In 1996 when I became a professor at the Royal Danish School of Educational Studies in Denmark, I was invited to give a lecture to a large group of mathematics teachers. As it happened, I did not have much time to prepare my presentation, but I felt confident that it would all come out well. I do not remember the exact title of the lecture, but the topic was project work in mathematics education, and how this might relate to the outlook of critical mathematics education. I had very many examples to draw on with respect to elementary and secondary education, as well as to university education. Since 1982 I had been working at Aalborg University, where all study programmes, including mathematics, were project-based.However, I could not stop myself from worrying a little. At that time in Denmark, the discussion of project work had taken on a predictable format. It was emphasised again and again that the starting point of such projects had to be embedded in real-life problems—if possible, problems formulated by the students themselves—and that the students had to be working in groups. The teachers had heard such recommendations many times before, and this was exactly what I had planned to say. The teachers also knew in advance what questions they were going to ask, and so did I: how do you address the solutions of quadratic equations through real-life problems? How do you find time to cover the curriculum through project work? What do you do if the students do not like working in groups? How do you prepare the students for tests and exams?