Knowledge of teachers trainers of teachers in life trajectory and the teaching mathematics in the early years of elementary school is the subject of this narrative research based Connelly, Clandinin (2008), Benjamin (1994), Gill (2011) and others authors. Source in the literature of knowledge and professional knowledge teachers Tardif (2000, 2002); Tardif, Raymond (2000), Shulman (1986, 2005), Gauthier et al (2006), I ask as knowledge are constructed along of life trajectory teachers trainers and how manifest themselves in training practices for teaching math of teachers in initial training. The research objective is examine the construction and expression of knowledge over life experiences and training that impact on thinking and develops the practices in preparation contexts of student for be the teacher of children. Based in the dialogue with authors and constructs about the life trajectory and training (NÓVOA, 1992, 2000; MOITA, 2000) advocate that knowledge erected in each trajectory delimit ways of thinking and acting in the practices. In the narratives and us movement of mobilization there knowledge's repercussions in tune biographical and pragmatic that provides an education for teachers with particular defining features of training according to each personal history and training contexts where they occur. My interlocutors were five university professors from three universities located in Belém, Pa; who agreed to participate and work as teachers trainers of teachers in curricular activities related to mathematics. Analyses are constructed from questionnaires and semi-structured interviews, field notes, classroom observations, various documents, and narrative texts written by them. I interpret by life trajectory and professional training experiences the constitution of knowledge during each narrative outlining times in the spaces, plots, conflicts, characters. In the present analysis is presented the singularity each subject with through successive and dialogical interpretations that emerge from the implicit knowledge in the various manifestations silent or declared since the start of the acquisition of knowledge through the family, school and professional socialization in the degree course in mathematics, demonstrating knowledge in these processes; well as analyzing subsequent processes of professional socialization in professional practice, emphasizing striking and recursive experiments, and finally crowning the analytical texture about the object of the thesis discuss the pedagogical knowledge in motion or action included in the reasoning process pedagogical organized in two dimensions for which the maker movement converges for the diverse knowledge built in the trajectories investigated: knowledge of teachers trainers of teachers related to teaching mathematics and professional training for the teaching in mathematics. This movement supports the thesis that the thought and practice forming reflects their beliefs, conceptions and learning in formative processes justifying choices, attitudes and approaches taken and featuring making didactic model and is representing a model of professional training of teachers to teach mathematics in the early years of elementary school.
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