...trying to teach calculus to 3rd and 4th graders. Let me tell you a story... One of my sons had ADD (or that's how he was mis-diagnosed at the time.) Very intelligent. In the 4th grade, they taught the kids to do math in their HEADS. He did great with it, and he eventually got to the point of just answering the math questions and not showing his work. Alright, he made it through the next few grades. Low and behold, he arrives at his freshman year of high school algebra. He never showed his work. Always got the answers right, but the teacher actually flunked him because he didn't show his work, in spite of his correct answers. And "F" in math, in his first year of high school! (He had never made a "C" or "D" in his entire previous 8 yrs in school in ANY subject!) No, the teacher didn't contact me at any point and ask me to encourage him to show his work. The "F" woke him up. He did have to take the class again, did show his work and got an "A" in the class. As a matter of fact, all of his grades shot up as he proceeded through HS. He went on to graduate from college with high grades.
I'm sorry people, I think PO did the wrong thing by putting so much faith in Arne Duncan's way of looking at education. The education of our children should never be gambled with/sold to the highest bidder and slickest debaters of privatization. We need to back up this education ship about 15 years and start over again.
K&R