Notes are generally important information that you need to remember to apply to problems or may aid in the construction of a solution. In general, you should do what is necessary to be able to solve the problem and that usually means remembering information. So basically, as much as you need to.
You also may not need notes.
Basically, if you can't solve a problem then you're likely missing information and notes may help. It also helps to write it in your own words, it doesn't necessarily have to be a pure logical form. The most important thing is being able to apply the information and notes can help with that.