Physics students face the double challenge of grasping both complex concepts and their mathematical descriptions, and students need to be able to understand and confidently manipulate these mathematical representations. Solving conceptual and mathematical problems is an established method in physics teaching, it reinforces theory and improves the ability to apply broad physical principles and equations to specific situations. The capability to confidently solve problems goes beyond being able to tackle exam questions; it is much more powerful than memorizing a list of facts. Analytical skills and problem-solving abilities can be applied to new situations and are useful both for solving homework problems and for applying physics in everyday life.