Developing mathematical maturity?

[bonfire09]

One of the problems that I come across is my bad habit of glancing at the solutions. I usually look at them after I struggle on a problem for 20 minutes. Almost always its a proof problem like in linear algebra such as "Prove that there is one and only one way to write A as the sum of a symmetric matrix and a skew-symmetric matrix." Then I go back and finish the problem after looking the solution up. Some people say to keep struggling it out while others say its fine to look at the solution after you struggled for sometime. Anyone have any input on that?

 

[symbolipoint]

Only two reasons for looking at the solutions:

• Check your result or work after you answer an exercise,
• Find help or hints if you are stuck after spending a long time struggling with an item.

You judge when to look at the answer key. Do the work as well as you can before checking the key.

Thread topic title is about "mathematical maturity". This requires experience of study over several months, maybe even years, and also requires using some mathematical skills in your science or engineering laboratory sections, or even in employment situations. Not always linear systems, but I had sometimes needed to develop systems of two or three equations and to find sometimes values for three variables; the systems, although only consisting of maybe three uncomplicated equations, had linear and ratio terms involved. There was no answer key in the back of a book!