Methods of Teaching Problem Solving in Higher Education Institutions: A Review of Instructional Approaches and Their Effectiveness

Problem solving is a core competence that higher education institutions aim to develop, particularly in mathematics, natural sciences, and engineering. However, students often learn to reproduce solution procedures without understanding the underlying principles. This article reviews the principal methods used in universities to teach problem solving and compares their cognitive and pedagogical characteristics. A narrative review of peer-reviewed literature was conducted, and the methods were classified by the type of problems used, the degree of instructional guidance, and the social organization of learning. Five groups of methods were identified: (1) explicit heuristic and strategy instruction, (2) worked examples and faded guidance, (3) cooperative problem solving, (4) problem-based and inquiry-oriented learning, including productive failure, and (5) technology-supported tutoring. The literature suggests that worked examples and explicit strategies are especially effective for novices, that cooperative and problem-based methods develop reasoning, teamwork, and knowledge application, and that guidance should be gradually reduced as expertise grows. The article concludes that effective problem-solving instruction requires sequencing methods according to students' prior knowledge, using well-designed problems, and providing timely feedback.