Theoretical Perspectives on Youngsters Solving Mathematical Problems with Technology

Given that solving mathematical problems entails developing ways of thinking and expressing thoughts about challenging situations where a mathematical approach is appropriate, this chapter unveils a theoretical framework that aims to guide a better interpretation of students’ capability to solve mathematical problems with digital technologies, in the context of online mathematical competitions. The main purpose is to provide a way of understanding how students find effective and productive ways of thinking about the problem and how they achieve the solution and communicate it mathematically, based on the digital resources available. By discussing several theoretical tools and constructs, a theoretical stance is developed to conceptualise problem-solving as a synchronous process of mathematisation and of expressing mathematical thinking in which digital tools play a key role. This theorisation draws on the role of external representations and discusses how a digital-mathematical discourse is used to express the development of the conceptual models underlying the solution. In this conceptualisation, a symbiotic relation between the individual and the digital tools used in problem-solving and expressing is postulated and outlined: the inseparability of humans and media sustains the idea that students and tools are agents performing knowledge in co-action, while approaching mathematical problems. Looking at the solution to a problem is seeing a fusion of the solver’s knowledge and the tool’s built-in knowledge, rather than an aggregate of both or a complementarity between them.

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