Knowledge gaps and biased beliefs concerning both climate change and climate policy represent major obstacles to the decarbonization process. Climate education may offer a scalable solution to address such obstacles. In the context of a national reform of the school curriculum in Italy, we implemented a nationwide field experiment, training thousands of secondary school teachers across thousands of schools using a staggered design. Our intervention, a comprehensive course on climate change and climate policy, goes beyond the light-touch interventions typical in the literature. Using extensive survey data, we examine how training affects teachers' knowledge, beliefs, attitudes, behaviors, and policy preferences and, in turn, those of students. Our study highlights important initial knowledge gaps and biased beliefs about climate change among teachers and students, and provides evidence that climate education can address them at scale. Following our intervention, teachers and students also reconsider their support for climate policies.