Our kids are in a public school that is generally considered to be great (it better be, given the school taxes we are paying).  Yet the math teaching is appalling compared to the teaching of English.  In English there is a huge amount of repetition of basic exercises at every level.  English is woven into other subject areas as well.  Neither of these is true for math.  There are ridiculous jumps from one level to the next.  For instance, kids are introduced to subtraction and within short order are given multi-digit problems where they need to “borrow."  There is a lack of repetition and re-enforcement before moving to the next level.  It’s not surprising that kids resort to treating math problems mechanically, which runs completely counter to the professed goal of teaching them a deep understanding of math.  When other subject areas are taught, there is an occasional math problem thrown in, but the emphasis is on building English skills.  Much of this arises from treating Math as some kind of unfortunate necessity akin to brushing your teeth as opposed to a beautiful language that can be used to think about the world and express those thoughts to others.  Approaching Math as a language would make many of the current practices stand out as wrong and suggest a myriad ways to improve teaching, like incorporating the history of math, number systems used by other civilizations and so on.