Contrary to the idea that the world is broken and beyond repair, ongoing care and maintenance are primary concerns of people learning with technologies. This paper advances a perspective that an ethic of care has epistemic significance and locates families' caring practices in technologically-mediated home learning environments. I develop this perspective on human-technology relations, which I call "cherished world thinking," as a response to social-ecological perspectives on "broken world thinking" (cf. Jackson). I frame family learning through critical care studies and feminist epistemologies, focusing on sociotechnical dimensions of care and maintenance. As I consider how families enacted care for and with their cherished technologies, I interrogate the social-ecological conditions that are simultaneously held in place through maintenance. Drawing from ethnographic data of 13 families in 2 US cities--including fieldnotes, informal interviews, and video collected in homes and neighborhoods--I found that families engaged in "cherished world thinking." I develop this concept through interaction analysis of two cases where families caring for each other and their environments were sociotechnical achievements, calling attention to forms of learning that emerge when people care for that which they hold dear.