Learning By Doing: Is It Worth It?

[Tyrion101]

After hours of trying and failing to do the problem on my own, what I usually do is, find out the part I'm missing, and just do it, even though it doesn't really make any sense to me at the time, like why is there the extra x, that is in the word problem I don't know and it doesn't explain but I'll do it anyway. That kind of thing. Am I hurting myself by doing this?

 

[symbolipoint]

WHAT DO YOU MEAN?

You must be more precise. After hours trying to do WHAT problem? What is the exact problem description?

 

[Tyrion101]

I'm just asking if it is a wrong idea to do the problem without really understanding why it works.

 

[Nugatory]

I'm just asking if it is a wrong idea to do the problem without really understanding why it works.

It depends on the problem. Sometimes, working through a problem and watching the machinery at work is a good way of understanding how and why it works. Other problems... not so much. And because different people learn in different ways, the answer may be different for different people.

So I'm inclined to agree with symbolipoint - you'll get better answers and more insightful discussion if you can provide a few specific examples.

 

[Tyrion101]

We'll the main thing I do this on is word problems, the wording confuses me most of the time and I usually find out I had written it backwards from how it's supposed to be, and I never can figure out when to wire things backwards.

 

[Mark44]

The equation you come up with when you're working a word problem should be an exact representation in math symbols of what's given in the word problem. If there's an extra x or some missing term, it means you don't understand the problem as well as you need to. Solving an equation that doesn't reflect the scenario of the word problem is not productive, and doesn't do you any good.

 

[Tyrion101]

When does it matter to have numbers us letter or letter minus number?

 

[Mentallic]

When does it matter to have numbers us letter or letter minus number?

?

This makes absolutely no sense.

 

[Tyrion101]

Sorry I think auto correct stuck again. Anyway what I mean, let's say you have a word problem and you know it wants either x-30 or 30-x, what is the phrasing I should be looking for that tells me hey it should be 30-x?

 

[Mark44]

When does it matter to have numbers us letter or letter minus number?

Assuming you meant "numbers minus letter or letter minus number",
the expressions x - 2 and 2 - x are opposite in sign. If x = 5, say, then x - 2 = 3 and 2 - x = -3.

 

[Mark44]

Sorry I think auto correct stuck again. Anyway what I mean, let's say you have a word problem and you know it wants either x-30 or 30-x, what is the phrasing I should be looking for that tells me hey it should be 30-x?

The problem doesn't "want" anything. You have to translate what the problem says into symbols.

For example, if you have a stick that's 30 inches long, and you need to cut it into two pieces, one of them will be x inches long and the other piece will be 30 -x inches long. If you add the lengths you get 30". If you switch the order and get x and x - 30, then the sum of these lengths will no longer be 30.

 

[symbolipoint]

Sorry I think auto correct stuck again. Anyway what I mean, let's say you have a word problem and you know it wants either x-30 or 30-x, what is the phrasing I should be looking for that tells me hey it should be 30-x?

Understanding the common human language in which the problem is written is a requirement.

Studying and doing exercises for translating worded descriptions into numeric symbolism is necessary in order to develop skill in formulating numeric expressions and equations from the worded descriptions. This is often the goals of Basic Math, Basic Arithmetic, Pre-Algebra, Algebra 1,2,3.