Mathematics teacher training is intended to inculcate teaching skills for success in all learning levels. The aim of this study is to examine the questions: Which factors contribute to the successful assignment of teachers to learning levels? Can teachers teach all levels or only some? The findings should help to clarify which factors to consider for the proper assignment of teachers. Three hundred and twelve academic mathematics teachers were asked about their suitability to teach low and high levels of mathematics, feelings of teaching efficacy, attitudes toward high- and low-achieving students and efficacy and preferences in teaching underachievers. Extensive information was collected about their mathematics education. As most high school students are tested at the low level, most mathematics teachers are assigned to this level. Many more mathematics teachers feel suited to teach the high level rather than the low level. Factors explaining the success of teachers in the various levels were assessed. Academic educational level was not among the factors. The hypothesis is examined that new ways of thinking are required for developing teacher efficacy for lower mathematics levels. It is doubtful whether solely expanding teachers' academic education will attain this objective. Principals are offered educational considerations for the optimal assignment of teachers.