Today a physics student has to face a wide variety of problems in a growing number of career options. She may have to develop an understanding in the basic sciences, solve challenging engineering problems, or make high-stakes business decisions. The diverse set of skills required for today's job opportunities is best achieved by teaching the student to think result-oriented, as opposed to method-oriented, and by encouraging her to work collaboratively.
Pure recitation of textbooks by the instructor is never adequate to achieve this goal: students only learn to apply a limited set of tools to a limited set of standard exercises. While learning to apply these tools is certainly important, focusing solely on solving such problems is not sufficient. As a popular saying goes “if your only tool is a hammer, all tasks will have to look like a nail”. Instead, students must be taught to be problem-oriented. For example, rather than asking in a mechanics class “what is the Lagrange function for this system?” we must ask “is there a simpler way to solve this problem?”
As a member of the teaching staff at Wuppertal University I had success in posing open-ended problems — in other words, to formulate tasks that can be solved in several different ways. The Computertheoreticum class at Wuppertal University is an excellent example of the implementation of such a strategy. In this class, once students have achieved a basic set of abilities, including numerical and analytical problem solving skills, they can be given a specific assignment which they will then have to solve by a method of their choice. While a purely analytical solution is not possible, the students could use different combinations of analytical and numerical approaches and are free to design their own program.
Of paramount importance to the success of this method was the collaborative spirit which was achieved by having the students form groups of two to four. After a period of group work, each group presents their solution to the entire class. The development of presentation skills is as crucial as teamwork abilities. The best way to measure a student's understanding of a subject is to let her explain the subject herself. Being able to explain it is the last step in the learning process and helps to solidify the student's understanding. Therefore, the quality of the presentations of the projects can and should be a measure of the student's performance.
To conclude, I base my instruction on two major principles: fostering result-oriented thinking and encouraging the development of crucial soft-skills, foremost collaborative group work and presentation abilities.