In this study, we investigated the relationship between teachers' post-instruction noticing (PIN) and the quality of their mathematics instruction. We analyzed the conversations of elementary teachers around five coached lessons and scored their level of post-instruction noticing and the mathematical quality of the instruction of the lesson. We compared teachers' PIN levels with their instructional quality, using scores from the Mathematical Quality of Instruction (MQI) rubric, for each coached lesson. There was both alignment and discrepancies between the level of PIN and MQI scores. Explorations of the cognitive and psychological constructs that seemed to influence teacher's noticing showed that mathematical knowledge for teaching (MKT), efficacy, beliefs, emotions, and identity was influential on teachers' PIN although they seemed to influence teachers differently. In some cases, the constructs appeared to support attentiveness to students' thinking and in other cases they did not. We discuss implications for professional development and future research on teachers' noticing.