptions that must be true for a correct answer.

Lastly, with some problems there are many ways to arrive at the correct answer. You can focus on all the different ways to solve a certain type of problem.

In my opinion, to solve any problem, you must know what it is you're trying to do and how you will do it. Once that is done, strive to understand why.

 

[Incognito310]

For me, khanacademy.org has been a lifesaver.

 

[Arcthor]

At a very basic level, you can use problems as templates and use different numbers.

If that becomes too easy, you can imagine scenarios where you can apply some of the concepts you've learned.

If you can imagine scenarios, then you should also be aware of the conditions where the method you want to use is correct. Quite often problems have assumptions that must be true for a correct answer.

Lastly, with some problems there are many ways to arrive at the correct answer. You can focus on all the different ways to solve a certain type of problem.

In my opinion, to solve any problem, you must know what it is you're trying to do and how you will do it. Once that is done, strive to understand why.

Thank you for your reply, really helpful :) Imagining scenarios seems like a good idea actually, I'll do that and define some conditions to remember. And also, will I even be able to go to a reputable university with C in maths? I'm going to focus 100% this year to get an A in the two remaining courses, but am I already academically ****ed?

 

[Arcthor]

For me, khanacademy.org has been a lifesaver.

I use KhanAcademy too, but that is not the problem I am having. I absorb information like a sponge. I just have trouble expressing my thoughts in math, over-analyzing questions and performing under pressure. But thank you for your reply!

 

[homeomorphic]

You might benefit from trying to really over-learn the material, so that it's very automatic once you get to the test. Of course, they may still throw tricking questions at you that you didn't specifically prepare for, but it helps to have all the basics down almost reflexively because then you can reach into your bag of concepts and tricks for anything you might need, very quickly, so that you free up as much time as possible for coming up with whatever new idea is needed.

 

[Arcthor]

You might benefit from trying to really over-learn the material, so that it's very automatic once you get to the test. Of course, they may still throw tricking questions at you that you didn't specifically prepare for, but it helps to have all the basics down almost reflexively because then you can reach into your bag of concepts and tricks for anything you might need, very quickly, so that you free up as much time as possible for coming up with whatever new idea is needed.

Thanks, sounds good. I am a creature of repetition, I once read through my material 220 times before giving an oral examination, lol. But I will try this, however, have you got any tips on how to improve the creative process aswell? I find myself over-analyzing the questions and missing simple observations. One example of this is when I tried too hard on a question and completely forgot about the kindergarten formula "s=v*t".

 

[homeomorphic]

Thanks, sounds good. I am a creature of repetition, I once read through my material 220 times before giving an oral examination, lol.

Well, you probably don't want to just do reading alone. It's best to practice remembering without looking. Reading, by itself, doesn't implant things in your mind so well, unless maybe it's very active reading. It also helps to have a good understanding. Sometimes, problem-solving is a matter of knowing the tricks, sometimes, it's a matter of understanding, and sometimes it's a matter of being original. The first two are easier to deal with.

But I will try this, however, have you got any tips on how to improve the creative process aswell?

It's difficult to do that for a test situation. Most of my strategies for getting unstuck on problems apply more to non-testing situations. So, one thing I could say is that being original on a test is not the most important thing. It's more important to be original outside of a test. A test is a pretty contrived environment. That being said, confidence can make a big difference. Knowing the material inside and out can help with confidence, but you can also try to pump yourself up and tell yourself that you are ready to go in there and beat the crap out of the exam. Also, as I just mentioned in that other thread, exercise has been shown to improve all kinds of cognitive performance, so these days, whenever I have an interview or exam, I go for a run beforehand, if I can fit it in.