Teachers participate in social networking sites to share knowledge and collaborate with other teachers to create education-related content. In this study we selected several communities in order to better understand the networks that these participants establish in Twitter and the role that the social network plays in their activity within the community, especially related with peer production. We analyzed the topology of these networks in two ways: a) the indirect relations by counting "followers" and "followed" people; and b) the conversational networks by counting mentions in "tweets." We also analyzed the communities' websites in order to elucidate whether their production was lightweight or heavyweight peer production. Results indicate that teacher networks adopt a community clusters archetype in which some teachers act as bridges between several groups. Although these networks do not form a tight crowd, their degree of tightness is superior to that of the general networks established in Twitter. Our results also indicate that the degree of tightness is important for sustaining heavyweight peer production and strong leadership can play a crucial role in establishing long-term commitment to a collective task.