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We aim to identify what prospective mathematics teachers indicated that they learned regarding mathematics and mathematics teaching as they participated in a lesson study. The theoretical framework is supported by models about teachers' knowledge and prospective teachers learning processes. The methodology is qualitative and interpretative, with data collected by interviews and documents made by participants. The participants indicated to understand the importance of different representations in mathematics. They also indicated to appreciate the value of the detailed planning of the lesson, the careful selection of tasks, the analysis of possible student strategies and difficulties, and the preparation of classroom communication. [ABSTRACT FROM AUTHOR]

The research, guided by the question "What professional knowledge is mobilized in a Calculus lesson study conducted with university instructors?", involved eight instructors from higher education institutions in southern Brazil who are dedicated to the training of prospective mathematics teachers. The lesson study, structured in twelve weekly two-hour meetings, addressed the topic "maxima and minima". The qualitative analysis showed that the approach and dynamics of lesson study mobilized and deepened professional knowledge regarding mathematics, mathematics didactics and the mission of the trainer of future mathematics teachers. [ABSTRACT FROM AUTHOR]