Research Article

Impact of a mathematical pre-course on first-year physics students

Jonas Gleichmann 1 * , Hans Kubitschke 1 , Jörg Schnauß 1
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1 Institute for Didactics of Physics, Leipzig University, Leipzig, GERMANY* Corresponding Author
European Journal of Science and Mathematics Education, 13(3), July 2025, 172-190, https://doi.org/10.30935/scimath/16363
Published Online: 09 May 2025, Published: 01 July 2025
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ABSTRACT

The transition from school-level mathematics to the more abstract and formal structures in universities poses challenges for many first-year physics students. To address this gap, most physics faculties offer a mathematics pre-course. Here, we report about a pre-posttest study investigating the impact of a pre-course on N = 56 first-year physics students at the Leipzig University. The according tests were conducted in October 2022, which were correlated to the subsequent first and second-semester exam results. Thus, the research focused on measuring the knowledge gain and changes in mathematical abilities before and after the pre-course as well as the resulting medium-term effects. The results show a significant improvement in the math skills of the participants in the pre-course, especially among participants with intermediate prior knowledge. Additionally, the study reveals a correlation between the level of school mathematics instruction and learning success in the pre-course. Medium-term effects revealed that pre-course participants displayed higher pass rates and better grades, particularly in modules directly influenced by pre-course contents. This research underlines the effectiveness of the pre-course in mathematics in improving and reactivating the mathematical skills of first-year physics students.
Keywords: pre-course, mathematic prior knowledge, first-year students, higher education teaching

CITATION (APA)

Gleichmann, J., Kubitschke, H., & Schnauß, J. (2025). Impact of a mathematical pre-course on first-year physics students. European Journal of Science and Mathematics Education, 13(3), 172-190. https://doi.org/10.30935/scimath/16363

REFERENCES

  1. Almeida, D. (2000). A survey of mathematics undergraduates’ interaction with proof: Some implications for mathematics education. International Journal of Mathematical Education in Science and Technology, 31(6), 869–890. https://doi.org/10.1080/00207390050203360
  2. Bausch, I., Biehler, R., Bruder, R., Fischer, P. R., Hochmuth, R., Koepf, W., & Wassong, T. (2014). VEMINT – Interaktives Lernmaterial für mathematische Vor- und Brückenkurse [VEMINT – Interactive learning material for mathematical preparatory and bridging courses]. In I. Bausch et al. (Eds.), Mathematische Vor- und Brückenkurse. Konzepte und Studien zur Hochschuldidaktik und Lehrerbildung Mathematik (pp. 261–276). Springer. https://doi.org/10.1007/978-3-658-03065-0_18
  3. Biehler, R., Fischer, P. R., Hochmuth, R., & Wassong, T. (2011). Designing and evaluating blended learning bridging courses in mathematics. University of Rzeszów.
  4. Buschhüter, D., Spoden, C., & Borowski, A. (2016). Mathematische Kenntnisse und Fähigkeiten von Physikstudierenden zu Studienbeginn [Mathematical knowledge and skills of physics students at the beginning of their studies]. Zeitschrift für Didaktik der Naturwissenschaften, 22(1), 61–75. https://doi.org/10.1007/s40573-016-0041-4
  5. Cohen, J. (1960). A coefficient of agreement for nominal scales. Educational and Psychological Measurement, 20(1), 37–46. https://doi.org/10.1177/001316446002000104
  6. Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Routledge. https://doi.org/10.4324/9780203771587
  7. Coletta, V. P., Phillips, J. A., & Steinert, J. J. (2007). Interpreting force concept inventory scores: Normalized gain and SAT scores. Physical Review Physics Education Research, 3, Article 010106. https://doi.org/10.1103/PhysRevSTPER.3.010106
  8. de Guzmán, M., Hodgson, B. R., Robert, A., & Villani, V. (1998). Difficulties in the passage from secondary to tertiary education. Documenta Mathematica, 1998, 747–762. https://doi.org/10.4171/dms/1-3/72
  9. Deeken, C., Neumann, I., & Heinze, A. (2020). Mathematical prerequisites for STEM programs: What do university instructors expect from new STEM undergraduates? International Journal of Research in Undergraduate Mathematics Education, 6, 23–41. https://doi.org/10.1007/s40753-019-00098-1
  10. Department for Education. (2021). National curriculum in England: Mathematics programmes of study. GOV.UK. https://www.gov.uk/government/publications/national-curriculum-in-england-mathematics-programmes-of-study/national-curriculum-in-england-mathematics-programmes-of-study
  11. Derr, K., Hübl, R., & Ahmed, M. Z. (2018). Prior knowledge in mathematics and study success in engineering: Informational value of learner data collected from a web-based pre-course. European Journal of Engineering Education, 43(6), 911–926. https://doi.org/10.1080/03043797.2018.1462765
  12. Engzell, P., Frey, A., & Verhagen, M. D. (2021). Learning loss due to school closures during the COVID-19 pandemic. PNAS, 118(17), Article e2022379118. https://doi.org/10.1073/pnas.2022376118
  13. Gahrmann, D., Borowski, A., & Neumann, I. (2023). Höhere mathematische Komplexität in der Studieneingangsphase? In Proceedings of the Annual Conference of the Society for Chemistry and Physics Education (pp. 567–570).
  14. Galligan, L. (2004). Preparing international students for university: Mathematics as part of an integrated program. Australian Senior Mathematics Journal, 18(1), 28–41.
  15. Greefrath, G., & Hoever, G. (2016). Was bewirken Mathematik-Vorkurse? Eine Untersuchung zum Studienerfolg nach Vorkursteilnahme an der FH Aachen [What effect do mathematics preparatory courses have? A study on academic success after participation in a preparatory course at the FH Aachen]. In A. Hoppenbrock, R. Biehler, R. Hochmuth, & H. G. Rück (Eds.), Lehren und Lernen von Mathematik in der Studieneingangsphase. Konzepte und Studien zur Hochschuldidaktik und Lehrerbildung Mathematik (pp. 517–530). Springer. https://doi.org/10.1007/978-3-658-10261-6_33
  16. Gregory, R. (2013). Psychological testing: History, principles, and applications (7th ed.). Pearson.
  17. Hake, R. R. (1998). Interactive-engagement versus traditional methods: A six-thousand-student survey of mechanics test data for introductory physics courses. American Journal of Physics, 66(1), 64–74. https://doi.org/10.1119/1.18809
  18. Hazari, Z., Tai, R. H., & Sadler, P. M. (2007). Gender differences in introductory university physics performance: The influence of high school physics preparation and affective factors. Science Education, 91(6), 847–876. https://doi.org/10.1002/sce.20223
  19. Heinze, A., Neumann, I., Ufer, S., Rach, S., Borowski, A., Buschhüter, D., Greefrath, G., Halverscheid, S., Kürten, R., Pustelnik, K., & Sommerhoff, D. (2020). Mathematische Kenntnisse in der Studieneingangsphase – Was messen unsere Tests? [Mathematical skills in the initial phase of study – What do our tests measure?]. In A. Frank, S. Krauss, & K. Binder (Eds.), Beiträge zum Mathematikunterricht 2019 (pp. 345–348). Gesellschaft für Didaktik der Mathematik. https://doi.org/10.17877/DE290R-20862
  20. Herzog, A. R., & Bachman, J. G. (1981). Effects of questionnaire length on response quality. Public Opinion Quarterly, 45(4), 549–559. https://doi.org/10.1086/268687
  21. Holton, D. (2001). The teaching and learning of mathematics at university level. An ICMI study. Kluwer. https://doi.org/10.1007/0-306-47231-7
  22. Hudson, H. T., & McIntire, W. R. (1977). Correlation between mathematical skills and success in physics. American Journal of Physics, 45(5), 470–471. https://doi.org/10.1119/1.10823
  23. Hudson, H. T., & Rottmann, R. M. (1981). Correlation between performance in physics and prior mathematics knowledge. Journal of Research in Science Teaching, 18(4), 291–294. https://doi.org/10.1002/tea.3660180403
  24. Johnson, P., & O’Keeffe, L. (2016). The effect of a pre-university mathematics bridging course on adult learners’ self-efficacy and retention rates in STEM subjects. Irish Educational Studies, 35(3), 233–248. https://doi.org/10.1080/03323315.2016.1192481
  25. Konferenz der Fachbereiche Physik. (2011). Empfehlung der Konferenz der Fachbereiche Physik zum Umgang mit den Mathematikkenntnissen von Studienanfängern der Physik [Recommendation of the conference of physics departments on dealing with the mathematical knowledge of first-year physics students]. KFP. https://www.kfp-physik.de/dokument/KFP-Empfehlung-Mathematikkenntnisse.pdf
  26. Krause, F., & Reiners-Logothetidou, A. (1981). Folgerungen aus dem Studieneingangstest Physik 1978: Vorschläge zum Abbau der festgestellten Defizite [Conclusions from the 1978 physics entrance test: Suggestions for reducing the identified deficits]. Physikalische Blätter, 37(9), 295–299. https://doi.org/10.1002/phbl.19810370911
  27. Krosnick, J. A. (1991). Response strategies for coping with the cognitive demands of attitude measures in surveys. Applied Cognitive Psychology, 5(3), 213–236. https://doi.org/10.1002/acp.2350050305
  28. Kruger, J., & Dunning, D. (1999). Unskilled and unaware of it: How difficulties in recognizing one’s own incompetence lead to inflated self-assessments. Journal of Personality and Social Psychology, 77(6), 1121–1134. https://doi.org/10.1037/0022-3514.77.6.1121
  29. Leviatan, T. (2008). Bridging a cultural gap. Mathematics Education Research Journal, 20(2), 105–116. https://doi.org/10.1007/BF03217480
  30. Nasir, A. M., Omar, N. A. B., Sarudin, E. S. B., Masrom, S., & Ahmad, N. H. (2018). Teaching and learning of pre-calculus: An insights of educators. Journal of Fundamental and Applied Sciences, 9(6S), 452–467. https://doi.org/10.4314/jfas.v9i6s.35
  31. Nunnally, J. C., & Bernstein, I. H. (1994). Psychometric theory. McGraw-Hill. https://doi.org/10.1007/BF02301419
  32. Nurjannah, S., & Kusnandi. (2021). Literature study: The role of abstraction ability to strengthen students early knowledge in mathematics learning. Journal of Physics: Conference Series, 1806, Article 012064. https://doi.org/10.1088/1742-6596/1806/1/012064
  33. Okey, I. F., & Charles-Ogan, G. (2017). Effects of mathematics knowledge on physics students performance in electromagnetism. Journal of Education and Leadership Development, 7(1), 36–49.
  34. Popanao, M., Smith, M. F., & Pairor, P. (2023). Analyzing pre-instruction math knowledge and its correlation with introductory physics exam results. Journal of Physics: Conference Series, 2431, Article 012026. https://doi.org/10.1088/1742-6596/2431/1/012026
  35. Rach, S., Sommerhoff, D., & Ufer, S. (2021). KUM/MOAS: Technical report - Knowledge for university mathematics (KUM) and mathematics online assessment system (MOAS). Munich Center of the Learning Sciences. https://doi.org/10.5282/ubm/epub.76294
  36. Sangwin, C. (2013). Computer aided assessment of mathematics using stack. Oxford University Press. https://doi.org/10.1093/acprof:oso/9780199660353.001.0001
  37. Solomon, R. L. (1949). An extension of control group design. Psychological Bulletin, 46(2), 137–150. https://doi.org/10.1037/h0062958
  38. Tall, D. (1992). The transition to advanced mathematical thinking: Functions, limits, infinity and proof. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 495–511). Macmillan Library Reference.
  39. Tan, U.-X., Zhu, Y., Lee, C. H., Toh, T. L., Sze, G. K., Tay, S.Wong, D., & Pey, K. L. (2017). Preliminary study of integrated physics and mathematics bridging course. In Proceedings of the IEEE Global Engineering Education Conference (pp. 1146–1151). IEEE. https://doi.org/10.1109/EDUCON.2017.7942993
  40. Trapmann, S., Hell, B., Weigand, S., & Schuler, H. (2007). Die Validität von Schulnoten zur Vorhersage des Studienerfols - eine Metaanalyse [The validity of school grades in predicting academic success - A meta-analysis]. Zeitschrift für Pädagogische Psychologie, 21(1), 11–27. https://doi.org/10.1024/1010-0652.21.1.11