In the example you gave and for anything that goes along with learning how to read notes, you DON'T want to memorize the tune. I don't know the lesson you're talking about, but I'm talking about reading standard notation. Memorizing the tunes defeats the purpose of you having to look at and recognize what notes you are reading. Always try practicing new pieces. If you know the song by heart, you are cheating in a way because your brain automatically plays the note that is supposed to be played, even if you may not know the note on the staff.
For technique I would say memorizing would be helpful. This would allow you to be able to look at your hands and concentrate on proper form and all that, rather than having to look up and follow along.
