More on our failing teachers

Coryoth of kuro5hin shares the concerns I noted earlier this week.

The real tragedy is that, because mathematics is a heavily layered subject, each new topic building upon the previous ones, once students fall behind catching up can be a nightmare. Indeed, students often meet a rude awakening in late high school or at college when their limited mathematical repertoire fails to provide the necessary tools to fully grasp the next topic. Even worse, by failing to impart the core skills of abstraction, and logical systematic approaches to dealing with abstract objects, we are denying students the very skills necessary to even begin to expand their mathematical toolkit. At its heart mathematics is about abstract and logical thought, and without these core skills no student can hope to succeed in mathematics.

This elaborates on a point I had made.

...down the road, they need a mastery of the standard algorithms... To understand the more advanced mathematics, I definitely needed the basics. Middle school teachers cannot be expected to have to teach students why multiplication and division work because they did not learn by the fifth grade

And I think we are already seeing the results. They were sure there would be 100,000, but they cannot even seem to count.