Mental calculation strategies used by teachers in the additive field: from mathematical knowledge to methodological implications for teaching

Abstract

The new curricular guidelines highlight the importance of the development of mental calculus skills and their relationship with the objects of knowledge for the early years of elementary school.  This paper presents the clipping of a research developed by Brazilian and Portuguese researchers. We present the strategies and understanding of mental calculus used in the additive field of whole numbers up to 100 per teacher and work in the public network of a municipality located in the northwest region of the State of Paraná, in the initial years of elementary school.  Twenty-six teachers who solved mentally and in two different ways participated in this project,  six propositions that involved the addition and subtraction with numbers of two digits of whole numbers up to 100. The analysis of the results showed that this group used the algorithmic procedures mentally and the strategies 1010 and N10, in addition to the commutative, and associative properties of the addition and the distributive multiplication of the addition. Subsequently, we interviewed to identify what mathematical knowledge was underlying the resolutions undertaken.  It is observed that although they use the characteristics of the Decimal Numbering System (NdS), even in algorithmic resolution, the properties of operations and strategies already presented in studies on the subject were not identified by the participants about the mental calculus undertaken, and the mathematical knowledge underlying and Le. These data reveal the little knowledge of teachers about the characteristics of ndS and the properties of operations that allow us to flexible mental calculation strategies and their variations according to the numbers involved in the operations, evidencing the need for teaching training on the subject investigated. This cutout of the researched data brings significant aspects to be considered in a process of continuous training of teachers and teachers who teach mathematics as a contribution to this process.

DOI: https://doi.org/10.56238/methofocusinterv1-079