When Nathanael was in kindergarten, he told his mother, Diana Lopez, that he did not want to return to school — ever. His teacher yelled at him, he said. And when Ms. Lopez picked him up from school, he would often immediately start to cry.

Nathanael has autism, and in a busy classroom of 25 children, the teacher seemed to have few strategies for working with him, Ms. Lopez recalled.

This year at a new school, Nathanael, 7, was happier. He shared a teacher with only six other students —…