Cybersafety has been a mainstay of digital education since computers arrived in classrooms in the mid 1990s. Whether schools encourage students to be "cybersmart" (Australia), "netsafe" (New Zealand) or to be aware of "cybersecurity strategies" (Mexico and Chile) most now devote a relatively large amount of time and money to teaching young people how to "stay safe" online. In this article, we argue that it is time for schools to move beyond the cybersafety discourse to encourage students to think more critically about the digital media they use. Reporting on the digital practices of 276 pre-teens aged 7-12 years in Australia and Uruguay, we contend that the everyday digital challenges young people face are now beyond the scope of most cybersafety programs. Our findings highlight that many of the issues preteens are negotiating call for more nuanced and sustained educational programs that support the development of "critical" social media literacies. In particular, with the proliferation of mass user platforms and artificial intelligence, there is a need for schools to educate students around managing and protecting their personal data. The article concludes with a discussion of the digital learning required for young people in an increasingly datafied society.