Math Is Fun Forum

PatternMan

Member

Registered: 2014-03-08

Posts: 199

Do you really want a solution?

When learning maths I'm used to looking at the rules, one or so examples of a method then going through some practice exercises and then checking the answer. With some problems With maths and physics some books do not give solutions. This may be because of space or to prevent cheating or something. However I noticed it forces you to check yourself and stick with a problem. I'm wondering are there is any way you could understand what you are doing so well that you would be pretty sure when your answer is right or wrong without looking at a solution?

Last edited by PatternMan (2014-12-17 05:55:09)

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"School conditions you to reject your own judgement and experiences. The facts are in the textbook. Memorize and follow the rules. What they don't tell you is the people that discovered the facts and wrote the textbooks are people like you and me."

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Do you really want a solution?

Hi PatternMan,

The key phrase in what you ask is "you could understand what you are doing so well".  If you have truly understood, then you'll know you're right.  If you're wrong, then you haven't properly understood.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Do you really want a solution?

Hi PatternMan;

It is hard to give specific advice without a specific example but you should always work in a manner that you have at least an approximately correct answer before even starting a problem. In other words before you bring the heavy machinery in you should know where, what type and how much you need.

And after all is done, check, check and check again.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

PatternMan

Member

Registered: 2014-03-08

Posts: 199

Re: Do you really want a solution?

Hi PatternMan;

It is hard to give specific advice without a specific example but you should always work in a manner that you have at least an approximately correct answer before even starting a problem. In other words before you bring the heavy machinery in you should know where, what type and how much you need.

And after all is done, check, check and check again.

I suppose what I'm asking is how do you develop the intuition of knowing whether you're answer is correct or at least approximately correct? With basic arithmetic I know that the answer will be within the 100s of 1000s unit. However when doing multi step problems at a higher level it becomes more difficult. The algebra ignores the specific values. Or for example when Even when physics where you have a feeling for the units, it is hard to conceptualize the scale of atomic particles and know that the answer will be 4*10^-16 or whatever instead of 4*10^-18

Basically I feel like I have to have fully mastered every piece of a topic knowing all the relationships to be confident I'm on the right track. So there is some way to cross reference what I have done to other methods of validation that I have. I am thinking that if I wanted to apply math or physics to the real world then I wouldn't be given a solution. At best my method would or wouldn't work in reality so I would know it's  right, or wrong. But there has to be some way to reason with a high probability that you're right.

Last edited by PatternMan (2014-12-17 09:24:34)

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"School conditions you to reject your own judgement and experiences. The facts are in the textbook. Memorize and follow the rules. What they don't tell you is the people that discovered the facts and wrote the textbooks are people like you and me."

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Do you really want a solution?

Basically I feel like I have to have fully mastered every piece of a topic knowing all the relationships to be confident I'm on the right track.

Nothing could be further from the truth. Check the first line of my signature, that is written by a top mathematician. You do not need to know very much about aerodynamics to get on a plane. You just need to know the departure time and what gate it is at. You will be surprised at how little you need to know to solve a problem. It is much more useful to have 10 techniques that you really can do well than to have a 1000 that you use poorly.

Problem solving requires patience, experience and confidence. You learn all 3 by doing as many problems as you can. Do not get the attitude that there are problems that are beneath you. This is another illusion. Do not worry about mistakes, everybody makes them.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.