This paper presents partial results of in-service formation acts for Mathematics teachers, through Education Observatory/2010, the Graduate Program in Mathematics and Science Teaching from Universidade Luterana do Brasil, accomplished in Public Elementary Schools from Sapucaia do Sul and São Leopoldo/RS. Will be presented three trajectories with following themes: Mathematics and Environment; In-service formation and mathematics Problems Solving; and Inclusive Education. The trajectories presented lead to realize that teachers need to learn to learn to learn to teach. It is believed that the qualification of teaching practice favors that school becomes a place of equality of humans' conditions.
mathematics education; continuing education; elementary school