A Mathematical Problem-Solving Approach Based on Digital Technology Affordances to Represent, Explore, and Solve problems via Geometric Reasoning

Abstract

It has been widely recognized that problem-solving activities are crucial in developing and learning mathematics. Indeed, it is common to structure and frame both mathematical curriculum and learning environments through problem-solving activities. Currently, significant developments of digital technologies are shaping both students' social interaction and ways of learning mathematics and solving problems. What types of strategies, representations, and resources emerge and are important in problem-solving approaches that rely on and foster the use of a Dynamic Geometry System affordances? The aim of this chapter is to analyze and discuss on how the use of a Dynamic Geometry System (GeoGebra) provides affordances to develop a geometric reasoning as a mean to work and solve mathematical problems. In this process, it becomes important to think of and represent problem statements and concepts geometrically, to construct dynamic models of problems, to trace and examine loci of particular objects, to analyze particular and general cases, and to communicate results.