Rocha, H. *A perspectiva de futuros professores sobre a demonstração matemática*. XV Congresso Internacional Galego-Portugués de Psicopedagogia. Corunha, Espanha: Asociación Científica Internacional de Psicopedagogía, 2019.

AbstractThe mathematical proof is assumed as a central element in the development of Mathematics. However, proof is conceived in different ways and assumed as having different functions in Mathematics. And when we move from mathematics to its teaching, the multiplicity of perspectives becomes even more significant. This diversity can have an impact on the students and on the relationship they establish with Mathematics. In these circumstances, this study seeks knowledge over the perspectives of future teachers regarding the mathematical demonstration. Specifically, it intends to achieve a deeper knowledge over the future teachers’ perspectives about what is a mathematical proof and about its functions. The study adopts a qualitative approach and uses interviews to collect data. The conclusions reached point to a traditional perspective of mathematical proof, closely tied to mathematical formalism and the validation function, where the teaching context introduces some changes, adjusting the formalism to the level of the students and highlighting the understanding function of proof, but maintaining the dominant character of the algebraic language.

Rocha, H. "

Pre-service teachers’ knowledge: impact on the integration of mathematical applications on the teaching of mathematics."

*Science and mathematics education in the 21st century*. Eds. L. Leite, and et al. Brussels: ATEE and CIEd, 2019. 26-37.

AbstractMathematics is present everywhere. However, uncovering the relevance of Mathematics requires, from the teachers, a special kind of knowledge. This study tries to characterize the knowledge used by pre-service teachers when developing a mathematical task intending to promote the students’ exploration of barcodes. The study adopts a qualitative and interpretative methodology and the data were collected using class observation and interviews. The analysis is guided by the Application and Pedagogical Content Knowledge, a model inspired on TPACK (from Mishra and Koehler) and MKT (from Ball and colleagues). The conclusions point to some difficulties to see the potential of the situation to promote mathematical learning. The knowledge on the mathematical content seems to be dominant on the options assumed and operated in a rigid way that prevent the pre-service teachers from exploring the richness of the situation on the tasks they developed.