As I am tutoring students I am blown away by the over-use of mnemonics in math classes these days. It seems that mnemonics are the crutch for math teachers to avoid actually teaching an UNDERSTANDING of math - or "numbers sense".
It seems that over the years that math teachers have lost their faith in students ability to learn math, or have lost their faith in their ability to teach students an understanding of math.
Whatever the cause, I run into students totally confused by all the mnemonics/algorithms running through their heads. They mix mnemonics with other mnemonics. They mix up the steps in an algorithm. They forget the algorithm altogether. They misapply the mnemonics or algorithm. They are not taught basic number sense. It's amazing to watch their faces light up when they start to UNDERSTAND.
Sadly the vast majority of students reach algebra, geometry and higher without achieving a solid basis of numbers sense.
I am also not a proponent for mastery by "pure endless repetition" - like Kumon for example. Practice to achieve mastery is a path to greatness - if it is accompanied by a solid understanding of what you are doing. Practice builds confidence and familiarity. I am particularly fond of practicing extra problems leading up to a test. Call it a mock test. Builds confidence and mastery at the same time
There are some basics in math - elementary math -- that should be taught through both repetition/memorization - best examples being long division
That said I can think of one mnemonic that I recommend: PEMDAS to help students with the "order of operations" when needed.
Bottom line: be careful with over-use of mnemonics and brute force memorization for mathematics. Teach an UNDERSTANDING OF MATH FIRST, use crutches like mnemonics and brute memorization sparingly. Make sure your tutor(s) is adding understanding not more mnemonics! Encourage your teachers to teach understanding of math!