In this paper we conceptualise Lakatos-style proof instruction (LSI) as a teaching approach based on the formulation and refinement of conjectures through the examination of supportive examples and counterexamples. We identify aspects of mathematical knowledge that LSI requires from teachers (MaKTeLaP) in relation to content, student perceptions and teaching practices, and we report findings of ten primary school teachers’ MaKTeLAP based on in-depth, vignette-based interviews. Participants’ responses indicate satisfactory content knowledge, intermediate knowledge of teaching practices, and weak knowledge of students. This study offers a theoretical basis for further research on the incorporation of LSI into the classroom and on the provision of support for the development of teachers’ MaKTeLAP.