Feynman beautifully summarizes the problem with 'rigor' in primary and secondary math textbooks

From the previously mentioned essay by Richard P. Feynman, this does a perfect job boiling down the reaction that teachers with math backgrounds so often have to the books they're told to teach from.

It was a pretty big job, and I worked all the time at it down in the basement. My wife says that during this period it was like living over a volcano. It would be quiet for a while, but then all of a sudden, "BLLLLLOOOOOOWWWWW!!!!" -- there would be a big explosion from the "volcano" below. 

The reason was that the books were so lousy. They were false. They were hurried. They would try to be rigorous, but they would use examples (like automobiles in the street for "sets") which were almost OK, but in which there were always some subtleties. The definitions weren't accurate. Everything was a little bit ambiguous -- they weren't smart enough to understand what was meant by "rigor." They were faking it. They were teaching something they didn't understand, and which was, in fact, useless, at that time, for the child.