Hi I've just discovered mathseducators stackexchange.
As a maths tutor in the UK, I am irritated that some of my students - particularly GCSE and sometimes below - use the table method for expanding brackets, rather than "each term in the first bracket gets multiplied by each term in the second bracket", the latter method being what I'm familiar with.
I also prefer my method because:
a) expanding brackets using my method is quicker. Drawing a table is unnecessary and tedious.
b) It is easier to see that my method can be derived from repeated applications of the Distributive Law (although students usually don't care about stuff like this).
c) It is easier to simplify algebraic expressions, for example showing where the "2b" comes from when completing the square.
Maybe it's the way they are teaching in schools nowadays, but the table method seems to me to be unnatural and unnecessary. My students insist on using it, however, and any attempts to get them to use my method are shut down because they are so used to their method being the "right one". They know theirs works, so they don't need my method. But then, for example, teaching some of them how/why "completing the square" works is more difficult if they only use their table method.
So I guess my question is, should I try to get students to use my method and/or abandon their method, or should I accept their method and get over it?
I think what makes this question different to usual "should I accept their method (assuming it works) or get them to use my method?" questions is that, they have probably used their table method for many years and for them, it is probably a fundamental part of multiplication.