5.2 Study 2: Students’ depictions of the quantum wave function
5.2.4 Possible ways of expanding the project
There are many ways of building on this study for future research, and in-deed, Study 2 is intended as a study that could inform even larger postgradu-ate studies.
One natural way of building on Study 2 is to design a larger study using only one or a few of the topics chosen for focused interviews. This is, of course, a suitable project if one or a few of the topics seems particularly promising for understanding students’ depictions of quantum mechanics – for example by shedding light on depictions of several quantum mechanics topics.
If my proposed next phase of studies is successful in describing students’
depictions of the quantum wave function in great detail, one possible way of building on this could be to embark on quantitative investigations into stu-dents’ depictions of the wave function. This could, for example, be made through the development of questionnaires to be used on larger populations, allowing a statistical analysis of students’ depictions.
One further way of building on what I have proposed, as Study 2 is to re-late students’ depictions of the quantum wave function to inappropriate de-pictions of quantum mechanics. For example, the research question could take on the following form, “Do students with inappropriate depictions of the wave function also give inappropriate depictions of other topics in quan-tum mechanics? If so, which?”
Another way that seems particularly interesting to me at this early point, is to undertake closer investigations on how students’ depictions of the quan-tum wave function relate to students’ classical depictions of quanquan-tum phe-nomena. If clear relations between depictions of particles and wave functions
can be found, depictions of wave functions may be a key to understanding inappropriate depiction in many quantum topics – since many depictions appear to be related to the classical particle model.
If my proposed future studies do not reveal any relation between students’
depictions of the quantum wave function and their depictions of particles, one conclusion to draw may be that the quantum wave function is not an appropriate conceptual framing to use for investigating students’ depictions of particles. In that case, one will need to choose between pursuing the ques-tion of students’ depicques-tions of particles, and students’ depicques-tions of the quan-tum wave function.
Finally, one possible way of building on my proposed future studies is to compare and contrast students’ depictions of the quantum wave function, and from that develop course material to contribute towards efforts aimed at improving students’ understanding of the wave function.
6. Sammanfattning på svenska
Denna licentiatavhandling handlar om inlärningsforskning i kvantmekanik, och mer specifikt tittar den på studenters beskrivningar av kvantmekanik.
Det huvudsakliga bidraget denna avhandling ger till fysikens didaktik är en sammanställning över forskning som gjorts kring just studenters beskriv-ningar av kvantmekanik – något som hittills saknats10, trots att sådan forsk-ning funnits i 25 år.
Litteratursammanställningen, som presenteras i Paper 1, bidrar på flera sätt till framtida inlärningsforskning i kvantmekanik. Som alla litteratur-sammanställningar ger den en överblick över vilken forskning som gjorts, och vilka resultat som hittills rapporterats – vilket givetvis hjälper till att hitta intressanta forskningsfrågor och också ökar möjligheterna att jämföra nya forskningsresultat med gamla studier. Men litteratursammanställningen bidrar också med en taxonomi för att grovt kategorisera inlärningsforskning i kvantmekanik, vilket ytterligare bidrar till att uppmärksamma områden som varit underprioriterade.
Huvudresultat i litteratursammanställningen är följande:
• Studenter har i regel stora problem med att lära sig kvantmekanik. I princip alla områden som har undersökts visar att studenter har be-tydande problem, och det finns också anledning att tro att många studenter har svårt att relatera kvantmekanik till den dagliga tillva-ron. De områden som undersökts kvantitativt i mer än en studie vi-sar typiskt att 20–50 % av studenterna beskriver de valda kvantme-kaniska begreppen på ett olämpligt sätt.
• Många av de olämpliga beskrivningar som studenter ger av kvant-mekanik hänger samman med en klassisk partikelbild (istället för en kvantmekanisk partikelbild).
• Den mesta inlärningsforskningen i kvantmekanik har skett på kvantmekaniska begrepp som tas upp i introduktionskurser i kvantmekanik. Framförallt dominerar studier kring studenters be-skrivningar av atomer, följt av bebe-skrivningar av endimensionella potentialsystem (så som tunnlingsfenomenet i en dimension).
10 En omfattande litteratursammanställning över framförallt tysk forskning finns utgiven på tyska, emedan engelska översikter i princip har varit begränsade till listor över referenser.
Detta presenteras närmare i artikel 1.
ningsforskning på mer avancerade kvantmekaniska begrepp är säll-synta eller extremt sällsäll-synta.
• Storskaliga studier, som omfattar fler än 500 studenter, är extremt sällsynta.
Litteratursammanställningen uppmärksammar också att studier i kvantmeka-nikinlärning sällan presenterar vilken tolkning av kvantmekanik som använts i undervisningen. Då det finns flera olika tolkningar av den matematik som beskriver kvantmekaniken – och dessa kan skilja sig ganska kraftigt åt gäl-lande exempelvis partikelbegreppet – torde även vilken tolkning studenter förväntas använda vara en viktig del av bakgrundsdata för studier.
Vidare presenterar avhandlingen också ett antal tips och förslag till kvantmekaniklärare, grundade i tidigare forskning kombinerat med erfaren-heter som både lärare och student i kvantmekanikkurser.
Slutligen presenteras också ett antal förslag för framtida forskning, med utgångspunkt i litteratursammanställningen. Bland annat innehåller avhand-lingen två detaljerade beskrivningar av forskningsprojekt för mina fortsatta doktorandstudier: en enkätstudie för att kartlägga vilka tolkningar av kvant-mekanik som används i svensk undervisning, och en förberedande intervju-studie för att undersöka studenters beskrivningar av den kvantmekaniska vågfunktionen och hur dessa beskrivningar är relaterade till en klassisk bild av partiklar.
7. Acknowledgements
In this thesis I would first like to thank my supervisor, Professor Cedric Linder, who made it possible for me to work in such an interesting, inspiring and important research field. I would also like to thank Rebecca Kung for all the advice she has given me in working with the literature review. Thanks also to my assisting supervisor, Professor Erik Sjöqvist, for all the invaluable comments, advice and teaching concerning quantum mechanics formalism and interpretation.
Huge thanks to my fellow research students for all rewarding discussions, and for all the fun time we have together.
I would also like to thank quantum mechanics education researchers gen-erously providing me with copies of their research. I would especially like to thank Dr. Bradley Ambrose, Dr. Thomas Bethge, Professor Rinaldo Cervel-lati, Professor Ádám Kiss, Professor Helmut Fischler, Peter Gnadig, PhD student Derek Muller, Professor Hans Niedderer, Dr. Rolf Olsen, and Asso-ciate Professor Chandraleka Singh. Apart from these, I would also like to thank Dr. Peter Fletcher and Dr. Azam Mashhadi for particularly inspiring and helpful research.
Much thanks also goes to the university library, whose work is seldom noticed as long as it is going well.
Finally, I would like to thank my family, and most of all Linda Åmand for inspiration, support, and an endless supply of patience in listening to me talk about quantum mechanics education research.
Thank you all.
8. References
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This manuscript has been submitted to Educational Research Review, and is currently (2006-12-19) in the peer review process. Please contact [email protected] or [email protected] before referring to this manuscript.
– S UBMITTED MANUSCRIPT –
R EVIEW OF EMPIRICAL STUDIES INTO STUDENTS ’
DEPICTIONS OF QUANTUM MECHANICS
Johan Falk, Physics Education Research Group, Department of Physics, Uppsala University, Sweden.
Cedric Linder, Physics Education Research Group, Department of Physics, Uppsala University, Sweden; and the University of the Western Cape, South Africa.
Rebecca Lippmann Kung, Physics Education Research Group, Department of Physics, Uppsala University, Sweden.
Correspondence to: [email protected]
This review summarises and compares empirical studies on students’ depictions of quantum mechanics. A taxonomy for classifying quantum mechanics education studies is presented, in order to facilitate comparisons between studies. Results are discussed, and suggestions for future research are presented.
Keywords: quantum mechanics education research; inappropriate depictions; student conceptions; alternative conceptions; misconceptions.
1 B ACKGROUND AND MOTIVATION FOR THIS REVIEW
1.1 Why quantum mechanics education research?
Research has shown that quantum mechanics education is struggling with many severe problems. These problems range from topics in the introduction of modern physics, such as the wave-nature of matter, to introductory topics such as tunnelling, and more advanced topics such as time-development of quantum systems. Today, physics students typically study quantum mechanics in their second or third year of university studies, and in for example Germany, quantum physics is introduced already at pre-university level.
Despite the importance of quantum mechanics from a scientific point of view, and also the important role it plays in physics education, research in quantum mechanics education has received little attention compared to many other branches of physics. However, the rapidly growing number of studies in quantum education indicates that quantum mechanics education will play a more important role in physics education research in the future.
For a non-physicist, it may be difficult to fully appreciate the role quantum mechanics
plays in our society, both in everyday life and scientific research. To help the
non-physicist reader, a few examples are presented to give a picture of the importance of
quantum mechanics.
This manuscript has been submitted to Educational Research Review, and is currently (2006-12-19) in the peer review process. Please contact [email protected] or [email protected] before referring to this manuscript.
Quantum mechanics is still the only theory that has been able to describe and predict nature at the atomic level without contradicting experimental results. In fact, considering numerical precision, quantum mechanics has so far produced the most accurate predictions any scientific theory has made. Quantum mechanics has, since its development during the beginning of the 1900’s, not only turned into the fundamental theory for small-scale physics, which also plays a crucial role in chemistry, molecular biology and medicine.
Without quantum mechanics, things such as computers, light emitting diodes, magnetic resonance imaging, lasers, compact discs, and many more would not have been developed. The theory is also the basis of nanotechnology, a technology playing an increasingly important role in our society. Apart from practical applications, quantum mechanics has also altered the map of how we perceive nature, challenging what we call space, time, and causality. Quantum mechanics is also the foundation of string theory, physics’ best attempt so far for attaining a theory of everything.
In short, quantum mechanics is an important scientific theory of today.
Despite its importance, it is uncommon for a non-physicist to even be aware of the impact quantum mechanics has on our society, let alone any technical details of the theory.
Unfortunately, education research shows that this is also the case for many physics students.
The aim of education research in quantum mechanics is to understand and resolve the difficulties associated with teaching and learning quantum mechanics. We hope, with this review, to make a contribution to this.
1.2 Existing reviews
Education research in quantum mechanics has expanded rapidly over the last ten years, with an increased number of research groups investigating an increased span of research questions. The growing interest for education research in quantum mechanics and the associated increasing number of publications in the field creates a demand for a comprehensive summary of research results. Despite this, there are only a few reviews available.
The most comprehensive reviews are, so far:
• Fletcher (1997) provides a quite comprehensive resource list of education research in quantum mechanics, and also some related education research in chemistry. A few representative studies are also described in more detail;
• Müller (2003) has published a summary of education research in quantum mechanics. This review covers the plentiful early German research in great detail, but also a large proportion of later and international research. It is written in German;
• Fletcher (2004) also presents an updated resource list of education research in mechanics education in his doctoral thesis. Unfortunately, the period 1997–
2004 is not covered as extensively as the research prior to 1997. Again, some selected studies are presented in detail.
This review contributes to the field in several ways. Firstly, it includes contemporary
research, and also contains a number of older resources not included in previous reviews.
This manuscript has been submitted to Educational Research Review, and is currently (2006-12-19) in the peer review process. Please contact [email protected] or [email protected] before referring to this manuscript.
Secondly, this review does not only list references, but also presents a summary of research results relevant for the focus of this review. Thirdly, this review presents research in themes, allowing comparison between different studies. It also presents a taxonomy to categorise studies, further facilitating comparing and contrasting.
1.2.1 Scope of this review
This article reviews studies on students’ depictions of quantum mechanics, since we believe that this is the most useful review focus for education researchers and also highly useful for quantum mechanics teachers.
By choosing this focus, education research into developing teaching methods and aids is left out. We feel that education research in quantum mechanics is still young, and our current focus would better suit the needs of the research field. Readers interested in teaching methods and aids are recommended to read Müller (2003), and also to investigate the reference lists presented by Fletcher (2004).
This review also only covers empirical studies, leaving out a large number of articles where authors share experiences and suggestions for teaching and curriculum design. Nor are historical descriptions of quantum mechanics covered. We feel that though such articles are important for the community of quantum mechanics teachers, education research must build on an empirical basis. A list of articles with teaching suggestions and presenting the historical development of quantum mechanics can be found in Fletcher (2004).
Due to language barriers, parts of the research published in German have not been included in this review. An extensive overview here is given by Müller (2003).
In doing this review, we have striven to collect research from many different sources. The main methods for finding articles have been examining reference lists, complemented by examining online publication lists of researchers. The main method of tracking down articles has been Google Scholar™, complemented by other library search resources and by contacting authors.
In order to make the review as comprehensive as possible, not only published articles are included, but also theses, conference presentations, proceedings, and some unpublished monographs.
1.3 Terms used in this review
When presenting research, we use a number of terms to describe the studies and the environment in which they were made. The purpose of using special terms is to make it easier to compare and contrast different studies.
We describe, as far as possible, the sizes of the studies, the locations of the studies, what year of university studies the participants come from, and how advanced the taught quantum mechanics was. In some cases, the population data has had to be deduced from the context. For example, in the cases where it is unclear at which university the study has been conducted, we use the location of the study by the country where the researcher is active.
1.3.1 Student depictions
The aim of this review is to summarise various problems in how students describe or
apply quantum mechanics. In particular, the aim is to describe students’ inappropriate
This manuscript has been submitted to Educational Research Review, and is currently (2006-12-19) in the peer review process. Please contact [email protected] or [email protected] before referring to this manuscript.