The NY Times has had a series running on math and science education. There was a comment in a response about expecting students to learn algebra without knowing "times tables.
Now, in my experience, this whole "times table" thing has always been a rote memorization experience designed to torture elementary school students. That is an example of what is totally wrong with teaching mathematics, or maths as they say in the rest of the world as their isn't just one. In 50 years of working with subjects mathematical I don't think I've ever remembered those "times tables" that we chanted in what I think was a 2nd grade or 3rd grade classroom.
Students need to learn what these abstract concepts like 7 x 3 mean and develop their own heuristic skill set to work the problems. But then, even that is the real critical missing piece in learning classical Algebra. The really important missing skill in mastering Algebra is fractions. I've taught a little Algebra and wrestling with fractions is the real hurdle for most students because in Algebra, those damn fractions come at you from every direction.