This paper uses the commognitive framework to analyse how a group of four primary school students classify odd and even numbers. The findings show how students' reasoning is grounded in their personal uses of "odd" and "even". The students attend to different features of "oddness" and "evenness" and agree on "which" numbers are odd and even but disagree about "why." The findings highlight the role that proving can play in signalling differences in reasoning within a group of students that may otherwise remain hidden. However, they also suggest students' awareness of the breach in communication may not be sufficient to engender a resolution, even when pedagogical moves toward this direction are made.