Overcome Struggles in Math and Physics

[Polyrix]

Hi there,

I have generally had a very strong aptitude towards Mathematics & Physics. Conceptually, that is. I find it very simple to grasp rudimentary as well as advanced Physics concepts very quickly, and can make connections easily. I love both subjects and wish to pursue both (primarily Physics) in my post-secondary education. The problem, however, is despite the fact that I can understand concepts as difficult as those in quantum & particle physics, my grades are not reflective of them at all. Percentage wise, I can never pull off anything above a mark in the low-90% range (I am currently in secondary school). I always struggle on test mainly because I seem to make a plethora of silly, predominantly mathematical errors. I tutor nearly every single kid in the class to understand and grasp concepts, and yet a significant proportion of them end up beating me. Right now I feel very frustrated & discouraged for not having the slightest idea whether Physics is right for me, and I am incredibly dissapointed in my self.

Are there any suggestions out there to help me?

 

[tmyer2107]

I had a similar problem in one of my classes. I corrected it by figuring out why I was making the silly math errors. If your low marks are because of basic math errors you need to go back and relearn whatever is causing you to make those errors. For me it was a few basic concepts in linear algebra and multivariate calculus. I spent a good amount of time going over it again and sat in on some classes. When I took both of these classes I got an A but because I crammed for a few of the tests the methods didn't stick which caused me to slip up later.

 

[Raghnar]

I also had your problem in high school and have it also today on PhD.
My grades was excellent but not the best in the istitute, anyway I was, in decades, the only high school student allowed to make physics lessons by the Dean himself (my class situation however was awful: math teacher died and no-one in months was able to replace. So I was granted a couple of hours a week to tutor the whole class).
In Math I could take a 10/10 in a classwork and a 4/10 in the next one.
Also in the B.Sc I had many difficoulties (low marks) with the basic examination.
But in the M.Sc, I had arise with an all 30/30 (sometimes cum laude) on every single examination. Also now in the PhD I can help both experimentalist and theoriticians on various subjects, but I've the constant feeling something is missing, that you should focus and solid realize something more and less jumping.

People wiser then me, after few tests, told me that is in fact the consequence of an intuitive mind.

If you are a good tank-thinker you go straight forward, learn to focus and never fail the math, learn that this becomes that and so on.
If you are an intuitive type of guy you go from a subject to another, sometimes jumping percieve the conclusion before do the math and loosing interest. Rarely truly focusing (because you have perceived a gross-solution and you are not interested in details) and this leads you to fail the details, because you work out with intuition not rigid thinking.

I watch it with my girlfriend: she's one of the best straight-thinker in the facoulty, she have the special power to remember a LOT of numbers and formulae and so on. But she have pratically no creativity and do very rational choices.

I'm the exact opposite, I'm the pure intuitive person and my life is full of creative hobbies: now I'm a semi-pro photographer, back in high school I was a good musician (problems to the hand stopped me :( ) and a decent painter () and in my personal life I'm a very sentimental and irrational.
Practically when comes to choose where to buy something or go somewhere...etc.. I buy/go/etc.. what I LIKE, my girlfriend where she think is the best (best price, best services, best relax...etc..) that can be a problem ;)

Physics teached me a lot about thinking straight and logical, teached me to focus on the details that are the most important things in science and not only "details". For me it was a good mind-gymn but cannot cure the way I think, I don't know if I will be a good scientist or not.
The people that guided me and told me to endure in my B.Sc because in the M.Sc and later (where the more complicated subject reward the intuitive thinking) I will be rewarded and make a hell of a scientist.
For now they are right, I'm also very sceptical but I'm sure I'm a bit uncommon thinker and uncommonness is what science is made of.

I'm obviously generalizing and extremizing, but only to bring my experience (hoping that it will be useful) and make the point: whatever type you are, you can be a good scientist if you have the right passion and make value your skills whatever they are, and science have need for practically all type of skills, from the number crunching girl that make data analysis to the crazy guy that try to do some theory.

PS: if my english isn't very good or there are obscure parts tell me. I'm Italian and trying to improving my language skills ;)

 

[Polyrix]

I also had your problem in high school and have it also today on PhD.
My grades was excellent but not the best in the istitute, anyway I was, in decades, the only high school student allowed to make physics lessons by the Dean himself (my class situation however was awful: math teacher died and no-one in months was able to replace. So I was granted a couple of hours a week to tutor the whole class).
In Math I could take a 10/10 in a classwork and a 4/10 in the next one.
Also in the B.Sc I had many difficoulties (low marks) with the basic examination.
But in the M.Sc, I had arise with an all 30/30 (sometimes cum laude) on every single examination. Also now in the PhD I can help both experimentalist and theoriticians on various subjects, but I've the constant feeling something is missing, that you should focus and solid realize something more and less jumping.

People wiser then me, after few tests, told me that is in fact the consequence of an intuitive mind.

If you are a good tank-thinker you go straight forward, learn to focus and never fail the math, learn that this becomes that and so on.
If you are an intuitive type of guy you go from a subject to another, sometimes jumping percieve the conclusion before do the math and loosing interest. Rarely truly focusing (because you have perceived a gross-solution and you are not interested in details) and this leads you to fail the details, because you work out with intuition not rigid thinking.

I watch it with my girlfriend: she's one of the best straight-thinker in the facoulty, she have the special power to remember a LOT of numbers and formulae and so on. But she have pratically no creativity and do very rational choices.

I'm the exact opposite, I'm the pure intuitive person and my life is full of creative hobbies: now I'm a semi-pro photographer, back in high school I was a good musician (problems to the hand stopped me :( ) and a decent painter () and in my personal life I'm a very sentimental and irrational.
Practically when comes to choose where to buy something or go somewhere...etc.. I buy/go/etc.. what I LIKE, my girlfriend where she think is the best (best price, best services, best relax...etc..) that can be a problem ;)

Physics teached me a lot about thinking straight and logical, teached me to focus on the details that are the most important things in science and not only "details". For me it was a good mind-gymn but cannot cure the way I think, I don't know if I will be a good scientist or not.
The people that guided me and told me to endure in my B.Sc because in the M.Sc and later (where the more complicated subject reward the intuitive thinking) I will be rewarded and make a hell of a scientist.
For now they are right, I'm also very sceptical but I'm sure I'm a bit uncommon thinker and uncommonness is what science is made of.

I'm obviously generalizing and extremizing, but only to bring my experience (hoping that it will be useful) and make the point: whatever type you are, you can be a good scientist if you have the right passion and make value your skills whatever they are, and science have need for practically all type of skills, from the number crunching girl that make data analysis to the crazy guy that try to do some theory.

PS: if my english isn't very good or there are obscure parts tell me. I'm Italian and trying to improving my language skills ;)

Wow, that was very inspiring. Thank you. I suppose I never saw there as being 2 sorts of thinkers. And your English is just fine. :) May I ask what you did your PhD on?

I had a similar problem in one of my classes. I corrected it by figuring out why I was making the silly math errors. If your low marks are because of basic math errors you need to go back and relearn whatever is causing you to make those errors. For me it was a few basic concepts in linear algebra and multivariate calculus. I spent a good amount of time going over it again and sat in on some classes. When I took both of these classes I got an A but because I crammed for a few of the tests the methods didn't stick which caused me to slip up later.

Thank you for the comment. I'm trying to consider ways to minimize my errors right now... it isn't that I do not know how to do the math, it's just I can't seem to avoid a plethora of mistakes.

 

[twofish-quant]

Percentage wise, I can never pull off anything above a mark in the low-90% range (I am currently in secondary school).

I don't think you need to worry. I know lots of theoretical physicists that are bad at arithmetic. Also if you to a decent school, they count off lightly for stupid arithmetic mistakes and look mainly to see if you got the point of the problem.

 

[Dembadon]

Usually working the problems slower and being more careful helps me to minimize stupid mistakes. I have found that most of the silly mistakes I make are when I am overconfident or rushing through a problem / problem set.

Take your time and work through the problems carefully.

 

[twofish-quant]

Also something that works for me is to do cross checks. For example if I do a long polynomial problem, then I put zero or one in the terms to make sure that the coefficients make sense. Also making sure that the units match gets rid of a lot of errors.

Then there is maple... :-) :-)

 

[Raghnar]

Wow, that was very inspiring. Thank you. I suppose I never saw there as being 2 sorts of thinkers. And your English is just fine. :) May I ask what you did your PhD on?

For now I'm doing Theoretical Nuclear Physics (nuclear superfluidity in fact).
I'm helping also a bit experimental nuclear physicist (where I did my B.Sc) and do some statistical and bio-physics workout, only to have a bit fun...

 

[lubuntu]

Yes don't worry about it I am really terrible at arithmetic and keeping track of signs etc while doing problems and I am doing okay. Keep in mind though at some point you will have some out of touch professor whose tests tend more to measure brute force computational skills as opposed to conceptual understand. This happened to me in my Calc I course, found the stuff trivial really but got marked down to 85's or so on tests due to silly silly mistakes. Now in Calc III, I have a much better professor and just got a 100 on a test with a few of those same silly sorts of mistakes.

I've noticed that older professors seem to be more of a stickler for the exact answer than conceptual understand. I don't know if its because they are so far removed from the time they learned the material to remember the computations aren't that important or because back in there day testing more emphasis was put on computational stuff.

ps. I think in high school the computational stuff is also more emphasized because frankly I don't think the high school teachers are also bright enough to even know what is important.

 

[Dembadon]

Yes don't worry about it I am really terrible at arithmetic and keeping track of signs etc while doing problems and I am doing okay. Keep in mind though at some point you will have some out of touch professor whose tests tend more to measure brute force computational skills as opposed to conceptual understand. This happened to me in my Calc I course, found the stuff trivial really but got marked down to 85's or so on tests due to silly silly mistakes. Now in Calc III, I have a much better professor and just got a 100 on a test with a few of those same silly sorts of mistakes.

I've noticed that older professors seem to be more of a stickler for the exact answer than conceptual understand. I don't know if its because they are so far removed from the time they learned the material to remember the computations aren't that important or because back in there day testing more emphasis was put on computational stuff.

ps. I think in high school the computational stuff is also more emphasized because frankly I don't think the high school teachers are also bright enough to even know what is important.

I don't understand, and likely never will, why one would expect "silly" mistakes to go unmarked. However silly the mistake may be, it is still a mistake. I realize there are a variety of different teaching styles and methods; but, in my opinion, when it comes to maths, it is not unreasonable to expect precise, exact answers.

I think it is bad form to view certain aspects of a problem as unimportant. I don't believe this encourages a quality of work, which is something that I believe is extremely important in anyone's job. It is completely reasonable to expect students to take their time and carefully work through problems.

 

[kote]

It is completely reasonable to expect students to take their time and carefully work through problems.

On timed exams? Should the student who flips a sign be marked off the same as the student who doesn't show any evidence of being able to solve a problem?

I agree that a 100% on a test with errors seems strange, but often the problem is the strict time limits that are often placed on exams. A calculus test should be graded in such a way that the person with the stronger grasp of the calculus receives a higher grade than the student who can do faster long division.

Then again, I've never understood why closed book exams needed to be such a race.

 

[Dembadon]

It is completely reasonable to expect students to take their time and carefully work through problems.

... On timed exams? Should the student who flips a sign be marked off the same as the student who doesn't show any evidence of being able to solve a problem? ...

No, they shouldn't, in my opinion. My post was an attempt to express my discomfort / disagreement with a mentality, not with a certain teaching style. The mentality being; certain aspects of problem solving are unimportant and should be overlooked.

 

[twofish-quant]

in my opinion, when it comes to maths, it is not unreasonable to expect precise, exact answers.

But we are talking physics. One thing that I do in intro astronomy classes for non-majors is to mark people off for giving answers that are too precise and too exact. If I ask you what 1.0 / 3.0 is and you reply 0.33333333333333, then I'll remove a point so you don't do it again. (And I write in big letters in the lecture notes that I'm going to do this.)

In physics problems there are errors that don't change the final outcome much, and then there are errors that mean that you get an answer that is totally, totally wrong.

I think it is bad form to view certain aspects of a problem as unimportant.

The trouble with that philosophy is that in physics there *are* certain aspects of the problem which are not important. If I want to calculate static loads on a bridge, I'm probably not including the effects of general relativity, and if it makes a difference to whether the bridge stands or falls, then I've got bigger problems than GR.

I don't believe this encourages a quality of work, which is something that I believe is extremely important in anyone's job. It is completely reasonable to expect students to take their time and carefully work through problems.

Not for my job it isn't. You have a trader that needs to know the price of a complex option. If you have twelve hours to calculate it, you can run it on the grid, and get a more complete answer. Sometimes you don't have twelve hours, but you have twelve seconds to make a decision, in which you just aren't going to get a complete answer, but a quick, rough, and perhaps incorrect one. Even if you run everything on the grid, the answer you get is *still* an approximation to reality, and you are hosed if you have the exact answer to the wrong problem.

In physics, every answer you give is wrong, because every model is wrong. The question is *how* wrong and does it matter.

 

[twofish-quant]

No, they shouldn't, in my opinion. My post was an attempt to express my discomfort / disagreement with a mentality, not with a certain teaching style. The mentality being; certain aspects of problem solving are unimportant and should be overlooked.

And that's *exactly* the type of mentality I'm trying to encourage when teaching physics. If you don't encourage that type of mentality then what you end up with are problems and questions that live in a perfect mathematical world that is totally disconnected from messy reality, and those end up to be completely useless.

 

[Dembadon]

twofish-quant:

What you say of physics is true; however, lubuntu's post (the one to which my response was directed) referenced his calculus course(s). Perhaps I have gone off-topic in talking about maths. My apologies.

 

[lubuntu]

Well dembadon I'm certainly glad I'll never take a class from you. I don't get it, some people are just kind of prone to these sorts of trivial mistakes especially in timed test environments. You really have to consider what you ar testing and what is important. Just as a hypthetical example in multivar calc if someone set up a triple integral correctly and evaluated but flipped a sign or made an addition error should they be marked the same as some one who has no idea what to do?

Frankly in thr real world you can always check your computations with technology so really hoe can you say that all parts of problems are equally important?

Should a test test conceptual understanding or being able to perform
precise calculations under pressure in short time!? Which do you really think is more important ?

 

[vanesch]

I think we're touching upon an important point. I tend to agree with dembadon, although others have also raised interesting points, and it touches upon what are "religious wars" in education science in as far as I know anything about it.
What we see is essentially a glorification of a dogma which started out as a healthy dose of criticism of "the old ways" of teaching. In many domains, the "old way of teaching" was routine, mechanical training on techniques. You were a good student if you were "drilled" enough to apply these techniques blindly, quickly, and accurately.
The justified critique was of course that what is lacking seriously, is insight and conceptual understanding, and that this is probably the most important aspect of learning something. Also, the development of some intuition about the material is important, and this will not be improved by doing series of drill exercises. But this has been turned into some kind of dogma that the only thing that is important now, is conceptual understanding, and that any kind of drill of training is for "idiots" who don't have enough "intuition" to "feel" the answer.

In fact, both are important. You need of course to understand the material conceptually, it is nice if you devellop a certain intuition for it, but you should also train to be able to apply techniques quickly, correctly, and without hesitation. And THAT, you only gain by "drilling". But it is very important, especially for subjects such as math and physics, to do so.

The reason is that what is "new material" now, and what may be conceptually challenging right now, will be just one little "routine" aspect of a more complicated problem next year. If you are not trained to do simple things fast, without hesitation, and correctly NOW, then it will be a burden in your tackling more complex things later. This is probably the kind of issue the OP has.

Understanding, and conceptual insight is a necessary, but not a sufficient condition to learn well.

What has been raised by quant is a totally different issue in fact. It is true that a working scientist, engineer, whatever needs to estimate also what kind of problem solving technique he will use in a real-world situation, and what kind of accuracy is feasible, reasonable, and necessary for the problem at hand, and how to reach it, and what means to put to it. But there's no comparison between using an approximation, and making a silly technical mistake. The first is done on purpose, needs insight and intuition, and is justified. The second is, well, a mistake.

It is true that 1.0 / 3.0 = 0.3333333333 lacks some insight concering the propagation of errors and the accuracy one might expect of the result. But 1.0 / 3.0 = 3.0 is an ERROR. A mistake. A silly one, but it is still wrong.
And if the calculation was part of designing a bridge, I prefer the first mistake, which will probably not affect the end result

 

[vanesch]

t?
Should a test test conceptual understanding or being able to perform
precise calculations under pressure in short time!? Which do you really think is more important ?

Both. That's my point.
One used to neglect "conceptual understanding" in the old days. But that's no reason to neglect precise technical skills right now.

 

[Dembadon]

... Just as a hypthetical example in multivar calc if someone set up a triple integral correctly and evaluated but flipped a sign or made an addition error should they be marked the same as some one who has no idea what to do? ...

As I stated in post number 12; no, they shouldn't be marked the same.

 

[fluidistic]

As I stated in post number 12; no, they shouldn't be marked the same.

I totally agree with you Dembadon. I can't even imagine say a volume which has to be positive and the student gets the same result with a negative sign. This is a tremendous error, the student must realize a volume cannot be negative, hence he must realize he made a mistake. If he doesn't have time to find it, at least, the bare minimum is to write on the copy "I made at least a mistake because of the negative sign, but I don't have time to check it out".
In physics, if one forgets to convert m to km and you get an impossible result and don't realize it, you should get some points off. Like for example calculating the distance between the Earth and the Moon, if you get 300,000 meters, or 300 km and you don't realize you made a mistake, you fully deserve to get points off.

 

[atyy]

The solution is to emigrate to Singapore - at least in the old days, 75% was an A - maybe not any more - I have been told that I would no longer pass elementary school.

 

[Raghnar]

Should a test test conceptual understanding or being able to perform
precise calculations under pressure in short time!? Which do you really think is more important ?

Everything can be important.
When you strive for an article in the final rush and get and workshop (or you are doing shift to a collider and your array must be recalibrated in hurry) with the best experts on the subject and they say "we should try to do this and see what happen, can do it for tomorrow?" 90% of the time you can say only "Yes, I'll do my best!", and then spend all night in a hurry to modify a reference system or a phase notation in order to match everything up.
And you can't do wrong anything, or you will play the dumb guy with the wrong people.

You can be not fitted for that work, as I am not so much, and you can be an outstanding scientist anyway. But making things right under pressure and make it right can be crucial for the career of a scientist.

In Science everything is important, from reasoning about the order of magnitude to get the right intuition in a matter of seconds to the sign of a phase and the most ludicrous details, even under pressure.
The good curriculum must be builded in order to develop this two way of reasoning with exams and professor that teach you their speciality of thinking.