Getting the right answer

Introduction
In doing mathematics homework, many students find in frustrating not able to get the answers provided.

"problems"
Couldn't get the [given] answer!

"solutions"
Look for careless mistakes and redo the workings. Some keep trying and spend more time than necessary. Some give up easily declaring they are bad in it. Some quickly discover their mistakes and happily conclude that they are not so bad.

My views
I like to tell my tuition students don't over worry about getting the right answer ... Why so and what do I suggest? . The answer is actually very uninteresting. The teacher, markers, question setters already knew it, and majority of the students will know it shortly.

More importantly, in doing homework, the goal is not to get the right answer, but to practice and reinforce the knowledge/skills/techniques being taught. The given answer serves to provide a feedback on your efforts. Some possible feedbacks are:
a) answer is correct ==> what you've done is probably right, and thus providing evidence to reinforce the methods that you have used.
b) answer is incorrect ==> what you've done is not right, thus you should check and learn from whatever mistakes you have made, and thus providing evidence to weaken the methods that you have used.

My point is that the above is achieved by doing the problem using a clear method, check for any careless mistake, compare with the given answer, recheck for mistakes if answers are different, make the conclusion and learn the lesson.

That's it for the purpose of education. Unless the number of correct answers affect your official score, then spend slightly more time to get it right for the purpose of gaining marks, if you know your mistake. However, the additional time spent in doing so doesn't benefit much in educational terms.

The problems with the above "solutions" are:

1) Some keep trying and spend more time than necessary. This is a bad habit that will affect efficiency and productivity in the future real world working environment. A person might be over focusing on a particular insignificant issue but overlooked the main objective and goal of his work.

2) Some give up easily declaring they are bad in it. Making mistake, or not getting the correct method the first time doesn't mean one is bad in maths. It just mean one need to admit that he need to put in more efforts and attention in lessons and revising to improve, but not by getting the answer right without bothering the meaning behind the methods used.

3) Some quickly discover their mistakes and happily conclude that they are not so bad. This is dangerous. It is good that they locate their mistakes quickly, but that isn't the end. Locating mistakes is not evidence that they are good, but overlook that making mistakes is evidence that they are weak. They should try to diagnose the reasons for their mistakes, which usually could be caused by weak foundation in something more elementary. Leaving this untouched, such weak foundation in elementary or fundamental knowledge will continue to haunt them in maths, and even in life.