This paper analyses the relationships among researching, teaching, and learning in students’ mathematics learning and in teacher’s professional practice. It also pays attention to the concept of task, taking into account the role of exercises, problems, investigations, explorations and projects in the teaching of this discipline. Using examples from activities carried out by Portuguese mathematics teachers, it analyses the learning activity that was promoted by exploration/investigation tasks and discusses their potential. Finally, it refers the conditions regarding the teachers’ professional culture, notably collaboration and associative activity, that favour the culture of researching his/her own professional practice.