May I ask: what point is there to teaching and testing children in elementary school on the *names* of mathematical properties (“associate property of multiplication”, “identity property of addition”)? To me, these are so lame and boring and suck all the fun out. Is there any good reason to insist on learning the names? There are much better ways to test their understanding that a property is true, usually found in fun “contest” problems, like: What is 10x9x8x…x(-8)x(-9)x(-10)? (Vs “zero property of multiplication”) What is 1/2 x 2/3 x 3/4 x 4/5 x … x 99/100? Quick, what is 34x3 +34x7? (Vs “distributive”) There’s a whole slew of such really fun problems, completely standard. I don’t care if you know what grownups call it. Do you understand how to use it as a “backdoor” to answer a problem immediately?