What does it mean to teach Mathematics for understanding? When to tell and when to listen

This article explores the question, 'What does it mean to teach mathematics for understanding?' in the context of the recent South African curriculum reforms. We report on lessons taught during an action research collaboration between Gerty, a female secondary mathematics teacher, and Satsope, a mathematics educator and first author of the article. We analyse detailed vignettes of three lessons from Gerty's Grade 9 mathematics teaching in a village school, focussing particularly on the problematic issue of the role of telling (and listening) in teaching and offer some observations about how understanding can be promoted in mathematics classrooms.