While measures of research quality are widely accepted in the education research community, there may be less agreement on what constitutes evidence of impact and on where to look for it. The aims of this symposium are to consider some key issues in undertaking the Australian government's national assessment of research engagement and impact, and to propose some approaches to evidencing engagement and impact in the context of mathematics education research. Each of the four symposium papers draws on the Numeracy Across the Curriculum (NAC) research program in order to ground discussion in specific cases of research that have been reported at previous Mathematics Education Research Group of Australasia (MERGA) conferences. The papers included in this symposium are: (1) Evidencing Research Engagement and Impact (Merrilyn Goos); (2) The Convoluted Nature of a Research Impact Pathway (Vince Geiger); (3) Engagement and Impact through Research Participation and Resource Development (Anne Bennison and Shelley Dole); and (4) "Numeracy for Learners and Teachers": Impact on MTeach Students (Helen Forgasz). Individual papers contain references.