An important aim of Inquiry Maths is to develop students' ability to direct, monitor and regulate their own learning.
The model encourages students to make decisions on the approaches the class will follow, the goals it will set itself and on the selection of mathematical tools it will employ. A key question for students to answer is "What shall we do next?"
When the teacher first asks, secondary school students often find the question baffling. "Surely, that’s what you're here for – to tell us what to do," they respond. The idea that they have a role in directing learning can seem strange. Regulatory cards help students structure their thinking. Stopping the lesson and asking the class (in pairs) to discuss the selection of a card has the advantage of making students conscious of how they are regulating their learning.
Read about why students need self-regulation in maths classrooms here.