Dynamic epistemic logic allows us to model agents who learn new information about the world from events which they observe. In this paper, I add a backward-looking modality to the dynamic language, to allow for our expressing statements about what an agent knew before an event took place. This allows us more completely to model what an agent learns from an event, since we can now talk about the difference in their knowledge before and after its occurrence. It is known that the addition of forward-looking temporal modalities require restrictions, since allowing for infinite forward iteration causes undecidability. However, our product update models have only finite pasts, which makes backward-looking modalities much more manageable. Yet they still allow for a rich increase in expressive power.