The mild issue with this is that if you are given the plural before the singular, as I was, you'd have no way of knowing that it is masculine. it's not the biggest issue, but maybe keeping plurals out of level one of the lessons, would be good while we get the gender memorized.
In the US, we call them fish sticks. The first time I heard Matt Smith talk about fish fingers and custard, it took me forever to figure out what he was eating. Then, when I figured it out, it made me sick :-) This has nothing to do with the conversation--it just made me laugh.
Since some of you have difficulty imagining a situation in which you can use this phrase:
Some friends visit you to watch some movies together (maybe all parts of "The Lord of the Rings"). Drinks and snacks are provided so you sit down on the couch and this long sleepless night of fun can begin. In the middle of the first movie you notice something's poking you in the side. First you think that might be a lost chip crumb but you are not able to find it. Everytime you try to pick it up - groping for it in the dark - there's nothing. No crumbs, no more poking. So you try to focus on the movie again, but then it starts again and seems to go into your jeans to your butt. You look accusingly at your friend next to you. The friend notices and asks what's wrong with you. You say: "Nimm deine Finger da weg!" He raises both his hands and says: "Hey, das sind nicht meine Finger!". In this very moment another friend reveals himself with a big grin on his face and you know where to throw the pillow. ;)
It might save your life to know this sentence in the right moment. ;P
In colloquial German I know another word for "die Finger". It's "die Griffel" which is only used for "Finger" in a negative context (unpleasent touching or stealing).
Where does it say that?
In https://en.wiktionary.org/wiki/Finger#Declension , I see that the genitive singular of Finger is (des) Fingers and the dative plural is (den) Fingern -- which is correct.
For the nominative plural -- the form that is usually meant when someone just speaks about "the plural" -- I see only one form, (die) Finger, which is also correct.
Are you looking in a different place than I am?