Manifestações de flexibilidade de cálculo mental em tarefas que envolvem multiplicação e divisão numa perspetiva do sentido de número - Silva, Cília Cardoso Rodrigues da (2023)
This study covers two countries: Portugal, where the theoretical and methodological framework was sought, and Brazil, where the empirical data was constructed, based on a learning and teaching experience carried out from the perspective of developing number sense. The objective was to understand manifestations of mental calculation flexibility in operations with natural numbers when 4th year students solve tasks involving multiplication and division. Answer two questions (i) What calculation procedures do students use to solve tasks involving multiplication and division with natural numbers? These classified into counting, additive, subtractive and multiplicative procedures. (ii) What manifestations of mental calculation flexibility are identified in the different calculation procedures? This issue is linked to the flexibility of mental calculation, in particular, to the manifestations in the sense of revealing the action of thought that emerge in different calculation procedures recorded on the students' answer sheets. The theoretical framework addresses the themes of number sense, operation sense, mental calculation and flexibility of mental calculation, with their different perspectives. The methodology is based on the interpretative paradigm with a qualitative research approach, in the form of a multiple case study, carried out in three cases: Ipê Amarelo, Sempre Viva and Caliandra, conducted by learning and teaching experiences that took place in two public schools in the Federal District, Brazil . The participants are students from three 4th year classes, their respective teachers and myself (researcher). It was concluded, with data analysis carried out in two stages, that: challenging and encouraging students to solve tasks without giving up, to invent their calculation procedures with meaning-producing strategies, to socialize and communicate their procedures and strategies with little or almost no contact with traditional algorithms were important aspects that contributed to the emergence of calculation procedures on student answer sheets; The flexibility of mental calculation expressed by students suggests that teaching mental calculation procedures and strategies does not make sense, as they are spontaneous in their mathematical practice as they have the opportunity to record on paper or express in speech what they are thinking from the experience and knowledge of numbers and operations; manifestations of mental calculation flexibility in operations with natural numbers in solving tasks involving multiplication and division emerge when students are able to look at the numbers involved in situations, know what to do with them, transform them, establish numerical relationships, understand the effects of operations and use procedures involving skip counting, addition two by two, successive additions, decimal decompositions or not, multiples of 5 and 10, ideas of half and double, reference numbers, intuitive use of the properties of numbers and operations (such as relative and absolute quantities), and use of inverse relationships.