Central goals of higher education in STEM domains include learning of problem solving and self-assessment skills. To achieve these goals, we propose a novel self-assessment method called the Solve-Correct-Assess-Negotiate (SCAN) method of assessing problem solving that includes both formative and summative elements. We study students' learning experiences in courses involving different methods of assessing problem solving (Course 1 including teacher-led assessment, N[subscript trad] = 53; Course 2 including SCAN method, N[subscript SCAN] = 56) and specifically associations between these learning experiences and students' perceptions of the SCAN method. We found that the students relied on teacher-led assessment more than the self-assessment. The perceived utility of the self-assessment was positively associated with a deeper approach to learning in Course 2 than in Course 1. Students who found the self-assessment less beneficial also perceived less support from the learning environment. Our findings suggest that the successful implementation of novel self-assessment-based practices for problem-solving requires personalized support for self-assessment, teachers' awareness of the different perceptions that students have towards these practices, and discussion among teachers and students on the rationale, utility, and reliability of the different practices.