Descriptors of the Professional Look Development in the Context of Pattern Generalization

Abstract The objective of this research is to generate descriptors of the development of the competence of professional looking into children's mathematical thinking for prospective teachers (PPT) in the context of pattern generalization. To this end, future teachers were asked to describe the answers of Elementary education students to one problem of the pattern generalization, interpret the students' understanding and propose actions to improve or enlarge the teaching-learning process. From the skills that conceptualize the professional look (identifying, interpreting, and deciding) descriptors of four development levels were generated: (1) PPT that does not identify the relevant mathematical elements in the process of pattern generalization, (2) PPT that identifies the mathematical elements, but does not use these elements to interpret the students understanding, (3) PPT that identifies the elements and uses these elements to interpret the students' understanding and (4) PPT that identifies the elements, uses them to interpret the students' understanding and proposes appropriate actions for the Elementary education students' learning progress. The generated descriptors and the determined levels can be the starting point in establishing a future learning trajectory of the professional look and offering information to the trainers to interpret the PPT progress in the development of the professional look competence of children's mathematical thinking in the context of pattern generalization.