Mathematical Competencies Framework Meets Problem-Solving Research in Mathematics Education

**Abstract** This chapter presents a theoretical framework for studying mathematical problem-solving processes supported by the use of digital tools. The framework is based on the mathematical competencies framework (Niss & Højgaard, 2011, 2019), which is used in combination with other compatible theoretical notions from mathematical problem-solving research. The chapter begins by outlining the mathematical competencies framework, which identifies six mathematical competencies: * Thinking mathematically * Posing and solving mathematical problems * Modeling mathematically * Reasoning mathematically * Representing mathematical entities * Handling mathematical symbols and formalisms The chapter then introduces the notion of networking of theories in mathematics education, which is a research approach that involves combining multiple theoretical frameworks to gain a more comprehensive understanding of a phenomenon. Finally, the chapter introduces some theoretical developments from problem-solving research in mathematics education, such as the notions of problem-solving strategies, problem-solving cycles, and problem-solving heuristics. The chapter then presents a case study of a preservice mathematics teacher solving a geometrical problem aided by digital tools. The case study is analyzed using the theoretical framework presented in the chapter. The analysis shows how the mathematical competencies framework can be used to identify and describe the different strategies and processes that the preservice teacher used to solve the problem. The chapter concludes by discussing the implications of the research for the understanding and teaching of mathematical problem-solving in technological environments. The chapter also discusses the potential of the networking of theories approach for studying mathematical problem-solving processes. The chapter contributes to the field of mathematics education in several ways. First, it provides a new theoretical framework for studying mathematical problem-solving processes supported by the use of digital tools. Second, it illustrates the potential of the networking of theories approach for studying mathematical problem-solving processes. Third, it provides new insights into the problem-solving strategies and processes of preservice mathematics teachers.UCR::Vicerrectoría de Docencia::Ciencias Básicas::Facultad de Ciencias::Escuela de Matemátic