Teaching really difficult concepts: How we did it and what the students say

^[1]Physics Education Research and Development Group, Department of Applied Physics
^[2]Science and Mathematics Education Centre
Curtin University of Technology
^[3]Institute of Physics Education, University of Bremen, Germany

This paper reports our experience in teaching first year university students' concepts of atomic and quantum physics and how their concepts changed during an introductory unit. The unit, which formed part of the first year physics course in the Department of Applied Physics at Curtin University of Technology, was based on a teaching unit developed at the Institute of Physics Education at Bremen University, Germany Another major difference between this and the traditional university approach to teaching this topic was that this unit was taught in a studio environment which supports student group work and interaction with computers.

Introduction

Atomic physics is one of the most demanding topics to be taught to first year students. The traditional introductory approach uses semi-classical descriptions such as the Bohr model in which the atom is likened to a planetary system with electrons orbiting the nucleus, analogous to planets orbitting the Sun. To reduce the difficult mathematical requirements (such as solving complex differential equations) introductory quantum mechanics courses usually present highly abstract, but at least visual, ideas such as the 'square potential well' and the 'simple harmonic oscillator' before atoms are described in a purely mathematical way.

The problems seen in introducing atomic physics in this way are:

• students find it very difficult to make connections between different complex ideas;
• content overload, making it difficult for students to identify the main concepts; and
• the abstract representations reduces students' ability to link the theoretical description with physical observations.

Structure and conception of the course

To give students confidence in using the software they start by modeling the differential equation of a standing wave where they can compare the theoretical results from the STELLA model with a real standing wave experiment they conduct themselves. This particular activity leads directly to students developing more appropriate mental pictures of 'states' of atoms.

The provision of 'pictures' of atoms supports the quantum mechanical description, rather than classical descriptions, by using appropriate terms such as energy level, Eigen-energy, Psi-function and quantum number. The two pictures used are the 'charge cloud', representing an electron as a charge distribution around the nucleus, and the 'probability density', representing the probability of finding an electron at a certain distance from the nucleus. Eventually, students learn to recognise the inherent difficulties in being able to 'draw' atoms and to determine their exact structure.

To demonstrate that the Schrˆdinger equation is a universal theoretical description and to develop a wide range of applications of microscopic structures, STELLA can model the structure of atoms such as helium which have more than one electron (no easy feat for any computer with the Schrˆdinger equation) as well as molecules and solids. Transitions between energy levels resulting from STELLA calculations can be directly compared with the energies of observed spectral lines. The size of atoms can also be calculated and compared with experimentally obtained values.

The Physics Studio environment at Curtin University of Technology

The evaluation design

The six key areas of the unit were:

Model of an Atom:	What models and which terms do students use? What does the word "model" mean to the students?
Psi-function:	What is the interpretation of the Psi-function? How is it used to describe atoms?
State:	Which quantities are connected to state? How is state used to describe atoms?
Schroedinger equation:	How do the quantities in the Schroedinger equation influence the results?
Experiment/Theory:	How can the line spectrum of an atom be explained with the quantum mechanical description? How can a atomic sizes be defined and compared?
Higher order Atoms:	How is the interaction between electrons taken into account? How can an atom with more than one electron be described?

Summary of students' statements

When students' statements from the pre-test and the post-test are compared, the most obvious change is in their drawings and descriptions of atoms. Most students moved away from a classical description of an orbiting electron towards a charge cloud representation. This is not too surprising because this representation was preferred by the instructors. The more interesting result is that many students refer to more than one model in the post-test which was not been observed in the pre-test. Prior to the course, students used a variety of terms to describe their models, usually mixing different descriptions. After the course, expert terms like "state", "charge cloud", "probability density" and "Psi-function" are clearly favored. Most students are able to separate the models from each other and to apply the correct terms to the appropriate models. This could be a result of the limited number of new terms and the attempt to structure and present them in a clear way, as well as using them in a variety of applications.

When it came to more complex problems like defining the size of atoms or explaining the stability of atoms (these topics were discussed in little detail or not at all), students tend to fall back to classical descriptions. This behavior has also been observed in earlier studies on teaching quantum physics (e.g. Niedderer 1997). The classical model has a high retentivity because it is easier to understand, is used in most introductory texts and is how the topic developed historically, while the new models have a higher status or "prestige" partly because they have been favored by the instructors and discussed in more detail. Nevertheless improvements could be seen from many students who either admit that they do not know how to answer a question or try to solve the problem in terms of the quantum mechanical description. In our interpretation their answers show that the new models not only had a higher status after the course but also gained some strength during the course.

Conclusions

References

Loss, R. and Thornton, D. (1998). Physics Studio - A progress report. In Black, B. and Stanley, N. (Eds), Teaching and Learning in Changing Times, 171-175. Proceedings of the 7th Annual Teaching Learning Forum, The University of Western Australia, February 1998. Perth: UWA. http://cleo.murdoch.edu.au/asu/pubs/tlf/tlf98/loss.html

Niedderer, H., Bethge, T., Cassens, H. and Petri, J. (1997). Teaching quantum atomic physics in college and research results about a learning pathway. In. E. F. Redish and J. S. Rigden (Eds.), The changing role of physics departments in modern universities. Proceedings of the International Conference on Undergraduate Physics Education (ICUPE). New York: American Institute of Physics, 659-668.