A group of Swedish teacher educators conducted a learning study in order to identifycritical features concerning the teaching and learning of Mathematical knowledge forteaching (MKT). Three seminars and 300 tests were analysed using variation theoryrevealing four critical features to take into account in teaching student teachers inmathematics education: namely their need to i) formulate proper goals for a lesson, ii)outline the lesson plan in detail, iii) shift perspective from the role of being a teacherto being a mathematics teacher, and iv) understand the underlying mathematicsof the lesson topic at hand. Thus, these are the four features of importance to thelearning and teaching of MKT.