Compreensão do valor posicional em crianças brasileiras do 2º ao 5º ano do ensino fundamental

Abstract

Mathematics is a complex domain that requires different skills for its learning. Place-value understanding is one of these skills, which is involved in both the acquisition and further development of arithmetic competencies. In Brazil, studies point to the importance of this skill, especially in writing Arabic numerals from the verbal form during elementary school. A hierarchical model of place-value understanding was built by researchers Herzog, Fritz, and Ehlert (2017) to describe developmental characteristics of acquisition of the place-value notion, from five hierarchical levels (pre-decadic level, level I, level II, level III, and level IV) that was empirically validated in Germany, South Africa, and Turkey. Thus, the present master’s thesis aims to evaluate the place-value understanding in Brazilian children based on the model of Herzog, Fritz, and Ehlert (2017). First, a scoping review is being developed to investigate how the concept of place-value understanding is defined and operationalized in the literature since it is possible to find studies with different instruments that assess this skill. In addition, an empirical study is being conducted, with Brazilian children from 2nd to 5th grade of elementary school, based on the theoretical model described. A numerical transcoding task and basic arithmetic calculations task were also included to verify the associations between these skills and the notion of place value. The results of the review point to an inconsistency in the literature on how the place-value understanding is defined and evaluated. In this way, we mapped the main definitions and tasks of place-value, relating them to the main research objectives of the selected studies. The results of the empirical study indicate that level IV (the last level of the model) is more difficult for children, and most students are in levels I, II, and III. Furthermore, we found a relationship between place-value understanding with numerical transcoding, and arithmetic calculations.