"How can you tell whether someone has truly mastered a skill? What is the measurable indicator
that a person really knows how to do something? These questions should be at the heart of every teaching decision, every observation of a child’s performance, and every evaluation we make about the success of an educational program. Yet for many educators, and certainly for most parents, answers to these questions are anything but clear. Most of us have grown up in a 'percentage correct world' where 100% correct is the best anyone can do. But is perfect accuracy the definition of mastery? Or is there another dimension that makes the difference? In fact, we see many children and adults who can perform skills and demonstrate knowledge accurately enough – given unlimited time to do so. But the real difference that we see in expert performers is that they behave fluently – both accurately and quickly, without hesitation."
The above quote was copied from this link that jh gave me on Lefty's blog in the comments section. I'd link to jh, but s/he hasn't enabled profile access. We were discussing the difference between Singapore and Everyday Mathematics. It so happens that I use both in our homeschool. I find EM much easier to teach, but not as rigorous. EM is more geared toward a large classroom and "group" work, which I usually skip.
I'm not above being cynical of the link, as I noticed some of the products listed at the bottom of the report juuuust so happen to seem to financially benefit at least one of the writers in some way. Then again, how often does someone truly BELIEVE in something, and then go develop the product they want to fit that perceived need? So, that fact alone wouldn't make me totally discount the idea that fluency, not accuracy, is a more reliable indicator of academic achievement.
If that's so, I'll have quite the difficulty teaching Emperor math in a few years alongside his brother. He is already two and a half grade levels ahead at the age of seven. I can't imagine that it would be right to let him go on just because he has demonstrated "fluency" in his subject matter. (No college would accept Mr. Jumpy at age 14, I'm thinking...) He keeps writing down answers - correct ones! - with no work shown. Meanwhile, the same work will take Elf two hours and I'll catch him counting on his fingers and asking questions of the "peanut gallery" nearby. I've recently noticed that Emperor can "scratch" with two fingers right at the moment I ask Elf a question with an answer of two. Or Emperor has neatly tucked his thumb under his chin when the answer is "four" and Elf looks over. Or, more commonly he "just can't help" yelling out the answer. It's just too tempting.
I'm solving this by sending Emperor upstairs with his GameBoy when I need Elfie math time. Poor Elf. Right now, he's finally finished with his math and he gets to colour and use his GameBoy as well. All is right with the world.