An embodied view of mathematical cognition should account not only for how we use our bodies to think and communicate mathematically but also how our bodies equip us to conceive of mathematical ideas. Research in cognitive semantics claims that the human conceptual capacity rests on a foundation of image schemas: topological patterns of spatial relations and simple dynamics abstracted from sensorimotor experience. A cognitive ethnography of elementary mathematics lessons in clock-reading reveals different image schemas used to read the hour for landmark times ("three o'clock"), relative times ("a quarter past three"), and absolute times ("three fifteen"). When considered together with the sequence of learning, the image schema analysis predicts the most common error observed in children's time-telling while also revealing the source of latent errors that lead to sudden breakdowns. Comparison of the image-schematic structure of different levels of sophistication in reading "quarter past" times illustrates how enriched image-schematic structure interrelates different aspects of time-telling, supporting flexible performance in novel situations. Relating visible actions to these aspects of ongoing conceptualization will help experts provide a more complete account of embodied mathematical cognition, teaching, and learning. (Contains 8 footnotes, 3 tables, and 10 figures.)