Why does my piano teacher ask me to memorise the songs I play?
I believe that the point of memorizing songs is to help you further develop the muscle memory. In other words, it becomes easier to find the proper keys when moving on to newer, more complex pieces, because you’ve trained your hands and mind to find them without referencing the sheet music. Plus, it’s faster to run through the memorized pieces as part of your daily practice, as you don’t have to stop to flip the pages. (And, yes, it does look more impressive if you don’t need the music to play!) And while the pace may seem slow and frustrating, don’t be in too big of a hurry to get through to the next level. Through repetition we gain familiarity and can approach proficiency.