Different Levels of Sophistication in Solving and Expressing Mathematical Problems with Digital Tools

Abstract

All over the world, several organizations have nurtured the development of students’ problem-solving abilities by organizing competitions and tournaments of different kinds. This is the case of the Mathematical Competitions SUB12 and SUB14, promoted by the University of Algarve, addressing students from grades 5 to 8 (10–14 year olds) in the south of Portugal. To each proposed problem, participants are required to explain their problem-solving process and find ways to express their thinking. They may use any of the digital tools they have available and they find useful for solving a given problem. Our research has uncovered the aptitudes of young competitors in taking advantage of everyday digital tools and its representational expressiveness to give form and substance to their reasoning and strategies. Another emerging aspect is the apparent existence of different degrees of robustness of the solutions submitted, mainly in terms of the strategies that competitors develop, with a particular technological tool, to solve the problems. In this chapter, we are taking a selection of solutions submitted to two problems, in which competitors resort to GeoGebra, in one case, and to Excel, in the other. We offer a proposal for identifying levels of sophistication and robustness of technology-based solutions to the problems, according to the characteristics of the tool use and its connection to the conceptual models underlying students’ thinking on the problems.