Helping students to construct robust understanding of physics concepts and develop good solving skills is a central goal in many physics classrooms. This thesis examine students' problem solving abilities from different perspectives and explores strategies to scaffold students' learning. In studies involving analogical problem solving between isomorphic problems, we evaluate introductory physics students' abilities to learn from the solved problems provided and transfer their learning to solve the corresponding quiz problems which involve the same physics principles but different surface features. Findings suggest that postponing the providing of the solved problems until student have attempted to solve the quiz problems first without help is a good way to scaffold students' analogical problem solving. Categorization of problems based upon similarity of solution provides another angle to evaluate and scaffold student's ability to reflect on the deep features of the problems. A study on categorization of quantum mechanics problems reveals that the faulty overall perform better categorization than the students. However, unlike the categorization of introductory mechanics problems, in which the categories created by the faulty are uniform and based on the fundamental physics principles, the categorization in quantum mechanics is based on the concepts and procedures, and is more diverse. In addition to investigating strategies that may guide students to develop a better knowledge structure in physics, from the learners' perspective, we also explore possible strategies to help instructors improve their teaching of problem solving and to assess student difficulties more efficiently. Investigating how teaching assistant (TAs) design problem solutions in view of the recommendations from research literature, we find that the TAs don't necessarily notice all components in a problem solution that are valued by the educational researchers. There is much room for improvement when it comes to actual practice. Another study involving comparison between different assessment tools reveals that carefully designed multiple-choice questions can reflect the relative performance on the free-response problems while maintaining the benefit of ease of grading, especially if the different choices in the multiple-choice questions are weighted to reflect the different levels of understanding that students display. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://www.proquest.com/en-US/products/dissertations/individuals.shtml.]