Riv. Mat. Univ. Parma, Vol. 14, No. 2, 2023

Sebastian Geisler [a]

Mathematical modelling with experiments: students sense of validation and its relevance

Pages: 265-280
Received: 1 May 2022
Accepted in revised form: 28 April 2023
Mathematics Subject Classification: 97M10, 97C70.
Keywords: mathematical modelling, experiments, validation.
Author address:
[a]: University of Potsdam, Potsdam, Germany

This research was supported by Deutsche Telekom Stiftung under grant 03 02821

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Abstract: Mathematical modelling is important yet challenging. Especially the validation of ones model seems to be a hurdle for many students. Thus, fostering students validation competence is an important aim in mathematics lessons. In this paper, I follow an idea to foster model validation that has been discussed in the literature before: the combination of modelling with scientific experiments. An analysis of the validation ideas from 111 students working on two different modelling tasks with experiments shows that a sufficient validation is not self-evident. In contrast, dealing with measurement errors that occur during experimentation might even hinder validation. It seems that some students put more trust in their mathematical models than in their experimental data and misinterpret the relation between data and model. Practical implications of these results are discussed.

W. Blum and D. Leiss, How do students and teachers deal with modelling problems, In: ''Mathematical modelling: Education, engineering, and economics-ICTMA 12'', Horwood, Chichester, 2007, 222-231. DOI
R. Borromeo Ferri, Theoretical and empirical differentiations of phases in the modelling process, ZDM Mathematics Education 38 (2006), 86-95. DOI
R. Borromeo Ferri, S. Grünewald and G. Kaiser, Effekte kurzzeitiger Interventionen auf die Entwicklung von Modellierungskompetenzen, In: R. Borromeo Ferri, G. Greefrath, G. Kaiser, eds, ''Mathematisches Modellieren für Schule und Hochschule'', Springer, Wiesbaden, 2013, 41-56. DOI
S. Carreira and A. M. Baioa, Students’ modelling routes in the context of object manipulation and experimentation in mathematics, In: G. Kaiser, W. Blum, R. Borromeo Ferri, G. Stillman, eds, ''Trends in Teaching and Learning of Mathematical modelling'', Springer, Dordrecht, 2011, 211-220. DOI
D. J. Carrejo and J. Marshall, What is mathematical modelling? Exploring prospective teachers’ use of experiments to connect mathematics to the study of motion, Math. Ed. Res. J. 19 (2007), 45-76. DOI
J. Engel, Anwendungsorientierte Mathematik: Von Daten zur Funktion, Mathematik für das Lehramt, Springer, Berlin, 2010. DOI
S. Ganter, Experimentieren - ein Weg zum Funktionalen Denken, Verlag Dr. Kovac, Hamburg, 2013. url
S. Geisler, Data-Based modelling with experiments - Students‘ experiences with model-validation, In: ''Proc. 44th Conf. of the Int. Group for the Psychology of Mathematics Education'', Vol. 2, PME 44, Khon Kaen, 2021, 289-296. url
S. Geisler, Mathematical modelling with experiments - Suggestion for an integrated model, In: ''Proc. 44th Conf. of the Int. Group for the Psychology of Mathematics Education'', Vol. 1, PME 44, Khon Kaen, 2021, p. 206. url
S. Geisler, Students' approaches concerning model validation and model improvement when solving modelling tasks with experiments, In: ''Proc. Twelfth Congress of the European Society for Research in Mathematics Education'' (CERME12, Feb 2022, Bozen), Free University of Bozen-Bolzano, Italy and ERME, 2022, hal-03759004.
S. Halverscheid, Building a local conceptual framework for epistemic actions in a modelling environment with experiments, ZDM Mathematics Education 40 (2008), 225-234. DOI
C. Hankeln, Mathematical modelling in Germany and France: a comparison of students’ modelling processes, Educ. Stud. Math. 103 (2020), 209-229. DOI
C. Hankeln and G. Greefrath, Mathematische Modellierungskompetenz fördern durch Lösungsplan oder Dynamische Geometrie-Software? Empirische Ergebnisse aus dem LIMo-Projekt, J. Math. Didakt. 42 (2021), 367-394. DOI
KMK Kultusminister Konferenz, Bildungsstandards im Fach Mathematik für die Allgemeine Hochschulreife, 2012, https://www.kmk.org/ fileadmin/Dateien/veroeffentlichungen\_beschluesse/2012/2012\_10\_18-Bildungs standards-Mathe-Abi.pdf
M. Ludwig and R. Oldenburg, Lernen durch Experimentieren. Handlungsorientierte Zugänge zur Mathematik, Mathematik lehren 141 (2007), 4-11.
W. Maull and J. Berry, An investigation of student working styles in a mathematical modelling activity, Teaching Mathematics and Its Applications 20 (2001), 78-88. DOI
P. Mayring, Qualitative Inhaltsanalyse, Beltz, Basel, 2010.
M. Niss, Mathematics in Society, In: ''Didactics of Mathematics as a scientific discipline'', Kluwer Academic Publishers, Dodrecht, 1994, 367-378. WorldCat
OECD, PISA 2015 Assessment and Analytical Framework, OECD Punlishing, Paris, 2017. DOI
A. H. Schoenfeld, Learning to think mathematically: Problem solving, metacognition, and sense-making in mathematics, In: D. Grouws, ed., ''Handbook for Research on Mathematics Teaching and Learning'', MacMillan, New York, 1992, 334-370. Article
H. Theyssen, Mythos Bierschaumzerfall - Ein Analogon für den radioaktiven Zerfall?, PhyDid 2 (2009), no. 8, 49-57. Article
S. Zell and A. Beckmann, Modelling activities while doing experiments to discover the concept of variable, In: Proc. Sixth Congress of the European Society for Research in Mathematics Education (CERME 6, Jan 28 - Feb 1, 2009, Lyon, France), Institut National de Recherche Pédagogique and ERME, 2010, 2216-2225.

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