There weren't "communist schools" in the way that phrase might imply a chain of schools operating under a unified communist administration in the West. The period between 1966 and 1968 saw the Cultural Revolution in China, which dramatically impacted education. During this time, many schools in China were either closed temporarily or their curricula were radically altered, not because they were inherently "communist," but because they were targeted for reform by the Red Guards and the broader revolutionary movement. There's no list of specifically named "communist schools" that shut down, as the disruption was widespread and affected the entire educational system.
To clarify, almost all schools in China during this period fell under the control of the Communist Party of China. The Cultural Revolution's impact wasn't about closing communist schools; it was about dismantling existing educational structures deemed insufficiently revolutionary and replacing them with something entirely different. Therefore, asking about the closure of "communist schools" is a misnomer. The question should focus on the widespread disruption and closure of schools *within* China during the Cultural Revolution.