Caleb Stewart Rossiter, a college professor and policy analyst, decided to try teaching math in the D.C. schools. He was given a pre-calculus class with 38 seniors at H.D. Woodson High School. When he discovered that half of them could not handle even second-grade problems, he sought out the teachers who had awarded the passing grades of D in Algebra II, a course that they needed to take his high-level class. There are many bewildering stories like this in Rossiter’s new book, “Ain’t Nobody Be Learnin’ Nothin’: The Fraud and the Fix for High-Poverty Schools,” the best account of public...