This commentary reviews each of the three content chapters in the integers section and offers questions to promote further discussion. In addition to the themes raised in the three chapters, I introduce the role of formal mathematical structure in generalizing systems of number, from natural numbers to integers, and analogously, from real numbers to complex numbers. Integers, in particular, are structured by algebraic relations, which imply, for example, that (-1) · (-1) = 1. Historical observations and anecdotal evidence of children's reasoning pertaining to this role raise important cognitive, pedagogical, and metaphysical questions. [For the complete volume, "Constructing Number: Merging Perspectives from Psychology and Mathematics Education. Research in Mathematics Education," see ED616587.]