>Performance is doing arithmetic fluently, taking tests, working at >the board etc. Working the exercises when they don't make you stop >and think too much. Drills to increase speed and accuracy. The >dreaded "rote" tasks.
The dreaded "drills to increase speed and accuracy" are not nearly as intimidating or dreaded as the industry portrays them to be. Our family's private school had regular timed drill targets with the elementary number facts in grades 1-3 that everyone met. A few, the very first time that they took them, more fairly quickly, and a few who struggled for months (but everybody made it). Just a few minutes several times a week with students excused after several demonstrations of success. At first just addition and subtraction, a 10 x 10 array, so 100 in 5 minutes in first grade and all mixed in 3 minutes in 3rd grade (if I'm remembering correctly). There was a chart on the wall - by name - with a bar graph that grew over time until it was a solid rectangle. All had the mathematical understanding well before, of course, but automaticity matters as well.
By contrast, no such pressure was applied to my children before we finally abandoned Pasadena Unified and I was insisting on a certain level of computational automaticity with the elder (8, I believe) and, from time to time, I would quiz him on his elementary multiplication facts. He understood the idea, of course, but there were a few that he'd get stuck on, most especially 3 times 7. Younger brother, 3 at the time, learned that the proper response to anything involving 3 and 7 was 21 so he was "sitting on it" to the frustration of his older brother. The younger had no idea of what multiplication even meant (the "rote" perception of today's so-called reformers) but the older did not realize that, at least not for a while. That was probably a motivating factor in meeting my standard.