This lecture covers the foundations for teaching problem solving in higher education, focusing on research evidence, problem categorization, student beliefs impact, and transfer in problem solving. It discusses a typology of problems including routine, non-routine, and ill-defined problems. The lecture also explores a cognitive study of problem solving in statics, addressing difficulties faced by students and differences between strong and weak students. It emphasizes the importance of analytical problem-solving skills in engineering education, highlighting the need for strong analysis and problem-solving skills. The session concludes by discussing the concept of learning to transfer knowledge and problem-solving skills between different contexts.