Subtraction decomposition algorithm: deepen knowledge through the use of a virtual manipulativea

Abstract

The use of virtual manipulatives in the classroom provides environments that generate more effective learning in mathematics. With these tools, students receive immediate feedback on their actions, involving them in valid reasoning processes and leading them to solid and meaningful learning. In the 1st Cycle of Basic Education, in Portugal, the subtraction decomposition algorithm is taught before the standard algorithm. It is essential that the future teacher has, therefore, an in-depth knowledge of the mathematical procedures involved in the various algorithms. A qualitative study, of an interpretative nature and with a case study design, was carried out with students of the 3rd year of a degree in Basic Education from a Portuguese Higher Education Institution and aimed to analyze how the use of a specific virtual manipulative allowed to deepen the knowledge of these students on the subtraction decomposition algorithm. The study consisted of solving a set of tasks with the aid of the Base Blocks Subtraction applet (National Library of Virtual Manipulatives). The results show that, when solving tasks using the applet, the mathematical terminology used by students improved, avoiding, for example, the systematic recurrence of expressions related to mnemonics. On the other hand, the use of the applet allowed students to become aware of their shortcomings in terms of the algorithm’s procedures, namely, the decomposition process of a higher order unit, if necessary.