Designing the <i>encounter</i> of teachers with meanings and levels of understanding of the derivative

Previous research has shown that mathematics teachers face difficulties teaching the derivative of a function at a point. One of these difficulties revolves around the lack of materials and specialized information on this topic that allows teachers to carry out this task. Seeking to contribute to overcoming this difficulty, we describe the design of an activity oriented towards the encounter of mathematics teachers with meanings and levels of understanding of the derivative of a function at a point. The design is theoretically founded on the concepts of learning and activity of the theory of objectification and incorporates relevant information in the analytical, analytical-numerical, and geometric meanings of the derivative as well as the intra, inter, and trans levels of understanding of the concept. Based on these references, we describe the tasks that make up our design. We see our design as contributing to the field of mathematics education regarding the promotion of in-service teachers’ learning from an historical-cultural educational perspective.