Teaching and Learning Forum 99 [ Contents ]

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

M G Zadnik[1], S Deylitz[3], S Yeo[1], R Loss[1] and D Treagust[2]

[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.


An innovative teaching unit developed at the Institute of Physics Education, University of Bremen, has been used to introduce year 13 German high school students to a quantum mechanics view of atomic structure. The idea of this new approach is to describe atoms from a quantum mechanics perspective from the very beginning instead of the traditional simpler and very limited, intermediate models.

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:

It has been observed in studies on students' conceptions in atomic physics (Bethge 1988), that when students learn classical approaches first, they retain and prefer to use a classical picture of atoms, despite subsequent instruction using quantum mechanics.

Structure and conception of the course

To help the students learn this conceptually difficult topic in this new way, the course content, in particular the number of new terms and concepts, were greatly reduced compared with the traditional approach. Furthermore, new concepts are used throughout the course and are applied to a variety of problems. To reduce the mathematical requirements of solving complex differential equations (such as the famous Schrądinger equation) students learn to use the dynamic modeling software STELLA. This enables students to model and solve differential equations on a graphical interface without detailed mathematical knowledge.

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 Schrądinger 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 Schrądinger 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

Conceptual ideas are best developed in a learning environment where experiments are integrated with discussion, group work and short presentations by students and instructors (Loss and Thornton, 1998). Computer work in groups of two or three students is done with some help from the instructors if needed. Classes are limited to 25 students. The above plus a computer with projector system for presentations from the instructor or for Net usage provide an ideal environment in which to undertake this course. In the last seven weeks of their second semester, about 50 students (25 per studio session) have been given an introduction to atomic physics at the Physics Department based on the course described above. The students attended a three hour session once a week and were provided with a textbook and regular homework designed for this teaching unit.

The evaluation design

The evaluation is based on written statements from the students. Twenty open ended questions were asked in pre-/post course questionnaires. For comparison purposes, most of the questions were the same in both tests. We gained additional information from attitude questionnaires about the course, as well as results from a mid course test and final exam. The aim of the evaluation was to find out if, and how well, the teaching unit enabled the students to develop concepts about atomic physics.

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

In the final class session the students answered six open-ended questions on their views of the course and the use of the software STELLA. The two most common comments about things the students liked most, were the conceptual rather than mathematical content and the discussion-based teaching environment as opposed to lecturing. Negative comments most commonly related to the perceived difficulty of weekly assignments and learning to use STELLA concurrently with the difficult physics. What students liked about STELLA was that it enabled them to visualise the physics through graphs and therefore gave a qualitative understanding of the description of atoms. Many also liked the reduced amount of calculation needed. On the other hand, many thought that STELLA was not explained well enough, and took too much time to use, reducing time spent on the physics. There were comments like "too much fiddling took away from the physics". Despite this fact, about 75% of students thought that STELLA helped them to understand atomic physics.

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.


Students appreciated the open discussions and the orientation towards a more qualitative description with pictorial representations of atoms in a quantum mechanical description. The negative attitude some students had towards STELLA could be avoided by introducing the software earlier in the year. STELLA is a powerful tool which is mainly used to solve differential equations and can therefore be applied on a variety of problems in classical mechanics. This would also save some time which could be spent on more student discussions. The improvement in describing the different models of an atom with the appropriate terms seems to indicate that the reduction of content and the use of the same description on more than one problem enabled the students to get a quantum mechanical understanding of atoms.


Bethge, T. (1988). Aspekte des Schuelervorverstaendnisses zu grundlegenden Begriffen der Atomphysik. Dissertation, Uni Bremen.

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.

Please cite as: Zadnik, M. G., Deylitz, S., Yeo, S., Loss, R. and Treagust, D. (1999). Teaching really difficult concepts: How we did it and what the students say. In K. Martin, N. Stanley and N. Davison (Eds), Teaching in the Disciplines/ Learning in Context, 480-483. Proceedings of the 8th Annual Teaching Learning Forum, The University of Western Australia, February 1999. Perth: UWA. http://lsn.curtin.edu.au/tlf/tlf1999/zadnik.html

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