Using a graphic calculator to promote a preservice teacher's didactic knowledge of functions

The initial teacher education courses for Mathematics aim to promote an adequate education in mathematics and mathematics didactics. Equally or even more important than this education is understanding how the preservice teacher should build new knowledge from the activities they undertake. Considering the teaching practicum, this study aims to understand the contribution of the graphic calculator that complies with the guidelines set by the Portuguese Ministry of Education for secondary education in promoting the didactic knowledge of a preservice teacher in the teaching of functions in 11th grade within the Portuguese education system. Adopting a qualitative and interpretive methodology, following a design-based approach, data were collected through her lesson plans, reflections and practicum report. Regarding content knowledge of functions, the preservice teacher identifies different representations and reveals knowledge of facts and procedures. In terms of specialised content knowledge, she explores the graphic calculator to connect representations and identifies different task-solving strategies. About content knowledge and the curriculum, she knows the curricular recommendations about the teaching of functions and the integration of the graphic calculator in mathematics lessons. Regarding content knowledge and students, she identifies factors that enhance or inhibit understanding and evaluates students' comprehension of the topics studied.