My material science teacher is willing to write me a "2-3 paragraph letter of recommendation" for an internship in the stem field. It will be a positive letter of recommendation. Would this short of a letter of recommendation look bad to the people who assess my application?
Not really. You're looking for an internship, nobody sensible expects long winded praises of your achievements in school for that. In fact, if somebody had a really long winded letter, that'd probably be more suspect.
There just isn't much to tell about you yet, hence why you want to get an internship.
Also, the content of the letter is significantly more important then the length in characters.