As a mathematician, throughout my academic life I have taught basic mathematics courses for engineers and advanced mathematics courses for applied mathematicians at undergraduate and graduate levels at the University of Chile. In 2008, as a professor of calculus for engineers, I had an experience that marked a change of direction in my work as a teacher and researcher. Although I had participated in several projects related to education, specially devoted to the development of standards and writing mathematics textbooks for prospective mathematics teachers, this was a very different experience. In my department it was decided to make changes in the calculus course by replacing the auxiliary class, a situation in which an advanced student solves problems for the students, with a tutorial following ideas that a colleague had seen in French universities. The tutorial took place in a room with tables for group work and students were expected to collaboratively solve a list of problems. In these tutorials I had the opportunity to observe engineering students solving mathematics problems, I could see their mistakes and successes, I could see how long it took them to solve a problem, and I could observe how they communicated and reasoned. It was something very different from anything I had experienced before as a teacher.