- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Physics Education Research

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Editors' Suggestion
  • Open Access

Assessing changes in physics students’ preparedness: Mathematics and physics prior knowledge of German first-semester students in 2013 and 2023

Dennys Gahrmann1,*, Irene Neumann2, and Andreas Borowski1

  • *Contact author: Dennys.gahrmann@uni-potsdam.de
PDF

Phys. Rev. Phys. Educ. Res. 22, 010110 – Published 28 January, 2026

DOI: https://doi.org/10.1103/vkyq-fmcv

Abstract

Insufficient prior knowledge in mathematics and physics is seen as a key factor for high attrition rates in physics degree programs. To investigate trends in students’ academic preparedness, this study examines how the mathematics and physics prior knowledge of first-year physics students in Germany has changed between 2013 and 2023. Using data from standardized diagnostic tests administered at multiple universities in both cohorts, we compared performance across cohorts and institutions. Results indicate small but meaningful increases in average performance from 2013 to 2023: mathematics knowledge improved slightly (Cohen’s d=0.10), and physics knowledge even more (Cohen’s d=0.21). Despite this improvement, students’ average performance remains only modest—67% correct in mathematics and only 38% correct in physics. Moreover, our findings indicate a growing heterogeneity in students’ preparation: while mathematics and physics performance improved at some universities, mathematics performance declined at others. Overall, the results underscore the importance of continued monitoring of incoming students’ prior knowledge and support the use of diagnostic tools to inform targeted instructional strategies transition to university-level physics.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (61)

  1. A. M. Porter, R. Y. Chu, and R. Ivie, Attrition and Persistence in Undergraduate Physics Programs (American Institute of Physics, College Park, MD, 2024).
  2. U. Heublein, C. Hutzsch, and R. Schmelzer, Die Entwicklung der Studienabbruchquoten in Deutschland, DZHW Brief (DZHW, Hannover, 2022).
  3. National Center for Education Statistics, Undergraduate Retention and Graduation Rates. Condition of Education. U.S. Department of Education, Institute of Education Sciences (2022), Retrieved from https://nces.ed.gov/programs/coe/indicator/ctr.
  4. A. Delahay, M. Lovett, D. Anderson, and S. Sen, Components of the preparation gap for physics learning vary in two learner groups, Phys. Rev. Phys. Educ. Res. 19, 020122 (2023).
  5. S. Sorge, S. Petersen, and K. Neumann, Die Bedeutung der Studierfähigkeit für den Studienerfolg im 1. Semester in Physik, Z. Didakt. Naturwiss. 22, 165 (2016).
  6. E. W. Burkholder, G. Murillo-Gonzalez, and C. Wieman, Importance of math prerequisites for performance in introductory physics, Phys. Rev. Phys. Educ. Res. 17, 010108 (2021).
  7. D. Buschhüter, C. Spoden, and A. Borowski, Physics knowledge of first semester physics students in Germany: A comparison of 1978 and 2013 cohorts, Int. J. Sci. Educ. 39, 1109 (2017).
  8. J. Stewart, J. Hansen, and E. Burkholder, Visualizing and predicting the path to an undergraduate physics degree at two different institutions, Phys. Rev. Phys. Educ. Res. 18, 020117 (2022).
  9. F. Thiel, D.-P. I. Blüthmann, D.-S. M. Richter, and D.-P. N. Csonka, Ergebnisse der Befragung der Studierenden in den Bachelorstudiengängen (Freie Universität Berlin, Berlin, 2006).
  10. G. Kuh, J. Kinzie, J. Buckley, B. Bridges, and J. Hayek, What matters to student success: A review of the literature, Report No. NPEC 2006-1, National Postsecondary Education Cooperative, 2006.
  11. C. Konegen-Grenier and C. Kuhlmann, Studierfähigkeit Und Hochschulzugang (Deutscher Instituts-Verlag, Köln, 2002).
  12. S. Salehi, E. Burkholder, G. P. Lepage, S. Pollock, and C. Wieman, Demographic gaps or preparation gaps?: The large impact of incoming preparation on performance of students in introductory physics, Phys. Rev. Phys. Educ. Res. 15, 020114 (2019).
  13. M. Solis-Foronda, Predictors of students’ knowledge in general physics, Univ. J. Educ. Res. 8, 3630 (2020).
  14. J. Fleischer, D. Leutner, M. Brand, H. Fischer, M. Lang, P. Schmiemann, and E. Sumfleth, Vorhersage des Studienabbruchs in naturwissenschaftlich-technischen Studiengängen, Z. Erzieh. 22, 1077 (2019).
  15. D. Buschhüter, C. Spoden, and A. Borowski, Mathematische Kenntnisse und Fähigkeiten von Physikstudierenden zu Studienbeginn, Z. Didakt. Naturwiss. 22, 61 (2016).
  16. E. W. Burkholder and C. E. Wieman, What do AP physics courses teach and the AP physics exam measure?, Phys. Rev. Phys. Educ. Res. 15, 020117 (2019).
  17. A. Gerdes, S. Halverscheid, and S. Schneider, Teilnahme an mathematischen Vorkursen und langfristiger Studienerfolg. Eine empirische Untersuchung, J. Math. Didakt. 43, 377 (2022).
  18. R. Henderson, C. Zabriskie, and J. Stewart, Rural and first generation performance differences on the force and motion conceptual evaluation, presented at PER Conf. 2018, Washington, DC, 10.1119/perc.2018.pr.Henderson.
  19. NAEP mathematics: National trends and student skills, https://www.nationsreportcard.gov/reports/mathematics/2024/g4_8/national-trends/?grade=8.
  20. PISA 2022: Analyse der Bildungsergebnisse in Deutschland, edited by D. Lewalter, J. Diedrich, F. Goldhammer, O. Köller, and K. Reiss (Waxmann Verlag GmbH, Münster, Germany, 2023).
  21. D. Gahrmann, I. Neumann, and A. Borowski, Comparing prior knowledge of first-semester physics students between the cohorts of 2013 and 2023, in Book of extended abstracts of the 4th World Conference on Physics Education. Embracing Changes Together, edited by M. Kaczmarek and D. Sokołowska (Astronomy and Applied Computer Science Jagiellonian University, Kraków, Poland, 2024), pp. 254–255, ISBN [Amazon][WorldCat].
  22. E. W. Burkholder, K. Wang, and C. Wieman, Validated diagnostic test for introductory physics course placement, Phys. Rev. Phys. Educ. Res. 17, 010127 (2021).
  23. S. Ufer, Studierfähigkeit als eine Zieldimension von Mathematikunterricht in der gymnasialen Oberstufe. Konzepte, Modelle und Beitrag des Mathematikunterrichts, in Das Fach Mathematik in der Gymnasialen Oberstufe, edited by T. Rolfes, S. Rach, S. Ufer, and A. Heinze (Waxmann Verlag GmbH, Münster; New York, 2022), pp. 75–102.
  24. D. Hewagallage, E. Christman, and J. Stewart, Examining the relation of high school preparation and college achievement to conceptual understanding, Phys. Rev. Phys. Educ. Res. 18, 010149 (2022).
  25. L. E. Kost, S. J. Pollock, and N. D. Finkelstein, Characterizing the gender gap in introductory physics, Phys. Rev. ST Phys. Educ. Res. 5, 010101 (2009).
  26. S. Z. Lahme, J. O. Cirkel, L. Hahn, J. Hofmann, J. Neuhaus, S. Schneider, and P. Klein, Enrollment to exams: Perceived stress dynamics among first-year physics students, Phys. Rev. Phys. Educ. Res. 20, 020127 (2024).
  27. T. Binder, A. Sandmann, B. Sures, G. Friege, H. Theyssen, and P. Schmiemann, Assessing prior knowledge types as predictors of academic achievement in the introductory phase of biology and physics study programmes using logistic regression, Int. J. STEM Educ. 6, 33 (2019).
  28. M. S. Feser, I. Haak, and T. Rabe, Sense of belonging among first-year physics students in Germany: Exploring intergroup differences and correlations, Eurasia J. Math. Sci. Technol. Educ. 19, em2345 (2023).
  29. J. P. Zwolak, R. Dou, E. A. Williams, and E. Brewe, Students’ network integration as a predictor of persistence in introductory physics courses, Phys. Rev. Phys. Educ. Res. 13, 010113 (2017).
  30. M. Franklin and E. Brewe, What correlates with persistence of women in physics?, Phys. Rev. Phys. Educ. Res. 21, 010115 (2025).
  31. D. Thomas and J. S. Brown, A New Culture of Learning: Cultivating the Imagination for a World of Constant Change (CreateSpace, Lexington, KY, 2011), Vol. 219.
  32. F. Almasri, Exploring the impact of artificial intelligence in teaching and learning of science: A systematic review of empirical research, Res. Sci. Educ. 54, 977 (2024).
  33. G. Roy, S. Sikder, and L. Danaia, Adopting scientific literacy in early years from empirical studies on formal education: A systematic review of the literature, Int. J. STEM Educ. 12, 26 (2025).
  34. U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), various years, 2009–2024 Science Assessments.
  35. OECD, PISA 2022 Results (Volume I): The State of Learning and Equity in Education (OECD, Paris, 2023).
  36. OECD, PISA 2022 Technical Report (OECD, Paris, 2024).
  37. OECD, Do Adults Have the Skills They Need to Thrive in a Changing World?: Survey of Adult Skills 2023 (OECD, Paris, 2024).
  38. A. E. Lawson, The development and validation of a classroom test of formal reasoning, J. Res. Sci. Teach. 15, 11 (1978).
  39. L. Bao, Y. Xiao, K. Koenig, and J. Han, Validity evaluation of the Lawson Classroom Test of scientific reasoning, Phys. Rev. Phys. Educ. Res. 14, 020106 (2018).
  40. R. J. Beichner, Testing student interpretation of kinematics graphs, Am. J. Phys. 62, 750 (1994).
  41. G. Zavala, S. Tejeda, P. Barniol, and R. J. Beichner, Modifying the test of understanding graphs in kinematics, Phys. Rev. Phys. Educ. Res. 13, 020111 (2017).
  42. F. Krause and A. Reiners-Logothetidou, Der bundesweite Studieneingangstest Physik 1978 (1981).
  43. D. Buschhüter and A. Borowski, Modellierung von Eingangsanforderungen für Das Studienfach Physik, in Naturwissenschaftliche Bildung Zwischen Science- und Fachunterricht, edited by S. Bernholt (Gesellschaft für Didaktik der Chemie und Physik (GDCP), München, 2014), pp. 540–542.
  44. D. Gahrmann, I. Neumann, and A. Borowski, Welche Mathematik- und Physikaufgaben sollten Studierende lösen können, um erfolgreich ins Physikstudium zu starten?—Die Perspektive von Physikdozierenden, Phydid A (to be published).
  45. C. Deeken, I. Neumann, and A. Heinze, Mathematical prerequisites for STEM programs: What do university instructors expect from new STEM undergraduates?, Int. J. Res. Undergrad. Math. Educ. 6, 23 (2020).
  46. R Core Team, r: A Language and Environment for Statistical Computing (R Foundation for Statistical Computing, Vienna, Austria, 2024).
  47. Y. Rosseel, lavaan: An r package for structural equation modeling, J. Stat. Softw. 48, 1 (2012).
  48. F. Hälsig, Branchenübergreifende Analyse des Aufbaus einer starken Retail Brand (Gabler, Wiesbaden, 2008).
  49. B. M. Byrne, Structural equation modeling with AMOS, EQS, and LISREL: Comparative approaches to testing for the factorial validity of a measuring instrument, Int. J. Nondestruct. Test. 1, 55 (2001).
  50. D. L. Streiner, Starting at the beginning: An introduction to coefficient alpha and internal consistency, J. Pers. Assess. 80, 99 (2003).
  51. M. A. Wirtz and F. Caspar, Beurteilerübereinstimmung und Beurteilerreliabilität: Methoden zur Bestimmung und Verbesserung der Zuverlässigkeit von Einschätzungen mittels Kategoriensystemen und Ratingskalen (Hogrefe, Verlag für Psychologie, Göttingen Bern Toronto Seattle, 2022).
  52. J. R. Landis and G. G. Koch, The measurement of observer agreement for categorical data, Biometrics 33, 159 (1977).
  53. F. Krause and A. Reiners-Logothetidou, Folgerungen aus dem Studieneingangstest Physik 1978: Vorschläge zum Abbau der festgestellten Defizite, Phys. J. 37, 295 (1981).
  54. J. Cohen, Statistical Power Analysis for the Behavioral Sciences (Routledge, New York, 1988).
  55. D. S. Yeager et al., A national experiment reveals where a growth mindset improves achievement, Nature (London) 573, 364 (2019).
  56. S. Büchele and F. Feudel, Changes in students’ mathematical competencies at the beginning of higher education within the last decade at a German University, Int. J. Sci. Math. Educ. 21, 2325 (2023).
  57. Kultusministerkonferenz (Hrsg., Beschlüsse der Kultusministerkonferenz: Bildungsstandards im Fach Mathematik für die Allgemeine Hochschulreife (2012), https://www.kmk.org/fileadmin/veroeffentlichungen_beschluesse/2012/2012_10_18-Bildungsstandards-Mathe-Abi.pdf.
  58. Kultusministerkonferenz (Hrsg., Beschlüsse der Kultusministerkonferenz: Bildungsstandards im Fach Physik für die Allgemeine Hochschulreife (2020), https://www.kmk.org/fileadmin/veroeffentlichungen_beschluesse/2020/2020_06_18-BildungsstandardsAHR_Physik.pdf.
  59. B. R. Wilcox, S. J. Pollock, and D. R. Bolton, Retention of conceptual learning after an interactive introductory mechanics course, Phys. Rev. Phys. Educ. Res. 16, 010140 (2020).
  60. OECD, PISA 2022 Results (Volume II): Learning During—and From—Disruption (OECD, Paris, 2023).
  61. European Commission. Directorate General for Education, Youth, Sport and Culture, Covid-19 Learning Deficits in Europe: Analysis and Practical Recommendations: Analytical Report (Publications Office, Luxembourg, 2023).

Outline

Information

Phys. Rev. Phys. Educ. Res. 22, 010110– Published 28 January, 2026
  • Received 2 September 2025
  • Accepted 3 December 2025
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation