Modern techniques for solving parameter problems with didactic applications in the development of higher cognitive abilities

Abstract

Abstract. The article examines the optimization of solving mathematical problems with parameters through modern heuristic strategies aimed at developing higher-order cognitive skills. The theoretical-methodological research draws on ERIC-indexed literature and recent studies on heuristics, complex problem-solving, and mathematical thinking. It analyses techniques such as systematic parameter variation, specialization and generalization, case analysis, multiple representations, mathematical modelling, heuristic dialogue, and metacognitive reflection. The main contribution is a methodological model integrating these techniques into the problem-solving process and highlighting the cognitive mechanisms involved at each stage. The proposed approach promotes critical thinking, cognitive flexibility, and the transfer of problem-solving strategies to new contexts.