Knowledge for teaching justifications and proofs for future Mathematics teachers

This article presents part of the discussions and results of a doctoral research project that analyzed issues related to the initial education of future math teachers, concerning the selection, organization, and preparation of situations that promote students’ academic learning of fundamental ideas related to justifications and proofs. This study involves a group of ten pre-service teachers who attend the Federal University of Sergipe. The first phase of data collection involved the application of diagnostic instruments. The second phase, named the ‘training process’, was carried out following principles of the Design Experiments methodology and aimed to investigate how activity sequences exploring knowledge about proofs, from a didactic and curricular perspective, foster new meanings for learning concepts and attitudes. To consider theoretically the knowledge that a mathematics teacher should possess, we considered the categories by Ball, Thames and Phelps. The answers by future teachers to the diagnostic instruments revealed a certain cautiousness regarding the inclusion of proofs in school curricula. Discussions and reflections on learning situations, proposed during this phase, broadened the knowledge base necessary for mathematics teachers and gave new meaning to working with proofs