.Jason Zimba one of the lead writers of the CC math standards, when asked to explain whether there is a distinction between being “fluent” with math and “memorizing” offered some explanations.
First, on the issue of whether CC requires memorization:
“The standards require students to know basic facts. Here is the language for multiplication (page 23): ‘By the end of Grade 3, know from memory all products of two one-digit numbers.’ We can debate the best ways to help students meet this expectation, and we can debate the best ways to assess whether students have met the expectation. Those are good discussions to have. But there is no room to debate the expectation itself. The language in the standards is unambiguous.”
Then he distinguishes between “fluency” and “memorization”
“Fluency pertains to an act of calculation. In particular, to be fluent with these calculations is to be accurate and reasonably fast. However, memory is also fast, so the difference between fluency and memory isn’t a matter of speed. The difference, rather, has to do with the different nature of calculating versus remembering. In an act of calculation, there is some logical sequence of steps. Retrieving a fact from memory, on the other hand, doesn’t involve logic or steps. It’s just remembering; it’s just knowing. The mental actions of calculating and remembering are different. The standards expect students to remember basic facts and to be fluent in calculation. Neither is a substitute for the other.”
So, they don’t mean the same thing, except when they do. Here, read it and tell me what it means. I’m having a beer.