Re-education is the name of the process: teaching people again so they think or behave in a new way. It is a noun, so you can have a re-education programme or a period of re-education. Like the verb, it has a soft use and a hard use. A workplace may offer re-education on safety rules, meaning a short course to change old habits. Though actually, in news and history the word is often heavier. Forced re-education, or a re-education camp, means the state is pushing people to drop their old beliefs. Learners who only know the gentle “teach again” sense can miss that chill. It names the process or the policy, not one lesson in class. British spelling often keeps the hyphen (re-education); American spelling often writes reeducation.