Research shows the salient place of mathematical teaching talk, including the mathematical-linguistic practices of naming and explaining, in the enactment of students' mathematical talk and learning with understanding in the classroom. Our study was developed to examine the noticing of two groups of secondary-school mathematics teachers in one-day workshops with tasks about these practices. The two workshops were mathematically content-specific, with teaching and learning accounts and prompts aimed at guiding focused attention to naming and explaining in the teaching of linear equations and probability. Thematic text analyses led to identify three foci of the two groups' noticing: (i) missing practices of mathematical naming in own teaching talk; (ii) relative impact of mathematical explaining in teaching talk; and (iii) tensions around mathematical naming and explaining in teaching talk. Our results show that the social construction of teacher noticing is a feature of noticing development that can be documented in the context of one-day workshops. Whereas time for individual thinking and responses to the tasks created a context of support for noticing development, participation in the group discussions allowed the teachers to notice nuances of mathematical naming and explaining in teaching talk unaddressed in the task prompts. The group discussions thus amplified and opened up the opportunities to develop some focused noticing on the content of the workshops, specifically in connection with the teachers' own teaching practice.