This paper describes an experience carried out in pre-service teacher education, aiming at the development of algebraic thinking of future kindergarten and elementary school teachers, held over a six-month period in a course of thethird year of the bachelor's degree in education. Teacher education at this level faces very specific dilemmas, including the separated or integrated treatment of contents and didactics. Using a design research methodology, we applied data from the case studies of three prospective teachers showing how they solved algebra tasks involving pictorial sequences before, during, and after the teacher education experience. In addition, we describe in-class episodes, relevant from the formative point of view, in order to have a global balance of the experience. We concluded that the exploratory work based on mathematical situations and real classroom occurrences, with the students' written productions and video records, and the opportunities for reflection and discussion that arose, have contributed to promote an effective development of the didactic knowledge of the three prospective teachers, and also of the mathematical knowledge of the prospective teacher with less previous mathematics training.
pre-service teacher education; algebraic thinking; sequences; generalization; didactical knowledge
