Through profiling and matching processes, technology provides individuals with information that becomes redundant to their previous beliefs, attitudes and preferences. The emergence of informational redundancies encouraged by some technologies is likely to influence the way knowledge is constructed by individuals in these settings. In this paper, we present a theoretical basis, rooted in cognitivist and socio-constructivist educational psychology, to characterize such knowledge-construction processes in informal settings. Learning processes in these environments are defined as cumulative: on the individual level, the most likely form of learning is through accretion of knowledge into previous schemata; on the social level, these environments foster learning through cumulative talk. We highlight the challenges that this might pose to education systems and suggest possible educational responses.