What is the Meaning of Mathematics Sense?

[superduck]

Hi,
When I am studying mathematics, I missed a problem.
I am considering what mathematics sense is.
Can you answer this question?
To be called that you have mathematics sense, what can I do?
Is some sense of mathematics required to learn mathematics deeply and understand it?
And what is mathematics sense?
I'll be grateful if you answer me.

 

[Simon Bridge]

You have "math sense" if you have an intuitive understanding or "feel" or talent for mathematics.
You know if you have this talent if you find math problems quite easy when the people around you find them difficult. If you look at a math problem you have not seen before and experience a feeling, physical or emotional, that pushes you towards a strategy that helps solve the problem - then you have it.

Most students either have it or not by the time they graduate high school but it is possible to learn it.
Some people develope one over time. For a lot of people it is like learning to whistle - you struggle and struggle and suddenly you "get" it.

It has no formal definition.

 

[superduck]

Thank you for advice

Thank you fo advice. You mean that math sense can be improved? Maybe I don't have it yet.Because my knowledge or skill to think or understand math problem deeply is not enough yet. But, if I think problem seriously or struggle to solve a problem many times, then can I get some math sense maybe?

 

[Simon Bridge]

That's right - it comes with time and improves with use.
It is possible that some people never get it very much - like some people never learn to whistle - but remember that everyone struggles with math sometimes and everyone always struggles when they are first learning.\

 

[lisab]

Practice, practice, practice. There are no short cuts.

I remember when I was first learning algebra, I watched the teacher solve problems using ingenious methods that seemed like tricks. It made me angry and frustrated because I knew I could not have figured that out all by myself.

For example, the first time I saw "completing the square" I was bewildered at how anyone could have thought of it!

But then I changed my attitude. I saw these "tricks" as tools -- tools I could own, tools I could put in my math "tool box". Making these tools your own comes through practice, though.

 

[Simon Bridge]

Yeah - one of the frustrating learning math is how methods get taught without the "how would anyone figure that out".

With experience you can figure out how anyone would figure about completing the square - why that may look like a good thing to try if you'd never seen it before - but you are right: you don't need to know because someone else already figured it out. We get to use their results as building blocks for our own. We can trust their results because we have a proof available ...

However, sometimes I have taken a bit of time to show students how some of the more "magic" or clever proofs can be obtained by the messier process of using even simpler results, playing around, and looking for patterns.

When I see questions like above I wonder sometimes if the querant is suffering through an old-style math course which just involves memorizing definitions and then crunching through endless exercises. Common enough in High School - I never got math before college where teachers were more interested in thought processes than answers.

You got to do the exercises, don't get me wrong, but you also have to see past them to get at the math.

 

[superduck]

Thank you for advice

Thank you for advice! I will practice, practice, practice! Somehow I don't feel any hesitation to start to study math. It easy to start studying math for me so far. The time is passed rapidly when I am studying math. Maybe it is because I am still in beginner level in math. When struggling against math problem will come some time. I hope I can bear it and continue study math. I need mathematics to understand physics or another phenomena. I will understand mathematics deeply, I must do it. Even I am still beginner. By the way I am a Japanese student, can you understand my English? I am always feeling sorry for my poor English. Why I want to study mathematics or physics or other science sujects in English is to discuss about these subject with you or question to you in English, becauuse Japanese website is not so good.

 

[ShayanJ]

Your English isn't that bad superduck!
Anyway,people explained it well,but the thing I think I should say is that never be satisfied by the thing that you have to do,continue farther.I mean,people may want you to just solve a problem but you should think about it deeply.While you're solving the problem,a question may come to your mind which isn't something you "should" know from the point of view of your teacher but it should be different from your point of view,you should go and search for the answer.At first think yourself,study and calculate and if you have had no results(its in no way no results,you learn lots of things in that process even if you don't get the answer,I just meant if you didn't reach to the answer)you can come and ask it here.
The main point is,you should love to do math,physics,etc. It should be one of your hobbies not that its one of the things you have to do.You should live with it,not that just having two hours a day in your schedule for math and physics!

 

[atyy]

http://press.princeton.edu/chapters/gowers/gowers_VIII_6.pdf

 

[papajo]

For me its about getting as elementary as it gets in principals and allocating your thought in respect to each of those principals. (also there must be an enternal research to validate and revalidate those principals and search if they are in essence a product of more elementary principals etc)

And by principals I am not referring stricktly to prooven theory but also to small "thoguht" mechanics that you do inside your mind.

For example when I was at junior high we learned that x +5 = 3 can be written as x = 3 - 5 because you can "swap the 5 to the other side " and "each time a number swaps sides you have to change its sign"

what is really happening though is that you have an equation of two quantities (like in a scale) X + 5 on one hand and 3 on the other you don't "swap" anything what you do is that you work on a small principal that sais if two quantities are equal and I add or substruct the same quantity from them they continue to be equal.

so what you do in the above example is that you add (-5) on both sides x + 5 -5 = 3 - 5 and since 5 -5 =0 you can say x = 3-5..

this might seem trivial and it is but ignoring this small processes as they really are (= ingoring the elementary principal) and just remembering a "picture" of the result that you need (as in saying "swaping sides and changing sign") will lead you to confusion in more complex matters

its ignoring those tiny details that create a bigger problem in understanding math.

thus If something complies with all of your principals then its correct... if it complies with 99% of them then it must be wrong !

 

[adjacent]

I get used to maths when I promote from one grade to another.In grade 7,I though algebra can never be understood by me and Got a B in maths,but when I got to 8,I suddenly got A*.What a surprise!
I believe it's the determination which made it.

 

[papajo]

I get used to maths when I promote from one grade to another.In grade 7,I though algebra can never be understood by me and Got a B in maths,but when I got to 8,I suddenly got A*.What a surprise!
I believe it's the determination which made it.

See here is an other problem that has to do with principals...

The question is what is math sense (if there is) and how to evolve one.

and yes since you pass your math exams it means that you have a math sense and yes you would not pass those exams if you didnt have determination.

But is math sense a matter of determination? did you evolve it because of determination? NO!

determination helped you trhough the way... what you did though is to brake bigger problems into smaller ones and then try to evaluate your data using axioms (principals) that's how you evolved it.

What I am trying to say is that math is a language and has a way of thought and we shouldn't confuse math language with our motherlanguage.

In english its ok to say I managed get better in my math classes because of determination.

In math language it would be a wrong...

It would be better to say that due to your determination you developed certain algorithms which were depented on basic principals that you accepted (due to reason a,b,c etc) and thus you achieved to get better results in your math classes.