Traditionally calculation exercises were solved by pen and pencil, or today by using a calculator or maybe by a spreadsheet's basic math functions. However, certain problems demand extensive calculations and are therefore generally not used for student exercises. This is a pity, as many such problems can provide important insights and learning. On this NucWik page you find links to "Computing in Science Education (CSE)" exercises that use the number crunching capabilities of modern computers to solve calculation intensive problems. Thus, students and teachers are provided the opportunity to work with more complex problems out of reach of traditional classroom methods.On NucWik we maintain a List of CSE type exercises. The link to this list is also found under the "Calculation Exercises" page which you reach from NucWik's main menu.
In general these exercises can be approached in at least two ways:
- The student (or group of students) write their own number-crunching software to solve the provided problem.
- The student use provided computer software to work a provided problem.
Which approach is selected depend on computer skills (also of the teacher!), how much time that can be assigned to the particular task and the available software tools. The exercises are primarily developed for students that will write their own software (using whatever suitable computer language they know). However, as soon as the software has been written it can of course be used directly at a later stage. For some of the exercises compile-ready source code and/or ready to run executables are provided.
Background
The concept of Computing in Science Education (CSE) has emerged steadily and in parallel with the introduction of e-learning and computers in the classroom. It might not always be performed under the CSE label or as such a definite concept, but it is obvious that harnessing the computing capabilities of modern computers enables teachers to include problems in student exercises that in former days were restricted to research teams using state-of-the-art computers not available to everybody.For NucWik and the CINCH project the inspiration to include CSE exercises was provided by a project at the Faculty of Mathematics and Natural Sciences at the University of Oslo (UiO). The project is of course appropriately named "CSE - Computing in Science Education". The goal is described as:
- "The goal of the CSE-project is to include computing as a natural tool for all science and engineering students from the first semester of their undergraduate studies. Not as a substitute for more traditional approaches, but as an extension of the classical toolbox."
The motivation for using CSE in teaching is well described at the project's UiO web-page and coincide with the CINCH-project motivation for including such exercises her at NucWik. The motivation is copied here for your convenience:
"Computer simulation has become such a fundamental tool in research and industry that it should be introduced to students in the first math and science courses. Surprisingly, the use of computers to solve mathematical problems still has little impact on university education around the world, particularly on bachelor level. Given today's dominance of numerical simulations among professionals, we think it is paramount to integrate numerical tools at all levels in the education system. Our focus is to teach students how they can attack mathematical problems by using numerical methods and programming, and how they can explore the mathematical models through experimenting with programs. The pedagogical benefits are three-fold:
- Programming helps to increase the “understanding” of the mathematical methods
- Simulation with aid of programmes moves the attention from possible intricate algebra with pen and paper to a greater focus on problem formulation and physical behaviour of systems, i.e., “physical insight"
- Numerical solutions allow much more realistic and inspiring problems to be addressed, and give students a taste of what research is about
A particular achievement of the CSE project in Oslo is that we have managed to implement the computer-based methods by modifying existing science courses, in contrast to the more common approach where modernization is taken care of in new "computational science" student programs with separate courses.
To summarize, CSE is about bringing the modern way of working with mathematical models from the professionals to the students, and the beginning students in particular."
It is clear that at the Faculty of Mathematics and Natural Sciences at UiO a substantial effort has been done to include CSE into teaching at all levels and a large number of courses. Please refer to the UiO CSE web-pages for more details. The UiO working group: Knut Mørken, Nina Sasaki Aanesen, Lars Oswald Dahl, Hugo Lewi Hammer, Terje Brinck Løyning, Anders Malthe-Sørenssen, Elisabeth Nøst, Ingve Simonsen, Jon Eivind Vatne and Tone Skramstad have published a report on how to introduce CSE as an integral part of first degree teaching (date: 1/2/2011. English edition: 15/6/2011). You might find the report useful even for less ambitious CSE projects.
Purpose of NucWik CSE exercises
Most universities have not gone to such lengths as UiO to implement CSE, but this do not exclude individual teachers from using CSE in their courses. It is the hope of the CINCH consortium (who set up these NucWik pages) that the CSE exercises provided here as examples can serve as inspiration and help for further exploring CSE in your own teaching.Students with extensive training in numerical problem solving (e.g. numerical solutions of differential equations, integration techniques, linear algebra methods, root finding and interpolation methods, processing of sound and images, etc.) can of course tackle really advanced problems. The exercises provided by the CINCH consortium and listed on NucWik is less complex and thus more generally applicable. That said, anyone who has developed more complex exercises is encouraged to share their ideas and material here on NucWik.