Teachers interested in developing students’ possibilities to take part in joint discussions in problem-solving often have to deal with challenges regarding norms in the mathematics classrooms. Dominating classroom norms is a factor in mathematics teaching, be it of social or sociomathematical type. Here we address challenges in relation to norms experienced when attempting to create possibilities for mathematics learning, starting at a general and algebraical point rather than a specific and arithmetical one. We draw on two projects that explored the Elkonin-Davydov curriculum in Swedish classrooms. The results indicate that norms, of different kinds, are impedimental in different ways, when performing a theoretical work in mathematics teaching.