Steinecke sustained massive injuries during the collapse and was Life Flighted to UTMB. Two other workers, Cody Key, 26, of Conroe and Escolastico Mendez, 44, of Houston, suffered less severe injuries. They were both treated and released from UTMB.
Police say all three injured workers are believed to work for P&C Construction Erectors of Porter.
According to its website, the high school is building a new auditorium on the site. The school is on Spring Break this week.
Police do not know the cause of the collapse. The incident is being investigated by OSHA, police say.