Real objects as a reason for mathematical reasoning – A comparison of different task settings

Simone Jablonski

doi:10.29333/iejme/13859

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Simone Jablonski ¹ ^*

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¹ Goethe University Frankfurt, Frankfurt, GERMANY^* Corresponding Author

Abstract

In this article, the goal is to describe students’ mathematical reasoning in the context of different settings of problem-solving tasks. The core of the tasks are real objects, which are presented to the students with the help of photos, a 3D model or in the environment itself. With reference to the experiential learning theory and relations to problem-solving and modelling, theoretical potentials for mathematical reasoning emerge. In a qualitative study with 19 secondary school students these are empirically tested. The evaluation of the video recordings of the students’ solution processes are coded with the help of qualitative content analysis, among others with references to problem-solving and linguistic categories of conclusive speech acts. The results show that mathematical reasoning can be observed especially in the work with photos and that the work with real objects generally evokes reasoning activities in the area of planning and exploration of strategies.

Keywords

argumentation
mathematical reasoning
outdoor mathematics
problem-solving
task settings

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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Article Type: Research Article

INT ELECT J MATH ED, Volume 18, Issue 4, November 2023, Article No: em0758

https://doi.org/10.29333/iejme/13859

Publication date: 05 Nov 2023

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Article Downloads: 587

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References

Ärlebäck, J., & Albarracín, L. (2019). An extension of the MAD framework and its possible implication for research. In U. Jankvist, M. Van den Heuvel-Panhuizen, & M. Veldhuis (Eds.), Proceedings of the 11^th Congress of the European Society for Research in Mathematics Education (pp. 1128-1135). Freudenthal Group & Freudenthal Institute, Utrecht University and ERME.
Baker, M. (2003). Computer-mediated argumentative interactions for the co-elaboration of scientific notions. In J. Andriessen, M. Baker, & D. Suthers (Eds.), Arguing to learn: Confronting cognitions in computer-supported collaborative learning environments (pp. 47-78). Springer. https://doi.org/10.1007/978-94-017-0781-7_3
Barlovits, S., & Ludwig, M. (2023). Effective or not? The impact of mobile learning on students’ interest, self-efficacy, and performance in outdoor mathematics education [Paper presentation]. The 13^th Congress of the European Society for Research in Mathematics Education.
Bergqvist, T., Lithner, J., & Sumpter, L. (2008). Upper secondary students task reasoning. International Journal of Mathematical Education in Science and Technology, 39(1), 1-12. https://doi.org/10.1080/00207390701464675
Blum, W., & Leiss, D. (2007). How do students and teachers deal with mathematical modelling problems? In C. Haines, P. Galbraith, W. Blum, & S. Khan (Eds.), Mathematical modelling (pp. 222-231). Woodhead Publishing. https://doi.org/10.1533/9780857099419.5.221
Boesen, J., Lithner, J., & Palm, T. (2010). The relation between types of assessment tasks and the mathematical reasoning students use. Educational Studies in Mathematics, 105, 75-89. https://doi.org/10.1007/s10649-010-9242-9
Buchholtz, N. (2021). Students’ modelling proceses when working with math trails. Quadrante, 30(1), 140-157. https://doi.org/10.48489/quadrante.23699
Budke, A., & Meyer, M. (2015). Fachlich argumentieren lernen–Die Bedeutung der Argumentation in den unterschiedlichen Schulfächern [Learning to argue professionally–The importance of argumentation in different school subjects]. In A. Budke, M. Kuckuck, M. Meyer, F. Schäbitz, K. Schlüter, & G. Weiss (Eds.), Fachlich argumentieren lernen. Didaktische Forschungen zur argumentation in den Unterrichtsfächern [Learn to argue professionally. Didactic research on argumentation in teaching subjects] (pp. 9-28). Waxmann. https://doi.org/10.25656/01:14021
Duijzer, A. C. G., Van den Heuvel-Panhuizen, M., Veldhuis, M., Doorman, L. M., & Leseman, P. P. M. (2019). Embodied learning environments for graphing motion: A systematic literature review. Educational Psychology Review, 31(3), 597-629. https://doi.org/10.1007/s10648-019-09471-7
Eames, C., Brady, C., Jung, H., & Glancy, A. (2018). Designing powerful environments for examining and supporting teachers’ models and modeling. In W. Blum, & R. Borromeo Ferri (Eds.), Lehrerkompetenzen zum Unterrichten mathematischer Modellierung. Realitätsbezüge im Mathematikunterricht [Teacher skills for teaching mathematical modeling. Reality references in mathematics lessons] (pp. 237-266). Springer. https://doi.org/10.1007/978-3-658-22616-9_11
Field, A., & Hole, G. (2002). How to design and report experiments. SAGE.
Habermas, J. (1981). Theorie des kommunikativen Handelns, band 1. Handlungsrationalität und gesellschaftliche Rationalisierung [Theory of communicative action, volume 1. Action rationality and social rationalization]. Suhrkamp.
Hallström, J., & Schönborn, K. J. (2019). Models and modelling for authentic STEM education: Reinforcing the argument. International Journal of STEM Education, 6, 22. https://doi.org/10.1186/s40594-019-0178-z
Hanna, G. (2000). Proof, explanation and exploration: An overview. Educational Studies in Mathematics, 44(1/2), 5-23. https://doi.org/10.1023/A:1012737223465
Hartmann, L.-M., & Schukajlow, S. (2021). Interest and emotions while solving real-world problems inside and outside the classroom. In F. K. S. Leung, G. A. Stillman, G. Kaiser, & K. L. Wong (Eds.), Mathematical modelling education in east and west. International perspectives on the teaching and learning of mathematical modelling (pp. 153-163). Springer. https://doi.org/10.1007/978-3-030- 66996-6_13
Hattie, J., Marsh, H., Neill, J., & Richards, G. (1997). Adventure education and outward bound: Out-of-class experiences that make a lasting difference. Review of Educational Research, 67(1), 43-87. https://doi.org/10.2307/1170619
Jablonski, S. (2022). Mathematical reasoning outside the classroom – A case study with primary school students solving math trail tasks. In J. Hodgen, E. Geraniou, G. Bolondi, & F. Ferretti (Eds.), Proceedings of the Twelfth Congress of the European Society for Research in Mathematics Education (pp. 201-208). Free University of Bozen-Bolzano and ERME.
Jablonski, S. (2023). Is it all about the setting? — A comparison of mathematical modelling with real objects and their representation. Educational Studies in Mathematics, 113, 307-330. https://doi.org/10.1007/s10649-023-10215-2
Jablonski, S., & Ludwig, M. (2022). Examples and generalizations in mathematical reasoning – A study with potentially mathematically gifted children. Journal on Mathematics Education, 13(4), 605-630. https://doi.org/10.22342/jme.v13i4.pp605-630
Jablonski, S., Läufer, T., & Ludwig, M. (2023). Make it real: Students’ mathematical modelling realized with 3D printing [Accepted paper for presentation]. In 13th congress of the European Society for Research in Mathematics Education (CERME13), Budapest, Hungary.
Kilpatrick, J., Swafford, J., & Findell, B. (2001). Adding it up: Helping children learn mathematics. National Academies Press.
Klein, J. (2008). Erklären und Argumentieren als interaktive Gesprächsstrukturen [Explaining and reasoning as interactive conversational structures]. In K. Brinker, G. Antos, W. Heinemann, & S. F. Sager (Eds.), Ein internationales Handbuch zeitgenössischer Forschung [An international handbook of contemporary research] (pp. 1309-1329). De Gruyter Mouton. https://doi.org/10.1515/9783110169188.2.18.1309
Kolb, D. (1984). Experiential learning: Experience as the source of learning and development. Prentice-Hall, Inc.
Kolb, D., Boyatzis, R., & Mainemelis, C. (2000). Experiential learning theory: Previous research and new directions. In R. Sternberg, & L. Zhang (Eds.), Perspectives on cognitive, learning, and thinking styles. Lawrence Erlbaum. https://doi.org/10.4324/9781410605986-9
Lakoff, G., & Nuñez, R. (2009). Where mathematics comes from: How the embodied mind brings mathematics into being. Basic Books. https://doi.org/10.2307/3072449
Lipowsky, F., Rakoczy, K., Pauli, C., Reusser, K., & Klieme, E. (2007). Gleicher Unterricht–gleiche Chancen für alle? Die Verteilung von Schülerbeiträgen im Klassenunterricht [The same instruction–The same chances for everyone? The distribution of contributions from students in whole-class discussions]. Unterrichtswissenschaft [Teaching Science], 35(2), 125-147. https://doi.org/10.25656/01:5489
Lowrie, T. (2002). The influence of visual and spatial reasoning in interpreting simulated 3D worlds. International Journal of Computers for Mathematical Learning, 7, 301-318. https://doi.org/10.1023/A:1022116221735
Ludwig, M., & Jablonski, S. (2021). Step by step – Simplifying and mathematizing the real world with MathCityMap. Quadrante, 30(2), 242-268. https://doi.org/10.48489/quadrante.23604
Ludwig, M., & Jesberg, J. (2015). Using mobile technology to provide outdoor modelling tasks–The MathCityMap-project. Procedia Social and Behavioral Sciences, 191, 2776-2781. https://doi.org/10.1016/j.sbspro.2015.04.517
Mayring, P. (2000). Qualitative content analysis. Forum: Qualitative Social Research, 1(2), 20. https://doi.org/10.17169/fqs-1.2.1089
Medina Herrera, L., Castro Pérez, J., & Juárez Ordónez, S. (2019). Developing spatial mathematical skills through 3D tools: Augmented reality, virtual environments and 3D printing. International Journal on Interactive Design and Manufacturing, 13, 1385-1399. https://doi.org/10.1007/s12008-019-00595-2
Mullis, I. V. S., Martin, M. O., Ruddock, G. J., O’Sullivan, C. Y., Arora, A., & Erberber, E. (2005). TIMSS 2007 assessment frameworks. TIMSS & PIRLS International Study Center.
Ord, J., & Leather, M. (2011). The substance beneath the labels of experiential learning: The importance of John Dewey for outdoor educators. Journal of Outdoor and Environmental Education, 15, 13-23. https://doi.org/10.1007/BF03400924
Pólya, G. (1945). How to solve it. Princeton University Press. https://doi.org/10.1515/9781400828678
Rott, B., Specht, B., & Knipping, C. (2021). A descriptive phase model of problem-solving processes. ZDM Mathematics Education, 53, 737-752. https://doi.org/10.1007/s11858-021-01244-3
Schoenfeld, A. H. (1985). Mathematical problem-solving. Academic Press.
Schukajlow, S. (2013). Lesekompetenz und mathematisches Modellieren [Reading skills and mathematical modeling]. In R. Borromeo Ferri, G. Greefrath, & G. Kaiser (Eds.), Mathematisches Modellieren für Schule und Hochschule. Realitätsbezüge im Mathematikuntericht [Mathematical modeling for schools and universities. Reality references in mathematics lessons] (pp. 125-143). Springer. https://doi.org/10.1007/978-3-658-01580-0_6
Schwarzkopf, R. (2000). Argumentationsprozesse im Mathematikunterricht [Argumentation processes in mathematics education]. Franzbecker.
Stylianides, G., Buchbinder, O., Cramer, J., Durand-Guerrier V., Moutsios-Rentzos A., & Valenta, A. (2019). Introduction to the papers of TWG01: Argumentation and proof. In U. T. Jankvist, M. Van den Heuvel-Panhuizen, & M. Veldhuis (Eds.), Proceedings of the 11^th Congress of the European Society for Research in Mathematics Education (pp. 100-103). Freudenthal Group & Institute, Utrecht University and ERME.
Sumpter, L. (2018). Students’ and teachers’ values, attitudes, feelings and beliefs in mathematics class-rooms. In H. Palmer, & J. Skott (Eds.), Grade 9 students’ reasoning about division of fractions: What are their arguments anchored in? (pp. 135-143). Springer. https://doi.org/10.1007/978-3-319-70244-5_13
Tall, D. O., & West, B. (1986). Graphic insight into calculus and differential equations. In R. F. Churchhouse, B. Cornu, A. G. Howson, J.-P. Kahane, J. H. van Lint, F. Pluvinage, A. Ralston, & M. Yamaguti (Eds.), The influence of computers and informatics on mathematics and its teaching (pp. 107-119). Cambridge University Press. https://doi.org/10.1017/CBO9781139013482.012
Tavsan, S., & Pusmaz, A. (2021). Examination of 7th-grade students’ mathematical reasoning and argumentation process during problem-solving. International Journal of Mathematical Education in Science and Technology. https://doi.org/10.1080/0020739X.2021.2005168
Trust, T., & Maloy, R. W. (2017). Why 3D print? The 21st-century skills students develop while engaging in 3D printing projects. Computers in the Schools, 34(4), 253-266. https://doi.org/10.1080/07380569.2017.1384684
Van Eemeren, F. H., Grootendorst, R., Johnson, R. H., Plantin, C., & Willard, C. A. (1996). Fundamentals of argumentation theory. A handbook of historical backgrounds and contemporary developments. Lawrence Erlbaum Associates, Inc.
Wirth, L., & Greefrath, G. (2022). Examining heuristic worked example videos in a collaborative setting: The conception of the project MoVie. In U. T. Jankvist, R. Elicer, A. Clark-Wilson, H.-G. Weigand, & M. Thomsen (Eds.), Proceedings of the 15^th International Conference on Technology in Mathematics Teaching (pp. 250-251). Danish School of Education, Aarhus University.
Wyndhamn, J., & Säljö, R. (1997). Word problems and mathematical reasoning–A study of children’s mastery of reference and meaning in textual realities. Learning and Instruction, 7, 361-382. https://doi.org/10.1016/S0959-4752(97)00009-1

How to cite this article

APA

Jablonski, S. (2023). Real objects as a reason for mathematical reasoning – A comparison of different task settings. International Electronic Journal of Mathematics Education, 18(4), em0758. https://doi.org/10.29333/iejme/13859

Vancouver

Jablonski S. Real objects as a reason for mathematical reasoning – A comparison of different task settings. INT ELECT J MATH ED. 2023;18(4):em0758. https://doi.org/10.29333/iejme/13859

AMA

Jablonski S. Real objects as a reason for mathematical reasoning – A comparison of different task settings. INT ELECT J MATH ED. 2023;18(4), em0758. https://doi.org/10.29333/iejme/13859

Chicago

Jablonski, Simone. "Real objects as a reason for mathematical reasoning – A comparison of different task settings". International Electronic Journal of Mathematics Education 2023 18 no. 4 (2023): em0758. https://doi.org/10.29333/iejme/13859

Harvard

Jablonski, S. (2023). Real objects as a reason for mathematical reasoning – A comparison of different task settings. International Electronic Journal of Mathematics Education, 18(4), em0758. https://doi.org/10.29333/iejme/13859

MLA

Jablonski, Simone "Real objects as a reason for mathematical reasoning – A comparison of different task settings". International Electronic Journal of Mathematics Education, vol. 18, no. 4, 2023, em0758. https://doi.org/10.29333/iejme/13859