The non-learning of school mathematics is now almost universally taken for granted, but this does not have to happen. This article takes a critical look at the root of this non-learning by pointing to the flagrant defects in the kind of mathematics--to be called TSM--that is predominant in almost all the school textbooks. By analyzing how the long division algorithm is taught and why it becomes so mystifying to school students, we explore how to provide the missing reasoning that makes sense of the algorithm. The article also suggests some concrete steps we can take to eradicate TSM.