The Most Important Thing

The most important thing my father ever taught me is that in a sentence when you want to include someone else, (for example: mine and my brother's hopes were high, or my brother and I went to the park) simply take out the other person and see if the sentence is grammatically correct. So, that is why it is: my brother and I went to the park, because if you took out 'my brother' it would be: I went to the park. Which is why "me and my brother went to the park" is the same as "me went to the park". Which is obviously incorrect.