whynotboth.gif paired with allofit.gif
We taught ours, now 9 and 11, to hammer all of the + - * / facts. Then, each new teacher was to be treated as a person with a new perspective, if not just slightly different, on the topics and strategies of + - * / as they cycle through the years. Be sure to do as each teacher instructs, show your work always, and double check your work with your hammered facts. Another thing is that in the elementary age years they are given plenty of time to do the work and almost another set of time. So be diligent to double-check your work.
We used flash cards in K and 1st for + and - . Then began early/mid second with multiplication that wasn't really asked for till 3rd by the public schools here in DFW.
Teach them the anything x 10 you add a zero. Anything x 0 is 0. Anything / by itself is 1.
Counting by 2's is just like multiplying by 2's to an extent. Counting by 5's, by 10's. All makes it easy if you can just do it and shows them early on when you compare 5x5 to 5+5+5+5+5 how it is interrelated just like 25/5=5. That * and / are the same 3 numbers just in a different order, so to speak.
Math at elementary level is finite, always an answer that never changes which is beautiful.
Girls, Boys, makes no difference since it is cool and you are giving them the practice at home to kill it at school.
Then starting in 3rd grade when there are only 5 questions on the quiz how important it is to get every one correct since missing one is an 80.
TLDR: Rote math helps get the fundamentals and more time to think about what each individual math teacher is saying so they can focus on the potentially slightly different strategy of their new teacher while already understanding the basic concepts from their home practice.