Mathematical reasoning and proving (R&P) are notoriously difficult for students at all  school levels as well as for many prospective teachers for elementary school. The latter is particularly worrying as current recommendations for school mathematics emphasise R&P as significant in their own right and as ways of supporting students’ learning of important mathematical contents. I outline the background and rationale to an intervention study that seeks to develop prospective elementary teachers’ own proficiency with reasoning and proving as well as their ways of working with these processes when teaching. The pilot to the intervention suggests that the research participants faced even greater difficulties than anticipated. We suggest balancing proving that and proving why in mathematics teacher education to address these difficulties, using tasks that arise or may be developed from school classrooms.