Pedagogic focus is shifting increasingly from teaching students to search the Internet efficiently to encouraging critical Internet literacy, but this paper argues that these more complex and subtle skills are both challenging to teach and difficult to identify. The paper presents an analysis of the discourse of triads of fifth graders undertaking an Internet search task that emphasised decisions relating to the trustworthiness and relevance of websites. The analysis uses two lenses -- the Vygotskian concept of "obuchenie" and Mercer's notion of 'inter-thinking' -- to help identify discourse markers that could support teachers in identifying and teaching critical Internet literacy. More work is needed, but it is argued that if our goal is to develop critical Internet literacy, the concept of obuchenie helps us to understand the socio-cognitive prerequisites of group learning in Internet searching tasks, while the concept of 'interthinking' offers us a distribution mechanism that can be applied in helping students acquire the skills of independent and critical analysis as they carry out those tasks.