Lecturing is the main method of teaching mathematics in Iran and many countries across the world. In the past two decades, several attempts have been made to change this approach to more active student-centred approaches. In this workshop, we talk about the principles of inquiry-based teaching and learning and share some mathematical examples that can be used for teaching mathematics at the university level. The examples that will be discussed have been used for teaching vertex colouring in a graph theory course in an Iranian university. In this workshop, we also kindly ask participants to design some inquiry-based tasks

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