Development of a Test Instrument to Investigate Secondary School Students’ Declarative Knowledge of Quantum Optics

Philipp Bitzenbauer 1 *
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1 Physics Education Research, Department of Physics, Friedrich-Alexander-Universität Erlangen-Nürnberg, GERMANY
* Corresponding Author
EUR J SCI MATH ED, Volume 9, Issue 3, pp. 57-79. https://doi.org/10.30935/scimath/10946
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ABSTRACT

This article reports the development and validation of a test instrument to assess secondary school students’ declarative quantum optics knowledge. With that, we respond to modern developments from physics education research: Numerous researchers propose quantum optics-based introductory courses in quantum physics, focusing on experiments with heralded photons. Our test instrument’s development is based on test development standards from the literature, and we follow a contemporary conception of validity. We present results from three studies to test various assumptions that, taken together, justify a valid test score interpretation, and we provide a psychometric characterization of the instrument. The instrument is shown to enable a reliable (α = 0.78) and valid survey of declarative knowledge of quantum optics focusing on experiments with heralded photons with three empirically separable subscales.
Keywords: quantum physics, test development, validation

CITATION

Bitzenbauer, P. (2021). Development of a Test Instrument to Investigate Secondary School Students’ Declarative Knowledge of Quantum Optics. European Journal of Science and Mathematics Education, 9(3), 57-79. https://doi.org/10.30935/scimath/10946

REFERENCES

  • Adams, W. K., & Wieman, C. E. (2011). Development and validation of instruments to measure learning of expert-like thinking. International Journal of Science Education, 33, 1289-1312. https://doi.org/10.1080/09500693.2010.512369
  • AERA (2014). Standards for educational and psychological testing. American Educational Research Association.
  • Anderson, J. R. (1996). ACT, a simple theory of complex cognition. American Psychologist, 51(4), 355-365. https://doi.org/10.1037/0003-066X.51.4.355
  • Ayene, M., Kriek, J., & Damtie, B. (2011). Wave-particle duality and uncertainty principle: Phenomenographic categories of description of tertiary physics students’ depictions. Physical Review Special Topics - Physics Education Research, 7, 020113. https://doi.org/10.1103/PhysRevSTPER.7.020113
  • Bagozzi, R. P., & Baumgartner, H. (1994). The evaluation of structural equation models and hypotheses testing. In R. P. Bagozzi (Hrsg.), Principles of marketing research (p. 386-422). Blackwell.
  • Bentler, P. M. (1990). Comparative fit indexes in structural models. Psychological bulletin, 107(2), 238-246. https://doi.org/10.1037/0033-2909.107.2.238
  • Bitzenbauer, P., & Meyn, J.-P. (2021). Fostering students' conceptions about the quantum world - results of an interview study. Progress in Science Education, 4(2), 40-51. https://doi.org/10.25321/prise.2021.1079
  • Bitzenbauer, P., & Meyn, J.-P. (2020). A new teaching concept on quantum physics in secondary schools. Physics Education, 55(5), 055031. https://doi.org/10.1088/1361-6552/aba208
  • Brell, C., Schecker, H., Theyßen, H., & Schumacher, D. (2005). Computer trifft Realexperiment - besser lernen mit Neuen Medien? [Computer meets real experiment - learn better with new media?]. PhyDid B - Didaktik der Physik - Beiträge zur DPG-Frühjahrstagung.
  • Britton, E. D., & Schneider, S. A. (2007). Large-scale assessments in science education. In S. K. Abell & N. G. Lederman (Eds.), Handbook of research on science education (pp. 1007-1040). Lawrence Erlbaum.
  • Bronner, P., Strunz, A., Silberhorn, C., & Meyn, J.-P. Demonstrating quantum random with single photons. European Journal of Physics, 30, 1189. https://doi.org/10.1088/0143-0807/30/5/026
  • Burde, J.-P., & Wilhelm, T. (2021). Teaching electric circuits with a focus on potential differences. Physical Review Physics Education Research, 16, 020153. https://doi.org/10.1103/PhysRevPhysEducRes.16.020153
  • Cataloglu, E., & Robinett, R. W. (2002). Testing the development of student conceptual and visualization understanding in quantum mechanics through the undergraduate career. American Journal of Physics, 70, 238-251. https://doi.org/10.1119/1.1405509
  • Debelak, R., & Koller, I. (2020). Testing the Local Independence Assumption of the Rasch Model With Q3-Based Nonparametric Model Tests. Applied Psychological Measurement, 44(2), 103-117. https://doi.org/10.1177/0146621619835501
  • di Uccio, S., Colantonio, A., Galano, S., Marzoli, I., Trani, F., & Testa, I. (2019). Design and validation of a two-tier questionnaire on basic aspects in quantum mechanics. Physical Review Physics Education Research, 15, 010137. https://doi.org/10.1103/PhysRevPhysEducRes.15.010137
  • Doran, R. L, Lawrenz, F. and Helgeson, S. (1994). Research on assessment in science. In D. L. Gabel (Ed.), Handbook of Research on science teaching and learning (pp. 388-442). Macmillan Publishing Company.
  • Engelhardt, P. (2009). An Introduction to Classical Test Theory as Applied to Conceptual Multiple-choice Tests. Getting Started in PER. https://www.compadre.org/Repository/document/ServeFile.cfm?ID=8807&DocID=1148
  • Engelhardt, P. V., & Beichner, R. J. (2004). Students’ understanding of direct current resistive electrical circuits. American Journal of Physics, 72(1), 98-115. https://doi.org/10.1119/1.1614813
  • Ericsson, K., & Simon, H. (1998). How to study thinking in everyday life: Contrasting think-aloud protocols with descriptions and explanations of thinking. Mind, Culture, and Activity, 5, 178-186. https://doi.org/10.1207/s15327884mca0503_3
  • Fischler, H., & Lichtfeldt, M. (1992). Modern physics and students’ conceptions. International Journal of Science Education, 14(2), 181-190. https://doi.org/10.1080/0950069920140206
  • Fisseni, H. (1997). Lehrbuch der psychologischen Diagnostik [Textbook of psychological diagnostics]. Hogrefe.
  • Flateby, T. L. (2013). A Guide for Writing and Improving Achievement Tests. https://evaeducation.weebly.com/uploads/1/9/6/9/19692577/guide.pdf
  • Fornell, C., & Larcker, D. F. (1981). Evaluation structural equation models with unobservable variables and measurement error. Journal of Marketing Research, 18, 39-50. https://doi.org/10.1177/002224378101800104
  • Galvez, E. J., Holbrow, C. H., Pysher, M. J., Martin, J. W., Courtemanche, N., Heilig, L., & Spencer, J. (2005). Interference with correlated photons: Five quantum mechanics experiments for undergraduates. American Journal of Physics, 73, 127. https://doi.org/10.1119/1.1796811
  • Glug, I. (2009). Entwicklung und Validierung eines Multiple-Choice-Tests zur Erfassung prozessbezogener naturwissenschaftlicher Grundbildung [Development and validation of a multiple choice test to record process-related basic scientific education]. IPN.
  • Goldhaber, S., Pollock, S. J., Dubson, M., Beale, P., & Perkins, K. K. (2009). Transforming Upper-Division Quantum Mechanics: Learning Goals and Assessment. Physics Education Research Conference 2009, 145-148. https://doi.org/10.1063/1.3266699
  • Grangier, P., Roger, G., & Aspect, A. (1986). Experimental Evidence for a Photon Anticorrelation Effect on a Beam Splitter: A New Light on Single-Photon Interferences. Europhysics Letters, 1, 173-179. https://doi.org/10.1209/0295-5075/1/4/004
  • Gray, G.L., Costanzo, F., Evans, D., Cornwell, P., Self, B., & Lane, J. L. (2005). The Dynamics Concept Inventory Assessment Test: A progress report and some results. In Proceedings of the 2005 ASEE Annual Conference and Exposition.
  • Haertel, E. (2004). Interpretive Argument and Validity Argument for Certification Testing: Can We Escape the Need for Psychological Theory? Measurement: Interdisciplinary Research and Perspectives, 2(3), 175-178.
  • Haladyna, T. M., & Downing, S. M. (1989). The validity of a taxonomy of multiple-choice item-writing rules. Applied Measurement in Education, 1, 51-78. https://doi.org/10.1207/s15324818ame0201_4
  • Hammer, T. H., & Landau, J. (1981). Methodological issues in the use of absence data. Journal of Applied Psychology, 66, 574-581. https://doi.org/10.1037/0021-9010.66.5.574
  • Hanbury Brown, R., & Twiss, R. Q. (1956). Correlation between Photons in two Coherent Beams of Light. Nature, 177, 27-29. https://doi.org/10.1038/177027a0
  • Henderson, C. (2018). Editorial: Call for Papers Focused Collection of Physical Review Physics Education Research Curriculum Development: Theory into Design. Physical Review Physics Education Research, 14, 010003. https://doi.org/10.1103/PhysRevPhysEducRes.14.010003
  • Henriksen, E. K., Angell C., Vistnes, A. I., & Bungum, B. (2018). What Is Light? Science & Education, 27, 81-111. https://doi.org/10.1007/s11191-018-9963-1
  • Hestenes, D., & Halloun, I. (1995). Interpreting the Force Concept Inventory. A response to Huffman and Heller. The Physics Teacher, 33, 502-506. https://doi.org/10.1119/1.2344278
  • Hestenes, D., Wells, M., & Swackhamer, G. (1992). Force Concept Inventory. The Physics Teacher, 30, 141-158. https://doi.org/10.1119/1.2343497
  • Hettmannsperger, R., Müller, A., Scheid, J., Kuhn, J., & Vogt, P. (2021). KTSO-A: KONZEPTTEST-STRAHLENOPTIK – ABBILDUNGEN. Entwicklung eines Konzepttests zur Erfassung von Konzepten der Lichtausbreitung, Streuung und der Entstehung reeller Bilder im Bereich der Strahlenoptik [KTSO-A: CONCEPT TEST RAY OPTICS - ILLUSTRATIONS. Development of a concept test to capture concepts of light propagation, scattering and the creation of real images in the field of ray optics]. Progress in Science Education, 4(1), 11-35.
  • Hobson, A. (2005). Electrons as field quanta: A better way to teach quantum physics in introductory general physics courses. American Journal of Physics, 73, 630. https://doi.org/10.1119/1.1900097
  • Holbrow, C. H., Galvez, E. J., & Parks, M. (2002). Photon quantum mechanics and beam splitters. American Journal of Physics, 70, 260. https://doi.org/10.1119/1.1432972
  • Hu, L., & Bentler, P. M. (1999). Cutoff criteria for fit indexes in covariance structure analysis: Conventional criteria versus new alternatives. Structural Equation Modeling: A Multidisciplinary Journal, 6(1), 1-55. https://doi.org/10.1080/10705519909540118
  • Huffman, D., & Heller, P. (1995). What Does the Force Concept Inventory Actually Measure? The Physics Teacher, 33, 138-143. https://doi.org/10.1119/1.2344171
  • Ireson, G. (1999). A multivariate analysis of undergraduate physics students’ conceptions of quantum phenomena. European Journal of Physics, 20(3), 193. https://doi.org/10.1088/0143-0807/20/3/309
  • Ireson, G. (2000). The quantum understanding of pre-university physics students. Physics Education, 35, 15. https://doi.org/10.1088/0031-9120/35/1/302
  • Jackson, D. L. (2003). Revisiting Sample Size and Number of Parameter Estimates: Some Support for the N:q Hypothesis. Structural Equation Modeling, 10, 128-141. https://doi.org/10.1207/S15328007SEM1001_6
  • Jones, D. G. C. (1991). Teaching modern physics-misconceptions of the photon that can damage understanding. Physics Education, 26, 93. https://doi.org/10.1088/0031-9120/26/2/002
  • Jorion, N., Gane, B. D., James, K., Schroeder, L., DiBello, L. V., & Pellegrino, J. W. (2015). An analytic framework for evaluating the validity of concept inventory claims. Journal of Engineering Education, 104(4), 454-496. https://doi.org/10.1002/jee.20104
  • Kane, M. T. (2001). Current concerns in validity theory. Journal of Educational Measurement, 38(4), 319-342. https://doi.org/10.1111/j.1745-3984.2001.tb01130.x
  • Kane, M. T. (2013). Validating the interpretations and uses of test scores. Journal of Educational Measurement, 50(1), 1-73. https://doi.org/10.1111/jedm.12000
  • Ke, J. L., Monk, M., & Duschl, R. (2005). Learning introductory quantum physics: sensori-motor experiences and mental models. International Journal of Science Education, 27(13), 1571-1594. https://doi.org/10.1080/09500690500186485
  • Kerlinger, F. N., & Lee, H. B. (2000). Foundations of behavioral research (4th ed.). Wadsworth.
  • Kimble, H. J., Dagenais, M., & Mandel, L. (1977). Photon Antibunching in Resonance Fluorescence. Physical Review Letters, 39, 691-695. https://doi.org/10.1103/PhysRevLett.39.691
  • Kline, R. B. (2005). Principles and Praxis of Structural Equation Modeling. Guilford Press.
  • Kline, T. J. B. (2005). Psychological Testing. A Practical Approach to Design and Evaluation. Sage. https://doi.org/10.4135/9781483385693
  • Kohnle, A., Bozhinova, I., Browne, D., Everitt, M., Fomins, A., Kok, P., Kulaitis, G. Prokopas, M., Raine, D., & Swinbank, E. (2014). A new introductory quantum mechanics curriculum. European Journal of Physics, 35, 015001. https://doi.org/10.1088/0143-0807/35/1/015001
  • Krebs, R. (2008). Multiple Choice Fragen? - Ja, aber richtig. Medizinische Fakultät; Institut für Medizinische Lehre IML; Abteilung für Assessment- und Evaluation AAE.
  • Kyriazos, T. A. (2018). Applied Psychometrics: Sample Size and Sample Power Considerations in Factor Analysis (EFA, CFA) and SEM in General. Psychology, 9, 2207-2230. https://doi.org/10.4236/psych.2018.98126
  • Landis, J., & Koch, G. (1977). The Measurement of Observer Agreement for Categorical Data. Biometrics, 33(1), 159-174. https://doi.org/10.2307/2529310
  • Liu, X. (2012). Developing Measurement Instruments for Science Education Research. In B. J. Fraser, K. Tobin, & C. J. McRobbie (Eds.), Second International Handbook of Science Education. (Springer International Handbooks of Education) (pp. 651-665). Springer. https://doi.org/10.1007/978-1-4020-9041-7_43
  • Loehlin, J. C. (2004). Latent variable models (4th ed.). Lawrence Erlbaum. https://doi.org/10.4324/9781410609823
  • MacCallum, R. C., & Widaman, K. F. (1999). Sample Size in Factor Analysis. Psychological Methods, 4(1), 84-99. https://doi.org/10.1037/1082-989X.4.1.84
  • Maloney, D. P., O’Kuma, T. L., Hieggelke, C. J., & Heuvelen, A. v. (2001). Surveying students’ conceptual knowledge of electricity and magnetism. American Journal of Physics, 69(7), 12-23. https://doi.org/10.1119/1.1371296
  • Mannila, K., Koponen, I. T., & Niskanen, J. A. (2002). Building a picture of students’ conceptions of wave-particle-like properties of quantum entities. European Journal of Physics, 23, 45-54. https://doi.org/10.1088/0143-0807/23/1/307
  • Marshman, E., & Singh, C. (2017). Investigating and improving student understanding of quantum mechanics in the context of single photon interference. Physical Review Physics Education Research, 13, 010117. https://doi.org/10.1103/PhysRevPhysEducRes.13.010117
  • Marshman, E., & Singh, C. (2019). Validation and administration of a conceptual survey on the formalism and postulates of quantum mechanics. Physical Review Physics Education Research, 15, 020128. https://doi.org/10.1103/PhysRevPhysEducRes.15.020128
  • Mashhadi, A., & Woolnough, B. (1999). Insights into students’ understanding of quantum physics: visualizing quantum entities. European Journal of Physics, 20(6), 511-516. https://doi.org/10.1088/0143-0807/20/6/317
  • Mayring, P. (2010). Qualitative Inhaltsanalyse: Grundlage und Techniken. Beltz Verlagsgruppe. https://doi.org/10.1007/978-3-531-92052-8_42
  • McKagan, S. B., Perkins, K. K., & Wieman, C. E. (2010). Design and validation of the Quantum Mechanics Conceptual Survey. Physical Review Physics Education Research, 6(2), 020121. https://doi.org/10.1103/PhysRevSTPER.6.020121
  • Meinhardt, C. (2018). Entwicklung und Validierung eines Testinstruments zu Selbstwirksamkeitserwartungen von (angehenden) Physiklehrkräften in physikdidaktischen Handlungsfeldern [Development and validation of a test instrument for self-efficacy expectations of (prospective) physics teachers in physics-didactic fields of activity]. Logos. https://doi.org/10.30819/4712
  • Meinhardt, C., Rabe, T. and Krey, O. (2018). Formulierung eines evidenzbasierten Validitätsarguments am Beispiel der Erfassung physikdidaktischer Selbstwirksamkeitserwartungen mit einem neu entwickelten Instrument [Formulation of an evidence-based validity argument using the example of recording physical-didactic self-efficacy expectations with a newly developed instrument]. Zeitschrift für Didaktik der Naturwissenschaften, 24, 131-150. https://doi.org/10.1007/s40573-018-0079-6
  • Moosbrugger, H., & Kelava, A. (2012). Testtheorie und Fragebogenkonstruktion [Test theory and questionnaire construction]. Springer Verlag. https://doi.org/10.1007/978-3-642-20072-4
  • Müller, R., & Wiesner, H. (2002). Teaching quantum mechanics on an introductory level. American Journal of Physics, 70, 200. https://doi.org/10.1119/1.1435346
  • Mummendey, H. D., & Grau, I. (2014). Die Fragebogen-Methode: Grundlagen und Anwendungen in Persönlichkeits-, Einstellungs- und Selbstkonzeptforschung [The questionnaire method: Basics and applications in personality, attitude and self-concept research]. Hogrefe.
  • Olsen, R. V. (2002). Introducing quantum mechanics in the upper secondary school: A study in Norway. International Journal of Science Education, 24(6), 565-574. https://doi.org/10.1080/09500690110073982
  • Özdemir, G., & Clark, D. B. (2007). An Overview of Conceptual Change Theories. Eurasia Journal of Mathematics, Science and Technology Education, 3(4), 351‑361. https://doi.org/10.12973/ejmste/75414
  • Pearson, B. J., & Jackson, D. P. (2010). A hands-on introduction to single photons and quantum mechanics for undergraduates. American Journal of Physics, 78, 471-484. https://doi.org/10.1119/1.3494251
  • Ramlo, S. (2008). Validity and reliability of the force and motion conceptual evaluation. American Journal of Physics, 76(9), 882-886. https://doi.org/10.1119/1.2952440
  • Robbins, N., & Heiberger, R. (2011). Plotting Likert and other rating scales. Proceedings of the 2011 Joint Statistical Meeting, 1058-1066.
  • Rost, J. (2004). Lehrbuch Testtheorie – Testkonstruktion [Textbook test theory - test construction]. Verlag Hans Huber.
  • Russell, D. W. (2002). In Search of Underlying Dimensions: The Use (and Abuse) of Factor Analysis in Personality and Social Psychology Bulletin. Personality and Social Psychology Bulletin, 28, 1629-1646. https://doi.org/10.1177/014616702237645
  • Sadaghiani. H., & Pollock, S. J. (2015). Quantum mechanics concept assessment: Development and validation study. Physical Review Special Topics - Physics Education Research, 11, 010110. https://doi.org/10.1103/PhysRevSTPER.11.010110
  • Schermelleh-Engel, K., Moosbrugger, H. and Müller, H. (2003). Evaluating the fit of structural equation models: tests of significance and descriptive Goodness-of-Fit measures. Methods of Psychological Research Online, 8(2), 23-74.
  • Schnell, C. (2016). Lautes Denken als qualitative Methode zur Untersuchung der Validität von Testitems. Zeitschrift für ökonomische Bildung, 5, 26-49.
  • Schumacker, R. E., & Lomax, R. G. (2004). A Beginner’s Guide to Structural Equation Modeling (2nd ed.). Lawrence Erlbaum. https://doi.org/10.4324/9781410610904
  • Scott, T. F., Schumayer, D., & Gray, A. R. (2012). Exploratory factor analysis of a Force Concept Inventory data set. Physical Review Special Topics - Physics Education Research, 8(2), 020105. https://doi.org/10.1103/PhysRevSTPER.8.020105
  • Singh, C. (2001). Student understanding of quantum mechanics. American Journal of Physics, 69, 885-895. https://doi.org/10.1119/1.1365404
  • Singh, C. (2007). Student Difficulties with Quantum Mechanics Formalism. AIP Conference Proceedings, 883, 185-188. https://doi.org/10.1063/1.2508723
  • Singh, C., & Marshman, E. (2015). Review of student difficulties in upper-level quantum mechanics. Physical Review Special Topics - Physics Education Research, 11, 020117. https://doi.org/10.1103/PhysRevSTPER.11.020117
  • Spatz, V., Hopf, M., Wilhelm, T., Waltner, C., & Wiesner, H. (2020). Introduction to Newtonian mechanics via two-dimensional dynamics - The effects of a newly developed content structure on German middle school students. European Journal of Science and Mathematics Education, 8(2), 76-91. https://doi.org/10.30935/scimath/9548
  • Stadermann, H. K. E., van den Berg, E., & Goedhart, M. J. (2019). Analysis of secondary school quantum physics curricula of 15 different countries: Different perspectives on a challenging topic. Physical Review Physics Education Research, 15, 010130. https://doi.org/10.1103/PhysRevPhysEducRes.15.010130
  • Steif, P. S., & Dantzler, J. A. (2005). A statics concept inventory: Development and psychometric analysis. Journal of Engineering Education, 94, 363-371. https://doi.org/10.1002/j.2168-9830.2005.tb00864.x
  • Steiger, J. H., & Lind, J. C. (1980). Statistically based tests for the number of common factors [Paper presentation]. Annual Spring Meeting of the Psychometric Society, Iowa City, IA.
  • Stone, A., Allen, K., Rhoads, T. R., Murphy, T. J., Shehab, R. L., & Saha, C. (2003). The Statistics Concept Inventory: A pilot study. In Proceedings of the 33rd ASEE/IEEE Frontiers in Education Conference (Vol. 1, pp. T3D-1–T3D-6). https://doi.org/10.1109/FIE.2003.1263336
  • Styer, D. F. (1996). Common misconceptions regarding quantum mechanics. American Journal of Physics, 64, 31-34. https://doi.org/10.1119/1.18288
  • Taber, K. S. (2018). The Use of Cronbach’s Alpha When Developing and Reporting Research Instruments in Science Education. Research in Science Education, 48, 1273-1296. https://doi.org/10.1007/s11165-016-9602-2
  • Tamir, P. (1998). Assessment and evaluation in science education: Opportunities to learn and outcomes. In B. J. Fraser & K. G. Tobin (Eds.), International handbook of science education (pp. 761-789). Kluwer Academic. https://doi.org/10.1007/978-94-011-4940-2_45
  • Theyßen, H. (2014). Methodik von Vergleichsstudien zur Wirkung von Unterrichtsmedien [Methodology of comparative studies on the effect of teaching media]. In D. Krüger, I. Parchmann and H. Schecker (Eds.), Methoden in der naturwissenschaftsdidaktischen Forschung (pp. 67-79). Springer Verlag. https://doi.org/10.1007/978-3-642-37827-0_6
  • Thorn, J. J., Neel, M. S., Donato, V. W., Bergreen, G. S., Davies, R. E., & Beck, M. (2004). Observing the quantum behavior of light in an undergraduate laboratory. American Journal of Physics, 72, 1210-1219. https://doi.org/10.1119/1.1737397
  • Tyson, L. M., Venville, G. J., Harrison, A. G., & Treagust, D. F. (1997). A Multidimensional Framework for Interpreting Conceptual Change Events in the Classroom. Science Education, 81(4), 387-404. https://doi.org/10.1002/(SICI)1098-237X(199707)81:4<387::AID-SCE2>3.0.CO;2-8
  • Urban-Woldron, H., & Hopf, M. (2012). Entwicklung eines Testinstruments zum Verständnis in der Elektrizitätslehre [Development of a test instrument for understanding electricity]. Zeitschrift für Didaktik der Naturwissenschaften, 18, 203-229.
  • van Someren, M. W., Barnard, Y. F., & Sandberg, J. A. C. (1994). The think aloud method: a practical approach to modelling cognitive processes. (Knowledge-based systems). Academic Press.
  • Wuttiprom, S., Sharma, M. D., Johnston, I. D., Chitaree, R., & Soankwan, C. (2009). Development and Use of a Conceptual Survey in Introductory Quantum Physics. International Journal of Science Education, 31(5), 631-654. https://doi.org/10.1080/09500690701747226
  • Zhu, G., & Singh, C. (2012a). Improving students’ understanding of quantum measurement. I. Investigation of difficulties, Physical Review Special Topics - Physics Education Research, 8, 010117. https://doi.org/10.1103/PhysRevSTPER.8.010117
  • Zhu, G., & Singh, C. (2012b). Surveying students’ understanding of quantum mechanics in one spatial dimension. American Journal of Physics, 80(3), 252-259. https://doi.org/10.1119/1.3677653