Quem dança com quem: o desenvolvimento do raciocínio combinatório do 2 ano do ensino fundamental ao 3 ano do ensino médio




In the present study, Primary to High School students performance and strategies were analysed (11 years of schooling) in relation to problem solving of situations that involve combinatorial reasoning, focusing on the dimensions pointed out by Vergnaud (1990): meanings, invariants and symbolic representations. With this purpose, 568 students of four schools from Pernambuco, two State and two private schools, took part in the study. The students solved eight problems that involved four Combinatorial meanings (arrangement, combination, permutation and Cartesian product), two of each kind. The results obtained were analysed according to students performance by gender, type of school, level and years of schooling, meanings involved in the problems and number size of answers. Students types of answers and the strategies they developed to solve the problems were also analysed. It was observed that gender did not affect student performance but type of school, years of schooling, type of combinatorial problem (and implicitly properties and relations involved in each kind of problem), symbolic representation used and number size were factors that interfered in performance. It was also observed that students from initial to final years of basic schooling (Primary to High School) are able to understand problems that involve combinatorial reasoning and that even if they do not complete their solutions and do not obtain correct answers, in different school years they develop strategies and use symbolic representations that show comprehension of meanings and invariants implicit in the problems. Thus, it is necessary to consider students previous understandings developed since the initial years of schooling and to aim to increase students combinatorial reasoning, a way of thinking that helps diverse understandings of mathematical nature and of other knowledge areas


combinatorial reasoning solution strategies conceptual development resolução de problemas estratégias de resolução ensino básico educacao raciocínio combinatório basic schooling desenvolvimento conceitual problem solving

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