A Virginia company leading a national movement to replace classrooms with computers — in which children as young as 5 can learn at home at taxpayer expense — is facing a backlash from critics who are questioning its funding, quality and oversight. K12 Inc. of Herndon has become the country’s largest provider of full-time public virtual schools, upending the traditional American notion that learning occurs in a schoolhouse where students share the experience. In K12’s virtual schools, learning is largely solitary, with lessons delivered online to a child who progresses at her own pace. Conceived as a way to teach...