Concept cartoons are cognitive drawings or "visual disagreements" that use a cartoon-style design to present mathematical conversations inside speech bubbles. The viewpoints portrayed are all different and it is this difference that acts as a catalyst for further conversations, as learners talk together to discuss their thinking. They make learners' ideas about mathematics explicit and they make mathematics interactive and discussion-based. As formative assessment tools they have real virtue because they are a highly effective way of probing learners' mathematical conceptions and, crucially, their misconceptions. In this article, the author describes how he uses concept cartoons to advance his learners' understanding of mathematics.