Thanks so much for reading and for your very helpful response. I hadn't thought of the math this way, and I really appreciate your insights.
I suppose I should have added somewhere in the piece that the concept of "standards" as we have thought of them in the past may not be the best yardstick for measuring educational success. I don't mean to play semantics, but I truly believe a better way of measuring outcomes requires a paradigm shift, a different way of looking at education and defining school standards.
After watching a program recently about the higher-than-average rates of suicide, substance abuse, and anxiety among Ivy League-bound top-achievers in well-to-do communities, I think we're due for a standard that does not threaten the well-being of our children even when they succeed.
Some years ago when I was on the staff at Stanford, I was sometimes startled to hear news that a student had committed suicide over a grade. There's something wrong with that.
When Shapiro was on Real Time, he used the phrase "doing school well." Which really gets to the heart of what I'm saying. Einstein couldn't "do school well." But who cares about that now?
What we really want, I think, is a paradigm that leads our kids into greater understanding of the material they're expected to know. And maye also help them take a few steps more into the fullness of their humanity.
Thanks again for the opportunity to think about the math issue a little further. And for your willingness to consider the rest of the piece in its entirety.