Various social and political factors within the school environment influence how teachers ultimately design their teaching and also their motivation to bring innovation into the classroom. The paper presents results of math teacher interviews about their vision of ideal mathematics teaching. From these answers, conclusions can be drawn about teachers' potential for bringing innovation into the classroom and the factors that might hinder them. Three different types have been derived, with varying levels of motivation to participate in in-service teacher training and to further develop the teaching. Teachers that like to teach in the way "it has always been done" show the least potential, in contrast to the idealists among teachers, who align their teaching with their high standards to design lessons that they believe best for their students' learning. To narrow the theory-praxis gap, the focus should be on the third type of teacherthe struggling oneswho need support to stay true to their ideals and to avoid adapting to more traditional patterns.