Background: Initial teacher education (ITE) research in South Africa shows gaps in preservice teachers' (PSTs) primary mathematics knowledge. Aim: We study the mental mathematics understandings and teaching experiences of three PSTs who achieved high gains for learners they taught mental mathematics to using the Mental Starters Assessment Project (MSAP) jump strategy materials. Setting: The three PSTs, from one urban university, taught the jump strategy to Grade 3 classes in three different Gauteng schools. Methods: Learner pre- and post-tests around the taught unit provided the basis for categorising the three 'high gain' PSTs. Extended interviews with each PST were then transcribed. Initial grounded analyses of these data were subsequently overlaid with categories drawn from the mathematical knowledge for teaching literature. Results: All three PSTs indicated relatively strong common content knowledge of jump strategies and connected specialised content knowledge. They also exhibited strong awareness of the MSAP content. They differed in how they saw the relationship between fluency, calculation and equivalence tasks. Conclusion: The study's findings indicate the need for more explicit attention to the connection between mental maths fluencies and strategic calculation in ITE. Contribution: The study points to ways in which mental mathematics can be understood and taught for strong learning gains.