The purpose is to make an intellectual map of the design space, which includes all the methods covered in the course. It is the instructor's job to point out the pros and cons of each method and describe the methodology on how to choose an appropriate method in solving practical problems. This task is like drawing a 3-dimensional map of the design space of the methods, so that the students can get a big picture about the problem and the solutions/methods and can perceive the relative distance (interrelation) between different technologies.
It is an art to make a sound engineering design, since many times we try to optimize over a functional space and try to solve an optimization problem with multiple objectives, which may be conflicting with one another. Optimization over a functional space is unsolvable; hence people tend to select a family of functions and optimize over this family of functions. It is an art to select the family of functions. Multi-objective optimization is hard since we have infinite many Pareto-optimal solutions and do not know which solution strikes the optimal trade-off among the objectives. So it is an art to select one out of infinite many Pareto-optimal solutions as the optimal solution. An effective way of teaching the art of engineering design, is to maximize the intuition while minimize mathematics, since your intuition always comes before rigorous mathematics when you do your engineering design.
Expertise in an area does not guarantee that one is good at teaching students about that area. In fact, expertise may hurt teaching because many experts forget what is easy and what is difficult for students. It is important to develop pedagogical content knowledge, which includes information about typical difficulties that students encounter as they attempt to learn about a set of topics; typical paths students must traverse in order to achieve understanding; and sets of potential strategies for helping students overcome the difficulties that they encounter.
Organize the subjects to be taught according to the background of students.
An important goal of education is to help students develop the learning strategies needed to acquire new knowledge and skills.
Typically, students can easily solve the problems at the end of each chapter in a textbook since they know they only have to use the formulae in that chapter. But if the problems are randomly selected from different chapters, they might not know how to solve the problem. The reason is that the students may not organize the knowledge around essential concepts and fundamental principles, and they may not have conditionalized knowledge which tells them when, where and why a certain method is applicable to solving the problem.
Typically, people construct new knowledge and understandings based on what they already know and believe. However, the pre-existing knowledge may be inaccurate, incomplete, or incorrect. To construct correct understanding about the new knowledge, it is necessary to fix the old misconceptions first. This can be achieved by deductive reasoning based on the pre-existing knowledge of the student. That is, under the student's assumption, one will end up with a contradiction after deductive reasoning. It may take some time (for intellectual or psychological reasons) for the student to be completely convinced. After achieving this, the student can easily accept the new knowledge being taught.
On the other hand, if the pre-existing knowledge is correct, the instructor can utilize the connection between the preconceptions and the new knowledge to effectively get across the key ideas embedded in the new knowledge.
Most students like inquire-based instruction, not just because it is fun, but more importantly, because it is natural to the learning process of a human. Only when you explore the area by yourself, will you get a sense about which method works, which method does not work, and why it works or does not work. The practice of "teaching by telling" typically does not achieve this effect.