Knowledge Extensions in the Construction of Decimal Numbers Understanding

Abstract Considering a perspective of numerical development where the concept of number is expanded as different number sets are approached, it's only natural that pupils rely on their knowledge and extend them to the new sets, which does not always lead to correct conclusions. Hence, in this paper we aim to understand the potential of situations that suggest incorrect knowledge extensions as a means to promote the construction of decimal number understanding. Part of a broader study that follows a Design Based Research is reported, within which a teaching experiment was carried out with 25 students and their teacher, in 3rd and 4th grades. In this paper, we analyze the discussions among four students, organized in pairs, regarding tasks that promoted the discussion of three common incorrect knowledge extensions. The results evidence that the proposed situations promote the use of justifications and counterexamples, developing mathematical reasoning. The results also reveal the potential to build decimal number understanding, namely in models use, unit conceptualization, and place value concept, in particular zero.