A constructivist computational tool to assist in learning primary school mathematical equations

In constructivist principles, learning is a process in which individuals construct knowledge. Research in Mathematics Education looks for ways to make mathematics education less dry and more attractive. When solving polynomial equations of the first degree, it is very common for teachers to work with the mistaken idea of ''changing the sign'' when ''moving'' the member. To minimize this problem, a balance can be used to illustrate the idea of equilibrium and also properties of equality. The objectives of this study were (1) develop a computational tool to replace a conventional balance in practical mathematics exercises thereby solving two material challenges for Brazilian teachers: verifying the accuracy of balances and the lack of student physical and social activity through direct participation; (2) determine how substituting the conventional balance with a computational tool for the solution of first degree polynomial equations affected the aspects inherent in the learning process like motivation, cooperation, dialogue, discussion, reflection, reciprocity, negotiation and responsibility. The results indicate that the cognitive computational tool met the challenges of Brazilian teachers. First, because it lacks mechanisms that need to be verified for accuracy in order to demonstrate equilibrium. Second, because it allows the direct participation of students (physical experience) and the use of the tool in small groups (social experience). The hands on completion of the activity, realistic appearance, the interaction with the tool, visual feedback on the panel, and two students using the same tool awakened motivation, responsibility for completing the activity, dialogue, cooperation, discussion and reflection. Doing the experiment with others aroused concern about the learning of others and reciprocity of knowledge for the improvement of the procedure to be constructed for solving 1st degree equations.