Explaining the complexity of mathematics teaching to others can be challenging. The Knowledge Quartet, a pedagogical content knowledge (PCK) framework from the UK, provides a fresh lens to reflect on mathematics classroom practice. Developed from videotaped mathematics lessons taught by final year pre-service teachers, the Knowledge Quartet describes four dimensions of teachers' knowledge for teaching mathematics: Foundation, Transformation, Connection, and Contingency. Each of these categories has several indicators that may be observed in the overall process of teaching, including during planning and preparation, classroom instruction, and reflection and evaluation phases.