Our mathematics cognitive technology noticing framework is based on professional noticing and curricular noticing frameworks and data collected in a study that explored how secondary mathematics teachers evaluate technology. Our participants displayed three categories of noticing: attention to features of technology, interpretation of the features, and response to these features. We believe this framework can potentially allow researchers to document the evolution of teachers' evaluation of mathematical cognitive technologies and examine how the inclusion or exclusion of particular features of technology influences their evaluation and subsequent selection of technology. [For the complete proceedings, see ED583608.]