ON A WINTER DAY five years ago, Doug Lemov realized he had a problem. After a successful career as a teacher, a principal and a charter-school founder, he was working as a consultant, hired by troubled schools eager — desperate, in some cases — for Lemov to tell them what to do to get better. There was no shortage of prescriptions at the time for how to cure the poor performance that plagued so many American schools. Proponents of No Child Left Behind saw standardized testing as a solution. President Bush also championed a billion-dollar program to encourage schools to adopt reading curriculums with an emphasis on phonics. Others argued for smaller classes or more parental involvement or more state financing.