Something like this book might help you understand the terminology of some of the different methods that are being taught, and you could then show her some of them and see if she recognises it, or ask her if she can do it on a number line, for example.
www.robeastaway.com/books/maths-for-mums-and-dads
Often they start with very practical methods at first, and move to written methods that seem long-winded and time-consuming, but are actually very good methods to understand what is going on (using number lines, drawing empty number lines and adding needed numbers, breaking numbers apart into tens and units and calculating each bit separately, doing a grid method for multiplication, or chunking methods for division). Then once the children have a good grasp of what the calculation is all about, and how the base-ten number system works, then they gradually move to the more old-fashioned written methods that are faster and more efficient, but not as explanatory. Sometimes this happens in stages.
With the recent changes to SATs, some schools are moving to the formal written methods much more quickly now.
It could be worth asking the school what methods they're teaching for various topics at various times, and the book might help you understand the terminology of those explanations.