What is the best long term approach to learning new songs?
Currently I learn one measure and then move onto the next measure until I get all the way through the song. Depending on the song it could take me days to weeks or more to even reach the last measure. Typically I find when learning a new song, at my level of playing ability, there are only a few measures that give me trouble.
I have started to wonder, is it better to build the skill of learning a song by setting a metronome at a very slow tempo and go all the way through the song to increase my ability to read new music and play at the same time. Then parts of the song that I have trouble with I can separate and practice them until I become proficient enough to incorporate them at a faster tempo.
I do like the idea of getting to the point of being able to take a new piece of sheet music and be able to play it, but I don't know if this is best practice so to say.
I don't think there really is a 'best' way, Jack. There are several ways of learning a piece and probably people find out by trial and error which suits them best. Learning sequentially from the start and progressing through to the end is a valid way but, speaking personally, it's one I only use on quite short pieces nowadays.
Depending on how proficiently a score can be read 'sight unseen', starting from the beginning can mean that the first bars are repeated several/many times before progress is made into 'unknown' i.e. unfamiliar bars, leading to a lot of repetition of already familiar bars before stumbling through new ones, which can be discouraging, not to mention tedious.
An alternative method I use is to learn the ending of a piece first, and then the bar preceding it, and then the one before that, and so on back to the beginning, playing to the end after each new bar learned, so that I'm always heading into familiar territory which feels much less of a struggle.
I agree that using a metronome to help gradually reach a faster tempo is a good idea, and isolating difficult bars to give them close attention is a very good way of dealing with whatever problem has arisen.
Thanks for raising the topic and I suggest trying out different methods to find out what suits you best - although it sounds like you might have already got there!