AAC n.º 02/SAICT/2017 e PTDC/CED-EDG/28022/2017 | [REASON] Raciocínio Matemático e Formação de Professores

To be able to have success in mathematics, a key school subject, students must be able to reason mathematically in a fluent way. To help students to develop this capacity, teachers need to understand the nature of mathematical reasoning and to use instructional strategies that promote it. To achieve that, they must provide students the opportunity to work on mathematical tasks which simultaneously require reasoning and stimulate its development, as well as to reflect on the reasoning undertaken. However, in most cases, mathematical reasoning processes are not addressed in an explicit way in mathematics classrooms. This leads to the need of a focused professional development work to support teachers in developing the knowledge and ability to promote their students? mathematical reasoning. Therefore, the aim of this project is to study the mathematical and didactical knowledge teachers need to carry out a practice that promotes students? mathematical reasoning and study ways to foster its development in prospective and practicing teachers of primary (grades 1-4 and 5-6), middle (grades 7-9) and secondary (grades 10-12) school. The design and implementation of instructional strategies that may foster students? mathematical reasoning is a rather complex task for teachers, requiring specific knowledge of mathematical processes as well as of mathematical content. Previous research carried out in different countries as well as by the project team members provides insights into key aspects of students? mathematical reasoning in topics such as numbers, algebra and geometry that will be used in the present project. Based on this knowledge, the project will prepare and conduct four teacher education experiments following a Design-Based Research approach. An experiment will involve practicing teachers of primary education and, another, teachers of middle and secondary school. A third teacher education experiment will be carried out with prospective teachers of primary education and a fourth teacher education experiment with prospective teachers of middle and secondary school. Drawing on the materials produced for the teacher education experiments and on the data generated on these experiments, the project will produce four booklets to be used by teacher educators and by practicing mathematics teachers to set up learning environments that support the development of students? mathematical reasoning. The project will undertake the dissemination of its results and perspectives both to mathematics teachers of all school levels and teacher educators and also to the general public, in order to show the importance of developing students? mathematical reasoning and supporting teachers and prospective teachers in creating the classroom conditions to foster such development.