Same terms, different meanings: the impact of semantic aspects on biology students’ reasoning in mathematical modelling tasks
DOI:
https://doi.org/10.7146/nomad.v30i4.164540Keywords:
Interdisciplinary education, mathematical modelling, biology undergraduates, science terminology, semantic differences, conceptual understandingAbstract
In response to a continuously growing need for quantitative literacy of biology graduates, more attention is being paid to their mathematics education. Mathematical modelling and simulations are viewed as the most efficient approaches impacting students’ learning of mathematics. Subject induced peculiarities in the training of future biologists influence students’ approaches to the solution of modelling tasks and mathematical modelling in general. This paper addresses semantic aspects which may hinder students’ understanding of tasks and affect their reasoning.
References
Adams, R.A., & Essex, C. (2018). Calculus: A complete course (9th ed.). Pearson.
Ausubel, D.P., Novak, J.D. & Hanesian, H. (1978). Educational psychology: A cognitive view. Holt, Rinehart, and Winston.
Bartholomew, G.A. (1986). The role of natural history in contemporary biology. BioScience, 36(5), 324-329. https://doi.org/10.2307/1310237
Benjafield, J.G. (2020). Vocabulary sharing among subjects belonging to the hierarchy of sciences. Scientometrics, 125, 1965–1982.
https://doi.org/10.1007/s11192-020-03671-7
Blum W. (2011). Can modelling be taught and learnt? Some answers from empirical research. In: G Kaiser, W Blum, R Borromeo Ferri, G Stillman, (Eds.), Trends in the teaching and learning of mathematical modelling (pp. 14–30). Springer. https://doi.org/10.1007/978-94-007-0910-2_3
Boyce, W. E., & DiPrima, R. C. (2013). Elementary differential equations and boundary value problems (10th ed.). Wiley.
Buono, P.L. (2016). Advanced calculus: Differential calculus and Stokes’ theorem. De Gruyter.
Campbell, N.A. & Reece, J.B. (2005). Biology (5th ed.). Benjamin Cummings.
Chapman, E.J. & Byron, C.J. (2018). The flexible application of carrying capacity in ecology. Global Ecology and Conservation, 13: e00365.
https://doi.org/10.1016/j.gecco.2017.e00365
Chiel, H. J., McManus, J. M., & Shaw, K. M. (2010). From biology to mathematical models and back: teaching modeling to biology students, and biology to math and engineering students. CBE-Life Sciences Education, 9(3), 248–265. https://doi.org/10.1187/cbe.10-03-0022
Coleman, A.B., Lam, D.P., & Soowal, L.N. (2015). Correlation, necessity, and sufficiency: common errors in the scientific reasoning of undergraduate students for interpreting experiments. Biochemistry and Molecular Biology Education, 43(5), 305–315. https://doi.org/10.1002/bmb.20879
Ferri, R. & Mousoulides, N. (2018). Mathematical modelling as a prototype for interdisciplinary mathematics education? - Theoretical reflections. In T. Dooley, & G. Gueudet (Eds.), Proceedings of CERME 10 (pp.900-907). DCU Institute of Education and ERME.
Giordano, F., Fox, W.P., & Horton, S.B. (2014). A first course in mathematical modeling (5th ed.). Brooks/Cole, Cengage Learning.
Harte, J. (1988). Consider a spherical cow. A course in environmental problem solving. University Science Books.
Hixon, M.A. (2008). Carrying capacity. In: S.E. Jørgensen, & B.D. Fath (Eds), Encyclopaedia of Ecology (pp. 528-530). Academic Press.
Iacobelli, M. (1949). The semantic discipline. The Modern Language Journal, 33(1), 16-22.
Jankvist, U.T., & Niss, M. (2020). Upper secondary school students’ difficulties with mathematical modelling. International Journal of Mathematical Education in Science and Technology, 51(4), 467–496.
https://doi.org/10.1080/0020739X.2019.1587530
Karsai, I. & Kampis, G. (2010). The crossroads between biology and mathematics: the scientific method as the basics of scientific literacy. BioScience, 60(8), 632–638. https://doi.org/10.1525/bio.2010.60.8.9
Keeling, D.M, Garza, P., Nartey, C.M., & Carvunis, A.R. (2019). The meanings of ‘function’ in biology and the problematic case of de novo gene emergence. eLife, 8: e47014. https://doi.org/10.7554/eLife.47014
Langer, G. (2018). Possible mathematical definitions of the biological term “breed”. Archives of Animal Breeding, 61(2), 229–243.
https://doi.org/10.5194/aab-61-229-2018
Marshall, S., Gilmour, M., & Lewis, D. (1991). Words that matter in science and technology. Research in Science & Technological Education, 9(1), 5–16.
https://doi.org/10.1080/0263514910090102
May, R.M. (2004). Uses and abuses of mathematics in biology. Science, 303(5659), 790–793. https://doi.org/10.1126/science.1094442
McArdle, B. H. (2013). Population density. In: S. A. Levin (Ed.), Encyclopaedia of Biodiversity (pp. 157–167). Academic Press.
McGhee, G.R. (2015). Limits in the evolution of biological form: a theoretical morphologic perspective. Interface Focus, 5(6).
https://doi.org/10.1098/rsfs.2015.0034
Miller, S.A & Harley, J.P. (2001). Zoology (5th ed.). McGraw-Hill Education.
Nicolson, H. (1947). On human misunderstanding, Atlantic Monthly, CLXXX(7), 113–114.
Niss M. (2017). Obstacles related to structuring for mathematization encountered by students when solving physics problems. International Journal of Science & Mathematics Education, 15, 1441–1462.
https://doi.org/10.1007/s10763-016-9754-6
Niss, M., & Blum, W. (2020). The learning and teaching of mathematical modelling. Routledge.
Novak, J.D. (1977). A theory of education. Cornell University Press.
Odum, E.P. (1953). Fundamentals of ecology. Saunders.
Odum, E.P. (1971). Fundamentals of ecology, 3rd ed. Saunders.
Ortiz, M. T. (2006). Numbers, neurons & tides, oh my! Mathematics, the forgotten tool in biology. The American Biology Teacher, 68(8), 458–462. https://doi.org/10.2307/4452042
Pachter, L. (2014, December 30). The two cultures of mathematics and biology. Liorpachter Wordpress. https://liorpachter.wordpress.com/2014/12/30/the-two-cultures-of-mathematics-and-biology/ Accessed 4 Oct 2025.
Pearl, R. (1927). The growth of population. Quarterly Review of Biology, 2(4), 532–548. https://doi.org/10.1086/394288
Rogawski, J., Adams, C. & Franzosa, R. (2018). Calculus: Early transcendentals (4th ed.). W.H. Freeman & Co.
Rogovchenko, S., & Rogovchenko, Y. (2024). Boundary crossing in mathematical modelling activities with biology undergraduates. In: Siller, H.S., Geiger, V., Kaiser, G. (Eds.) Researching Mathematical Modelling Education in Disruptive Times (pp. 653–663). Springer.
https://doi.org/10.1007/978-3-031-53322-8_54
Rogovchenko, Y. (2021). Mathematical modelling with biology undergraduates: Balancing task difficulty and level of support. In: Leung, F.K.S., Stillman, G.A., Kaiser, G., Wong, K.L. (Eds.) Mathematical modelling education in East and West (pp. 571–582). Springer.
https://doi.org/10.1007/978-3-030-66996-6_48
Rogovchenko, Y. & Rogovchenko, S. (2023). Mathematics education of future biologists: A strong need for brokering between mathematics and biology communities of practice. In: T. Dreyfus, A.S. González-Martín, E. Nardi, J. Monaghan & P.W. Thompson (Eds.), The Learning and Teaching of Calculus Across Disciplines – Proceedings of the Second Calculus Conference (pp. 161–164). MATRIC.
Sayre, N. F. (2008). The genesis, history, and limits of carrying capacity. Annals of the Association of American Geographers, 98(1), 120–134.
http://dx.doi.org/10.1080/00045600701734356
Steen, L.A. (2005). The “gift” of mathematics in the era of biology. In L.A. Steen (Ed.). Math and bio2010: Linking undergraduate disciplines (pp. 13–25). Mathematical Association of America.
Stillman G., Brown J., & Galbraith P. (2010). Identifying challenges with transitions phases in mathematical modelling activities at year 9. In: R. Lesh, P.L. Galbraith, C.R. Haines, & A. Hurford (Eds.). Modeling students’ mathematical modeling competencies: ICTMA 13 (pp. 385–398). Springer. https://doi.org/10.1007/978-1-4419-0561-1_33
Svoboda, J. & Passmore, C. (2013). The strategies of modeling in biology education. Science & Education, 22, 119–142.
https://doi.org/10.1007/s11191-011-9425-5
Tortora, G.J., Funke, B.R., Case, C.L., Weber, D., & Bair, W.B. (2021). Microbiology: An introduction (13th ed.). Pearson.
Verhulst, P.F. (1838). Notice sur la loi que la population suit dans son accroissement. Correspespondance Mathématique et Physique, 10, 113–121. https://doi.org/10.1007/BF02309004
Viirman, O., & Nardi, E. (2019). Negotiating different disciplinary discourses: Biology students’ ritualized and exploratory participation in mathematical modeling activities. Educational Studies in Mathematics, 101, 233–252. https://doi.org/10.1007/s10649-018-9861-0
Vygotsky, L. (1986). Thought and language. (A. Kozulin, Trans.). MIT Press.
Wandersee, J.H. (1988). The terminology problem in biology education: A reconnaissance. The American Biology Teacher, 50(2), 97–100.
https://doi.org/10.2307/4448654
Wellington, J., & Osborne, J. (2001). Language and literacy in science education. Open University Press.
Wisniewski, R.L. (1980). Carrying capacity: understanding our biological limitations. Humboldt Journal of Social Relations, 7(2), 55–70.
Yoshihara M., & Yoshihara M. (2018). ‘Necessary and sufficient’ in biology is not necessarily necessary - confusions and erroneous conclusions resulting from misapplied logic in the field of biology, especially neuroscience. Journal of Neurogenetics, 32(2), 53–64.
https://doi.org/10.1080/01677063.2018.1468443
Zukswert, J. M., Barker, M. K., & McDonnell, L. (2019). Identifying troublesome jargon in biology: Discrepancies between student performance and perceived understanding. CBE-Life Sciences Education, 18(1), ar6.
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