Mathematical knowledge and professional noticing of prospective teachers in the context of pattern generalization. Characterization of Profiles

The aim of this research is to study the relationship between mathematical knowledge and teacher competence of professional noticing of children's mathematical thinking in the context of generalization of patterns. For this purpose, 40 prospective teachers (PPT) were asked to solve a problem of generalization of patterns and to describe and interpret the answers of three elementary students to the same problem. The resolution of the problem allowed to determinate the degree of knowledge of the PPT and the ability to interpret the students' comprehension from the identification of the significant mathematical elements in the students' answers allowed to determine the degree of competence. From the analysis of the skills to identify and interpret were generated descriptors to characterize four profiles in the development of the competence, which were later refined by incorporating knowledge descriptors. The research evidenced that the PPT with low level of knowledge, and some with a sufficient level of knowledge, were not able to interpret the comprehension of the elementary students, therefore, although the mathematical knowledge of the content is necessary to have a professional noticing, this knowledge does not guarantee the teaching competence. The materials used and the inferred trajectory can be used as a reference to compose teaching modules about the competence of professional noticing of children's mathematical thinking in the context of generalization of patterns.