Designing Problem-Based Situations in Teaching The Topic "Sequences – Arithmetic Progressions – Geometric Progressions" to Develop Mathematical Problem-Solving Competence for Grade 11th Students

In the context of general education reform oriented toward the development of learners’ qualities and competencies, fostering mathematical problem-solving competence for students has become an essential requirement. This paper investigates the design and organization of problem-based situations in teaching the topic “Sequences – Arithmetic Progressions – Geometric Progressions” with the aim of developing mathematical problem-solving competence for Grade 11 students in accordance with the 2018 General Education Curriculum. Based on an analysis of theoretical perspectives on problem-based situations and mathematical problem-solving competence, the study clarifies the objectives and characteristics of the topic within the Grade 11 mathematics curriculum. A qualitative research approach is employed through document analysis, literature review, and examination of the current mathematics curriculum. The research proposes a process for designing and organizing problem-based situations in teaching sequences, arithmetic progressions, and geometric progressions, accompanied by a specific illustrative example. The findings provide practical references to support high school mathematics teachers in innovating teaching methods toward a competency-based approach.