At what grade or at what math level, should calculators be introduced into the classroom or lesson? Or should I never bring them into the classroom?
Welcome to the forum. As early as possible! And as early as possible they should be replaced by a CAS. These are what are being used now in industry and research. Prepare them to work in the real world otherwise they will find themselves unable to get a job anywhere.
In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.
Welcome to the forum.
A calculator can be a useful teaching resource.
My son was given a simple, 4 function calculator when he was about four. He played with it a lot and taught himself negative number theory.
eg -3 x -4 = + 12 1 - -3 = 4 etc, etc.
When we bought him a more advanced TI machine for his birthday, it was his best present. He read the manual with great interest and his comment when he got to the chapters on calculus was "I can see there are some things you've been hiding from me." grins
So there is no minimum age; you may need to guide the learning; not all pupils are magnetically attracted to learning maths like my son.
I can give you some suggestions for things you can try. Post the age / ability of your pupils and the type of calculator available.
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei