CASTRO VALLEY, Calif. — Jeffrey Esquivel let go of his mother’s hand and slowly brushed a miniature donkey, the only moment at his school’s Halloween carnival that the first-grader with autism stepped outside of his shell.

It was a contact with the world his mother, Helen Esquivel, deeply wishes he could learn more about in school, but for most of last year and so far this year, the 6-year-old had no credentialed special education teacher for his class at Proctor Elementary School.

Like many school districts, Castro Valley Unified has had a shortage of specialized teachers, especially special education ones. The demand for special education teachers nationwide has grown, as more children are diagnosed with autism.

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“Early intervention is key with autistic children. Jeffrey’s not getting the intervention he needs,” Esquivel said. “He used to talk more. He doesn’t make eye contact as much as he used to.”

Jeffrey’s older brother, Jesse Esquivel, also has autism. But a special education teacher working with him during his kindergarten and first-grade years helped the 8-year-old, and he may transfer to a class for children with mild and moderate special needs, Esquivel said.

“My older son couldn’t say, ‘More, please.’ He couldn’t put two words together. Now he’s speaking sentences and talking with people. Before, he wouldn’t wear clothes; he would strip them off. Now he dresses himself and puts his clothes away,” she said.

“Autistic kids can get better, but they need trained teachers,” she said.

At the carnival, Jesse dove into a bounce house obstacle course and played with other children inside. But Jeffrey stood and held his mother’s hand, silently watching, then staring at the ground.

Castro Valley Unified has been trying to hire special education teachers, said Assistant Superintendent Mary Boyle. The district even contracted with an agency to fill some spots, she said. The district also has been using substitutes and teachers who are in training.

“It’s not an ideal situation,” she said.

The good news for Jeffrey and the other Proctor students, Boyle said, is that the district found a credentialed special education teacher who has experience with children with autism and will be starting soon.

Schools historically have had trouble finding special education teachers, and it has become more difficult, said Boyle, who was a special education teacher herself.

“When I went into teaching, it was hard to find a job. So I went into special education and never looked back; there were jobs to be found,” she said.

Most area school districts are experiencing shortages of teachers, especially in specialized areas.

“It’s challenging to find teachers with credentials in special education, science, math and foreign language. It’s a very competitive market for those teachers,” said Oakland Unified spokesman Troy Flint.

Finding substitute teachers for specialized areas is even harder, said Fred Brill, San Lorenzo Unified superintendent.

More children are being diagnosed with autism, which increases the demand for special education teachers.

The result is that school districts have to have more special classes with small class ratios and aides for students with special needs, Brill said.

“The numbers are staggering,” he said.