How we do it
The CSE project has involved development of considerable amounts of lecture notes and other teaching materials, and many discussions on teaching related challenges. However, most of this would have little or even negative effect, if not accompanied by a couple of other initiatives.
To develop a unified computational perspective on undergraduate teaching programmes across course and departmental boundaries.
It would be much easier to introduce a computational perspective in physics if the physicists themselves taught the mathematics courses and computer science courses as well. However, in most universities this would mean duplicating teaching efforts and cause a waste of resources that would hardly be sustainable in the long run.
Cooperation across traditional boundaries
To avoid this duplication, there must be cooperation and alignment between courses and across departmental boundaries. The difficulty lies in the fact that this kind of cooperation is virtually nonexistent at many universities, and this cannot be changed overnight. In Oslo, the cooperation was triggered by two important events in 2003:
* The introduction of broad bachelor programs which required wide cooperation and discussions
* The introduction of Centers of Excellence, particularly the Centre of Mathematics for Applications. The centre is cross-disciplinary with strong emphasis on numerical computations, and therefore provided a second arena for discussing broad teaching reforms
The cooperation needed to achieve the goal stated above requires trust and personal bonds between the teachers involved, and as in all human interactions this takes time and effort to develop. The existence of natural and informal arenas for scientific discussions greatly simplifies and boosts this process.
Support from governing bodies
Even if a group of people from different departments have come to the conclusion that their teaching programs need to be revised, it is not obvious that this is shared by everybody. At most universities revision of entire teaching programs has the potential to cause debate, so it is essential to have support from the governing bodies. In Oslo, it was fortunate that the Faculty’s (School’s) strategic plan was just being revised, so when we approached the Dean and got his support, our plans found their way into the new strategic plan. The Department Heads were already familiar with our initiative, but when the strategic plan was passed, it was also important to develop a departmental understanding of what the reform amounted to.
Designing the teaching programs
When the atmosphere for cooperation is in place, and there is support from the leadership, it should be possible to revise the teaching programs with an emphasis on how they function as a whole, not just each individual course. This requires relatively broad agreement on what the reform is going to be, and how it can be implemented locally.It is important to agree on overall goals, but it is equally important to let each teacher makes his or her personal impression on the teaching. A good teacher has to have faith in what he or she does, and therefore should not be forced to do something to the contrary.
Developing the scientific content
The points raised above are all quite generic to broad revisions of teaching programs, but the CSE project is a reform which focuses on new content in the teaching. Over the years we have learnt some important lessons which are summed up briefly below.
- New understanding of mathematics and science. The students come to university with a set idea of what mathematics is, and what science is. For most students, the integration of programming and computer calculations into mathematics and science severely challenges these ideas, and causes confusion in the beginning. It is therefore important to explain why this integration is necessary, and not underestimate the difficulties for the students.
- Classical theory is still important. Some may think that calculations by computer may reduce the need for classical mathematics and science. In our experience, the opposite is true. Development of algorithms and algorithmic thinking requires a more unified and abstract view of mathematics, and therefore many students find computations difficult. A strong foundation in classical mathematics is therefore essential. The same applies to science. In order to derive computational models, it is absolutely essential to be confident within the general theory.
- Understanding, not black box. It may be tempting to develop flashy software which demonstrates what can be done by combining computers, mathematics and graphics. This may have its place as advanced figures, but keep in mind that the goal is understanding, not just facts. Most students will learn much more from writing a program that draws a very simple figure rather than being presented with a very flashy version of the same figure, produced by someone else.
- Integrate rather than add on. The natural approach when introducing computations in a course is to start with the existing course and add computations. This naturally leads to the common objection ‘there is no room for computations in my course’. If instead computations are integrated into the different parts of the syllabus it takes up much less space. In mathematics for example it is often possible to make use of numerical methods and examples in the development of the theory, and in this way the students learn numerics and theory simultaneously. However, this requires new text books where this approach is well implemented.
- Make sure computational skills are tested. Students are very good at distilling out parts of the curriculum that are not tested in the course. So if you want them to take computations seriously, they must also be tested in this area, either in the exam, in compulsory hand-ins, or some other way.
- Be patient. The traditional text books in elementary mathematics and science build on a tradition, with examples and exercises, that has been developed and refined over several centuries. We believe that changes like the present computational reform only happen once or twice a century, and therefore it would simply be arrogant to think that we would get it right on the first attempt. Therefore, be patient, it will probably take something like twenty years to develop computationally oriented text books with a quality that approach that of the classical texts. However, we are lucky to have an opportunity to take part in one of these major paradigm shifts!