Boundaries between formal and informal learning settings are shaped by influences beyond learners' control. This can lead to the proscription of some familiar technologies that learners may like to use from some learning settings. This contested demarcation is not well documented. In this paper, we introduce the term "digital dissonance" to describe this tension with respect to learners' appropriation of Web 2.0 technologies in formal contexts. We present the results of a study that explores learners' in- and out-of-school use of Web 2.0 and related technologies. The study comprises two data sources: a questionnaire and a mapping activity. The contexts within which learners felt their technologies were appropriate or able to be used are also explored. Results of the study show that a sense of "digital dissonance" occurs around learners' experience of Web 2.0 activity in and out of school. Many learners routinely cross institutionally demarcated boundaries, but the implications of this activity are not well understood by institutions or indeed by learners themselves. More needs to be understood about the transferability of Web 2.0 skill sets and ways in which these can be used to support formal learning.