> If you disagree that that's "long" I do. Some of the words might be changed, depending on what words have been used to describe the operation of addition and

> If you disagree that that's "long" I do. Some of the words might be changed, depending on what words have been used to describe the operation of addition and the set of counting numbers. But, as I think I've pointed out elsewhere in this thread, the very fact that the children know about addition and the counting numbers means they know what an operation is ("a thingie like addition") and what a set of numbers is ("a thingie like the counting numbers"). > you seem to reject the idea of giving the one caveat at the beginning of the course I don't know where you're getting that from. I have already said the contrary--once you've said it, you don't need to repeat in every sentence.