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*(The following are excerpts from McIntyre, Tate & Manogue (2008))*

In the last 25 years we have witnessed a computer revolution that has permeated all aspects of our society. For practicing scientists and engineers, the computer has become a ubiquitous problem-solving tool, following in the footsteps of the slide rule and the hand-held calculator. Unfortunately, the education students receive often does not represent this progression. Students do use, and sometimes overuse, their calculators and are certainly web-savvy computer users, but they do not yet use computers with the ease and regularity of practicing scientists, nor with the specific purposes that professionals do. Particularly in upper-level physics classes, we would be remiss in not using computational power to the fullest extent, to effectively deliver the advanced curriculum and to train students to use the same problem solving tools and techniques used by professional physicists.

At Oregon State University (OSU) we have developed a new upper-level undergraduate curriculum, designed to help students learn to work and think like professional physicists. We deliberately embrace many approaches to incorporating computation into the curriculum, from using computers to deliver interesting new curricular materials, to activities where students explore new physics by controlling parts of the code, to activities where the students have the opportunity to learn professional computational skills.

We use computation for in-class activities, classroom demonstrations, homework, laboratory projects, and senior theses. The use of computation in the curriculum supports our pedagogical approaches of active learning, spiral learning, and first studying examples before learning general theory. Continuous and frequent use of computation helps to breed familiarity and build student confidence. Our goal is for students to go beyond the notion of computer-as-calculator, and to embrace the full problem-solving power of visual graphics, fast data manipulation, simulation, and of course, calculation. Combined with effective active-engagement and group-learning activities, these computational activities give the computer in the physics classroom the status of the office water-cooler: a place where people gather to brainstorm.

## Types of Activities

### Computation

Physics curricula have traditionally focused on a few standard problems that could be solved analytically – for example, the quantum and classical harmonic oscillator; the charged line, plane or sphere; the two-body problem, etc. The power of modern computers now allows us to do calculations to solve those problems that were previously claimed to be too hard, or were simply never mentioned. Not only can we solve them, but in many cases we can solve them in real time in a way that allows us to see how changes in the parameters of the problem affect the solution. For example, we can easily extend the problem of a quantum mechanical particle in a square well to other well shapes to explore what is the same and what is different about differently shaped wells. Providing students with a broader range of examples and problems enriches the curriculum, and the ease with which they can explore complex problems encourages them to explore independently. We are always careful to strike a balance between using the computer to do calculations and developing students' paper-and-pencil skills.

### Visualization

Graphical visualization of physical phenomena and mathematical relationships is an important part of higher-level physics and it is becoming more so as computer visualizations become more commonplace. Students typically have a good understanding of classical mechanics built upon their everyday experiences, but as they venture into electromagnetism, statistical physics and quantum mechanics, they must rely less on this mechanical intuition, and more on their ability for abstract reasoning. Visualization is key to developing this ability for abstract thinking; a graph or animation seems to trigger connections with what they already know more easily than equations or words. Materials for upper-level physics courses have traditionally used many of the visual aids employed by professional physicists, but students are often not properly instructed in understanding and interpreting these graphics, and much of the power of visualization is lost when the fundamentals are not present. This is especially true of multiple representations. Professional physicists routinely use pictorial, graphical, algebraic, and verbal representations of physical quantities to the extent that they are often not conscious of switching from one to another. For example, a student's question about the equation y = mx + b almost always prompts an instructor to respond with a graph of a straight line. Students' facility to switch between representations is much more limited and they need specific training to develop this skill. We have found that consistent and frequent use of multiple representations can be effective in guiding students' professional development, and computation integrated with other types of activities that encourage students to really engage with the visualization is particularly helpful with the graphical aspect, especially with different types of graphs and with connecting algebra to graphs.

### Animation

While it is generally preferable to do real experiments, time, money, and accessibility factors make computer simulations very attractive for giving students a tangible view of how nature works and developing their physical intuition. As such, computer simulations are playing an increasing role in many facets of education. One of our Paradigms courses, Spin and Quantum Measurements, is centered about a Java application/applet to simulate Stern-Gerlach spin experiments. Another course on reference frames uses Mathematica-generated movies that illustrate the Coriolis effect on the rotating earth. Both simulation packages were developed or reformulated at OSU. We also use older software packages from the CUPS consortium to simulate waves in periodic systems, both classical and quantum mechanical, and are presently working on developing similar packages using Open Source Physics and Easy Java Simulations in order to make them multi-platform and open source.

## Tips

- Avoid the simple ah-hah experience. (The person who designs the visualization learns more than the students)
- Ask students to interpret the graph in some way. Kinesthetic interpretations can be very valuable. Example: Interpreting Effective Potential Plots

- Ask student to draw the visualization by hand first, so they have the opportunity to decide what should be plotted. Then let them see the fancy computer graphics. Example: visualizing electrostatic potentials.
- Do not string together long activities. Pick one central point for each worksheet. Then allow students time to reflect about the point of that experience before moving on.