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In this paper, I present contextualizing factors, dimensions, and key markers of algorithm literacies, paying attention to the context of parenting and parenthood amidst datafication. Analyzing data from "think-aloud" interviews with 30 parents of children aged between 0 and 18, across England, I draw upon media and digital literacies scholarship to focus, first, in this paper, on the competencies, conversations, and events which contextualize parents' literacies with algorithmic interfaces. Next, I draw out four dimensions of parents' algorithm literacies including algorithm awareness, technical competencies, critical capacities, and championing their and their children's best interests, identifying practical markers for each dimension. I reflect on the broader implications of these for parenting and parenthood in datafied societies, and note that algorithm literacies are, forever, a work in progress, in fluidity and flux across the diverse courses of parenting journeys, deeply contextualized in the resources and restraints that parents encounter in their daily lives. [ABSTRACT FROM AUTHOR]