A multivariate analysis of undergraduate physics students conceptions of quantum phenomena

Transcription

1 Eur. J. Phys. 20 (1999) Printed in the UK PII: S (99) A multivariate analysis of undergraduate physics students conceptions of quantum phenomena Gren Ireson Department of Education, Loughborough University, Leicestershire LE11 3TU, UK g.p.ireson@lboro.ac.uk Received 1 December 1998, in final form 5 February 1999 Abstract. Both pre-university and undergraduate students have conceptual problems with the ideas in quantum physics. The initial findings of a study to investigate undergraduate students understanding of quantum phenomena are presented. The study shows that a questionnaire approach can be used to elicit students ideas regarding quantum phenomena and that multivariate analysis can be used to draw out both clusters of conceptions and dimensions of understanding. 1. Introduction The success of quantum theory cannot now be open to doubt: with the exception of the gravitational force, everything from nucleon nucleon interactions to theories of cosmology can be accounted for. However, quantum phenomena represent something of a conceptual revolution in which the mechanistic and deterministic must give way to the non-deterministic and stochastic. What I am going to tell you about is what we teach our physics students in the third or fourth year of graduate school and you think I m going to explain it to you so you can understand it? No, you re not going to be able to understand it. Why, then, am I going to bother you with all this? Why are you going to sit here all this time when you won t be able to understand what I am going to say? It is my task to convince you not to turn away because you don t understand it. You see, my physics students don t understand it either. That is because I don t understand it. Nobody does. Feynman (1985) The Feynman view appears to have been that quantum phenomena are fundamentally different to other phenomena in physics. In order to address the above idea some working definition of understanding is required. To understand some new piece of information is to relate it to a mentally represented schema, to integrate it with already existing knowledge. Carey (1986) What do I mean by understanding? Nothing deep or accurate just to be able to see some of the qualitative consequences of the equations by some method other than solving them in detail. Feynman (quoted in Galison 1998) /99/ $ IOP Publishing Ltd 193

2 194 G Ireson White and Gunstone (1992) propose a definition of understanding based on overt performance rather than mentally represented schema. In this study, as in previous work with pre-university students (Mashhadi and Woolnough 1996), understanding is taken to be represented by the clustering of students conceptions. Hence, this means accepting the Feynman premise that it is nothing deep or accurate. Any findings should therefore be interpreted at the level of the group and not at the level of the individual. The questionnaire statements used, to elicit students understanding of quantum phenomena in this study, are given in table 1. Table 1. Statements addressing understanding of quantum phenomena. B01 B02 B03 B04 B06 B07 B08 B09 B10 B12 B13 B14 B15 B16 B18 B19 B21 B22 B23 B25 B26 B27 B28 B30 B31 B33 B35 B36 B39 The structure of the atom is similar to the way planets orbit the sun. It is possible to have a visual image of an electron. The energy of an atom can have any value. The atom is stable due to a balance between an attractive electric force and the movement of the electron. Coulomb s law, electromagnetism and Newtonian mechanics cannot explain why atoms are stable. The electron is always a particle. An atom cannot be visualized. Light always behaves as a wave. In passing through a gap electrons continue to move along straight line paths. The photon is a sort of energy particle. Electrons are waves. When an electron jumps from a high orbital to a lower orbital, emitting a photon, the electron is not anywhere in between the two orbits. How one thinks of the nature of light depends on the experiment being carried out. Electrons move along wave orbits around the nucleus. The photon is a lump of energy that is transferred to or from the electromagnetic field. Electrons consist of smeared charge clouds which surround the nucleus. Nobody knows the position accurately of an electron in orbit around the nucleus because it is very small and moves very fast. It is possible for a single photon to constructively and destructively interfere with itself. Since electrons are identical it is not possible to distinguish between them. Electrons move around the nucleus in definite orbits with a high velocity. When a beam of electrons produces a diffraction pattern it is because the electrons themselves are undergoing constructive and destructive interference. Electrons move randomly around the nucleus within a certain region or at a certain distance. Whether one labels an electron a particle or wave depends on the particular experiment being carried out. If a container has a few gas molecules in it and we know their instantaneous positions and velocities then we can use Newtonian mechanics to predict exactly how they will behave as time goes by. During the emission of light from atoms electrons follow a definite path as they move from one energy level to another. Individual electrons are fired towards a very narrow slit. On the other side is a photographic plate. What happens is that the electrons strike the plate one by one and gradually build up a diffraction pattern. Electrons are fixed in their shells. Orbits of electrons are not exactly determined. The photon is a small, spherical entity.

3 2. Methodology Students conceptions of quantum phenomena 195 The students in the sample (N = 338), who were first- and second-year undergraduates from six UK universities, were presented with a questionnaire. The questionnaire was composed of 40 items to which students responded on a five-point, strongly agree to strongly disagree, scale. The 40 items included 29 which elicited students conceptual understanding of quantum phenomena and 11 which examined their conceptual understanding of models. The latter 11 items are not the subject of this paper, as it is my intention to concentrate on students understanding of quantum phenomena. The responses were subjected to two multivariate techniques, cluster analysis and multidimensional scaling, to uncover groups or clusters of response and map them onto a Euclidean space, of three dimensions or less, representing the structure or dimensions of the students responses. Cluster analysis Cluster analysis is concerned with allocating individuals to a group in such a way that each individual member of a group is more like individuals in the same group than those outside the group. Multidimensional scaling Multidimensional scaling is used to describe a procedure which starts with the distances between a set of points, individuals or objects, or information about these distances and finds a configuration of these points in a small number of dimensions. Obviously, if the number of dimensions can be reduced to two or three then by plotting the data any groups or clusters will be evident from a visual inspection. This compares with the use of cluster analysis. The type of multidimensional scaling used in this study is known as non-metric scaling, since the responses are ordinal data and as such the numbers do not have a strict numerical significance. The goodness of fit produced by the scaling method, when the number of dimensions are reduced, is known as stress. The correlation between the percentage stress and the goodness of fit is given by Alt (1990) as: Stress (%) Goodness of fit 20.0 Poor 10.0 Fair 5.0 Good 2.5 Excellent 0.0 Perfect In this study the number of dimensions was guided by the desire for a visualizable outcome and the need to limit the stress value. All the analysis was carried out using SPSS for Windows, version 7. Interested readers are referred to Chatfield and Collins (1980) for an introduction to multivariate analysis. 3. Findings Cluster analysis generated three clusters (see figure 1), which can be labelled quantum thinking, intermediate thinking and mechanistic thinking. Cluster one contains statements, for example, It is possible for a single photon to constructively and destructively interfere with itself and Whether one labels an electron a particle or wave depends on the particular experiment being carried out.

4 196 G Ireson Cluster 1 Cluster 2 B15 B28 B12 B14 B16 B18 B26 B33 B19 B36 B06 B23 B22 B01 B04 B21 B25 B02 B13 B27 B31 B30 B35 B39 B08 B03 B07 B09 B10 Figure 1. Dendrogram showing the formation of clusters following cluster analysis. Cluster two contains statements, for example, Electrons are waves, Electrons move around the nucleus in definite orbits with high velocity and Electrons move randomly around the nucleus within a certain region or at a certain distance. Cluster three contains statements, for example, The energy of an atom can have any value, The electron is always a particle and light always behaves as a wave. A full list of statements by cluster is given in table 2. Multidimensional scaling allows the responses to be mapped onto a three-dimensional space with a stress of 9.3%, which is considered good. A two-dimensional space has a stress value of 12.4% which is still considered fair. For ease of visualization the two-dimensional model is presented here. Dimension one is labelled: Absolute thinking Dual thinking. This dimension represents the students thinking in terms of wave particle duality. At the absolute thinking end of the dimension statements, for example, Light always behaves as a wave and The electron is always a particle can be found. The dual thinking end of the dimension is typified by, Whether one labels an electron a particle or wave depends on the particular experiment being carried out.

5 Students conceptions of quantum phenomena 197 Table 2. Statements, by cluster. B06 B12 B14 B15 B16 B18 B19 B22 B23 B26 B28 B33 B36 B01 B02 B04 B13 B21 B25 B27 B30 B31 B03 B07 B08 B09 B10 B35 B39 Cluster 1 Coulomb s law, electromagnetism and Newtonian mechanics cannot explain why atoms are stable. The photon is a sort of energy particle. When an electron jumps from a high orbital to a lower orbital, emitting a photon, the electron is not anywhere in between the two orbits. How one thinks of the nature of light depends on the experiment being carried out. Electrons move along wave orbits around the nucleus. The photon is a lump of energy that is transferred to or from the electromagnetic field. Electrons consist of smeared charge clouds which surround the nucleus. It is possible for a single photon to constructively and destructively interfere with itself. Since electrons are identical it is not possible to distinguish between them. When a beam of electrons produces a diffraction pattern it is because the electrons themselves are undergoing constructive and destructive interference. Whether one labels an electron a particle or wave depends on the particular experiment being carried out. Individual electrons are fired towards a very narrow slit. On the other side is a photographic plate. What happens is that the electrons strike the plate one by one and gradually build up a diffraction pattern. Orbits of electrons are not exactly determined. Cluster 2 The structure of the atom is similar to the way planets orbit the sun. It is possible to have a visual image of an electron. The atom is stable due to a balance between an attractive electric force and the movement of the electron. Electrons are waves. Nobody knows the position accurately of an electron in orbit around the nucleus because it is very small and moves very fast. Electrons move around the nucleus in definite orbits with a high velocity. Electrons move randomly around the nucleus within a certain region or at a certain distance. If a container has a few gas molecules in it and we know their instantaneous positions and velocities then we can use Newtonian mechanics to predict exactly how they will behave as time goes by. During the emission of light from atoms electrons follow a definite path as they move from one energy level to another. The energy of an atom can have any value. The electron is always a particle. An atom cannot be visualized. Light always behaves as a wave. In passing through a gap electrons continue to move along straight line paths. Electrons are fixed in their shells. The photon is a small, spherical entity. Dimension two is labelled: Simple atom/deterministic mechanics Complex atom/indeterministic mechanics. This dimensions represents students thinking with regards to the stability and structure of the atom and the locatability of entities. The Simple atom/deterministic mechanics end of the spectrum is typified by, for example, The atom is stable due to a balance between

6 198 G Ireson 1.5 b30 b Simple atom deterministic mechanics Dimension Complex atom indeterministic mechanics -.5 b09 b03 b35 b07 b39 b10 b08 b02 b31 b13 b04 Cluster 2b01 Cluster 2 b16 b14 b27 b33b12 b18 b28 b15 b22 b21 b26 b23 b36 b19 Cluster b061 Cluster Figure 2. Two-dimensional space representing the questionnaire items showing the three clusters mapped onto the two-dimensional space. an attractive electric force and the movement of the electron and Electrons move around the nucleus in definite orbits with a high velocity. At the Complex atom/indeterministic mechanics end, example statements are: Coulomb s law, electromagnetism and Newtonian mechanics cannot explain why atoms are stable and Electrons consist of smeared charge clouds which surround the nucleus. The two-dimensional map for all statements is given in figure 2. The multidimensional scaling can be seen to be supportive of the cluster analysis since the three clusters can be mapped, without overlap, onto the space. The findings of this study point to the misunderstandings or misconceptions of beginning physics undergraduates. The findings are not unique to the UK, since recent work in the United States, using a different methodology, also reported similar misconceptions. For example: Mistaken belief that two or more photons are required for diffraction or interference minima to occur. Extension of incorrect ideas about photons to electrons. Ambrose et al (1998) In conclusion it can be said that a number of insights into students thinking have been gained. The use of the conceptual map allows a holistic picture to be presented. 4. Implications for teaching and learning In a typical pre-university physics course in the UK students are introduced to both wave and particle models of light. The photoelectric effect is often used to show the failure of classical wave theory with the inconsistency resolved by the photon model. This is generally taken as the starting point for a basic introduction to quantum phenomena or wave particle duality. Given that undergraduate physics students have been successful in their studies in order to gain a university place, what do the above findings say regarding student understanding? The real world is quantum mechanical in nature but the world view of a majority of undergraduate physics students remains mechanistic. This is the challenge for all involved in physics education. Attention should be drawn to the work of Fischler and Lichfeldt (1992).

7 Students conceptions of quantum phenomena 199 In this work the recommended approach to the teaching of quantum physics is one in which: 1. Reference to classical physics is avoided. 2. Teaching of the photoelectric effect begins with electrons, not photons. 3. Statistical interpretations of observed phenomena are used and dualistic descriptions avoided. 4. The Heisenberg uncertainty principle is introduced at an early stage for ensembles of quantum objects. 5. In the treatment of the hydrogen atom the Bohr model is avoided. Perhaps it is time for a reappraisal of both pre-university and undergraduate physics in the light of research into student understanding. References Alt M 1990 Exploring Hyperspace (London: McGraw-Hill) Ambrose B S, Shaffer S S, Steinberg R N and McDermott L C 1999 An investigation of student understanding of single-slit diffraction and double-slit interference Am. J. Phys Carey S 1986 Cognitive science and science education Am. Psychologist Chatfield C and Collins A J 1980 Introduction To Multivariate Analysis (London: Chapman and Hall) Feynman R P 1985 QED The Strange Theory of Light and Matter (London: Penguin) Fischler H and Lichtfeldt M 1992 Modern physics and students conceptions Int. J. Sci. Ed Galison P 1998 Feynman s war: modelling weapons, modelling nature Stud. Hist. Phil. Mod. Phys Mashhadi A 1996 Students conceptions of quantum physics Research in Science Education in Europe ed G Welford, J Osborne and P Scott (London: Falmer) Mashhadi A and Woolnough B 1996 Congnitive mapping of Advanced Level Physics students conceptions of quantum physics. Unpublished paper presented at Conference on Educational Research (Singapore, November 1996)