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Registramos uma consideravel atencao dedicada por parte dos autores de livros de Historia da Matematica (HM) concernentemente aos classicos fundamentos do Calculo Diferencial e Integral. Por outro lado, se mostra imprescindivel ao entendimento do professor de Matematica uma compreensao sobre um irrefreavel processo matematico e epistemologico evolutivo dos objetos matematicos, desde seu estadio de nascedouro ate o momento atual. Assim, o presente trabalho relata uma Engenharia Didatica de Formacao (EDF) desenvolvida com a participacao de cinco professores em formacao inicial, no Instituto Federal de Educacao, Ciencia e Tecnologia – IFCE, no ano de 2017. O tema abordado envolveu a nocao de Numeros Generalizados de Catalan (NGC) que representa uma contribuicao de varios matematicos e a pesquisa atual sobre inumeros problemas derivados confirmam seu processo de generalizacao ininterrupto. O estudo envolveu cinco tarefas e duas situacoes estruturadas de ensino, com o aporte da Teoria das Situacoes Didaticas (TSD). Os dados coligidos evidenciam varias propriedades e, sobretudo, teoremas e definicoes matematicas descobertas e formuladas pelos sujeitos participantes da investigacao o que concorreu para o incremento de suas habilidades profissionais e um conhecimento historico, epistemico e pragmatico sobre a nocao.  We have recorded considerable attention on the part of the authors of Mathematical History (MH) books concerning the classical fundamentals of Differential and Integral Calculus. On the other hand, it is essential to the understanding of the Mathematics teacher an understanding about an unstoppable mathematical and evolutionary epistemological process of the mathematical objects, from its nascent stage to the present moment. Thus, the present work reports a Training Didactic Engineering (EDF) developed with the participation of five teachers in initial formation, in the Federal Institute of Education, Science and Technology - IFCE, in the year 2017. The topic covered involved the notion of Numbers Generalized Catalan (NGC) that represents a contribution of several mathematicians and the current research on numerous derived problems confirm its process of uninterrupted generalization. The study involved five tasks and two structured teaching situations, with the contribution of the Theory of Educational Situations (TSD). The collected data show several properties and, above all, the theorems and mathematical definitions discovered and formulated by the subjects participating in the research, which contributed to the increase of their professional skills and a historical, epistemic and pragmatic knowledge about the notion.

educação matemática pesquisa

Engenharia Didática de Formação (EDF): sobre o ensino dos Números (Generalizados) de Catalan (NGC)&lt;br&gt;Didactical Engineering: about the teaching of generalized Catalan numbers