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Mexican authorities and universities are actively working to improve mathematics teaching and learning across the education system. Thus, efforts are underway to raise the historically low performance in mathematics, which include theoretically grounded pedagogy and curriculum development to raise mathematical knowledge in teacher education programmes. The purpose of this article is twofold. Firstly, I give an overview of the educational system in Mexico by outlining the evolution of the mathematics curriculum and teacher preparation programmes. Secondly, I describe and discuss, from my own practice, a lesson using dynamic tools for helping prospective teachers to understand the relationship between integration and differentiation within the context of the current literature from Mexico and abroad. While Mexico faces distinct issues within its educational system, challenges in how future mathematics teachers understand mathematical content appear universal. Thus, teaching mathematical content while modelling effective mathematical pedagogical practices is of relevance to all of us striving to enhance the quality of future mathematics teachers.