Didactic-Mathematical Knowledge and Teacher Education: An Investigation with Pre-Service and In-Service Mathematics Teachers

Background: The mathematical and didactic knowledge in mathematics teachers’ domain should constitute a permanent focus of investigations and reflections. Objective: To investigate the development of knowledge and procedures concerning geometry teaching among pre-service and in-service mathematics teachers engaged in the final years of elementary school. Design: The investigation is inserted in a qualitative perspective and follows the assumptions of action research. Setting and Participants: Fifty-four pre-service and in-service mathematics teachers from the Brazilian city of Paulo Afonso, Bahia, participated in a teacher education process. Data Collection and Analysis: Participant observation, data collection and analysis following an analysis protocol guided by the constructs of the onto-semiotic approach; analysis of productions. Results: Development and application of 24 sequences of activities focusing on the study of geometry. High epistemic adequacy was observed based on the application of the analysis protocol concerning structuring sequences of activities. Regarding the other dimensions, concerning the analysis of the application of the activities (cognitive-affective, interactional-mediational, ecological), high adequacy was observed. Conclusions: It is relevant to invest in teacher education courses proposing the expansion of didactic-mathematical knowledge to enhance the use of different ways to teach and learn mathematics.