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This study focuses on the research question: How do prospective elementary school teachers (FT) make decisions when considering the algebraic thinking of 9-year-old children? A specific type of noticing was used to describe the decisions of 21 FT when observing the strategies employed by 3 children to solve the equation 6+4=+5. The FT participated in a six-session course on the teaching and learning of algebra, based on video analysis as a means to approach teaching practice. Focusing on sessions 1 and 2, the written responses of the FT to two distinct questions were examined. The main results show that, although the FT's decisions frequently lacked evidential support, their reasoning aligned with specific aspects of algebraic thinking and research covered during the course. Finally, two positions adopted by the FT in decision making were identified: a) arithmetic, centred on the calculations that children should follow, and (b) relational, focused on the interplay of operations through the equals sign. The role of noticing and video analysis as tools to bring future primary school teachers closer to the practice of teaching algebra in primary education was discussed. [ABSTRACT FROM AUTHOR]

Problem solving is central in teaching and learning of mathematics, an accepted premise in the community of mathematics educators. However, the frameworks that describe or characterize teachers' knowledge have given little relevance to this process. Starting from curricular and theoretical revisions, we present a proposal of organization for the knowledge of primary teacher about problem solving. We differentiate a knowledge of the process from which the components related to the concept of problem, resolution process and disposition to face a problem emerge; and a pedagogical knowledge where we distinguish a component referring to learning and another to the teaching of problem solving. Our reflection confirms the idea that the different nature of a process such as problem solving, causes a knowledge that the models have omitted. [ABSTRACT FROM AUTHOR]