Marisa Renteria, mother of a 3-year-old and a newborn, recently saw her son’s vocabulary drop from 50 words to 10; he was diagnosed with speech delay. After attending school, her son’s vocabulary sprang back to 60 words. But since schools have closed with no end in sight, Renteria worries that her son may regress and has seen hints of it.

“School really helped with progressing his speech,” Renteria said, “even his social interactions. He doesn’t have cousins or...