This article begins from the premise that it is important to explore how people unlearn, as well as learn, specifically in terms of extremist or violent attitudes. It shows the implications of two aspects of complexity theory--turbulence and self-organisation--for educational practice and the fostering of a complex adaptive school, which can aid peacebuilding. Positive turbulence for adaptation requires interruptive democracy, the habits of dialogue and dissent, and learning resilience to offence. Self-organisation relates to the current phenomenon of horizontal networking, in particular the use of social media by young people, and the new democracy of messaging. Three different country examples are given of intergroup encounters that interrupt rigidities in attitudes: working across ethnic groups in Sri Lanka, tackling religious divides in Northern Ireland through shared classes, and initiatives to prevent violent extremism in the United Kingdom. Pedagogical implications of unlearning involve working with the four Ds of deradicalisation, debiasing, disengagement and desistence. This involves disturbing essentialising categories of "others" and of good and evil, as well as capitalising on horizontal participation in social action--that is, learning skills and competences around movements for change that do not involve violence.