Stack-Exchange, I am a freshman in Mathematics Department.
I always learn mathematics the hard way. Everytime I learn mathematics on my own by reading from Mathematics textbooks, I would read the definition, try to figure out what it really means, stick new definitions which concepts that I already know, prove theorem without ever reading given proof.
But recently, I find this method cumbersome. In order to get a deep level of understanding those concept and solve a good amount of problems, I trade it off with a lot of my time, and my energy.
My seniors tell me that I should learn from different source of material to get more insight view, and separate the processes of learning theory and problem solving. I should read all the theory before trying to apply them to save times. But I'm used to the way of Pólya's mouse, so I am worried that I won't be able to catch up with all my classes like this. I want to try the way my seniors told me; that might be faster. But I want to know if the method would come with a loss of depth in understanding.
So I am asking for help. Also, please give me some tips to boost up the performance and the quality of learning mathematics all by myself. Thank you all very much.