Exploring the role of conceptions and views of mathematics in shaping the perception and interpretation of statistical graphs

Andrea Amico; Chiara Andrà; Luca Doria

doi:10.31129/LUMAT.14.4.2789

Authors

Andrea Amico University of Eastern Piedmont, Italy
Chiara Andrà University of Eastern Piedmont, Italy https://orcid.org/0000-0001-7064-1581
Luca Doria University of Eastern Piedmont, Italy https://orcid.org/0009-0000-6719-8750

DOI:

https://doi.org/10.31129/LUMAT.14.4.2789

Keywords:

conceptions, mathematical views, socio-environmental issues, statistical graphs

Abstract

It is evident that climate change, pollution, population growth rate, and environmental and social issues have become prominent subjects in recent years. Statistical graphs have emerged as the predominant method for scientists to communicate data regarding these phenomena. Within the Factfulness project, the incidence of certain facts interpreted on the basis of personal conceptions is presented in graphical form, which may present a different narrative to that which individuals believe to be true, thus purportedly correcting the most common biases. However, research in the field of Mathematics Education has indicated that individuals frequently encounter challenges in comprehending graphs. The present study investigates the role of affect-related variables in shaping the manner in which individuals approach graphs. A sample of 80 undergraduate students in Psychology was considered for this study. The students were invited to: (i) respond to a Factfulness questionnaire concerning environmental issues, (ii) read and interpret graphs from which they could infer the correct answers to the questionnaire, and (iii) rate the aesthetics and the transparency of the graphs proposed to them. The analysis of the participants' comments and their appreciation of graphs provides a foundation for enhancing the communication of environmental issues through statistical graphs, with a particular focus on affect-related aspects.

References

Ainley, J. (2000). Transparency in graphs and graphing tasks: An iterative design process. Journal of Mathematical Behavior, 19, 365-384

Amico, A., Andrà, C. & Doria, L. (2025). Factfulness: theoretical and empirical considerations within affect-related research in Mathematics Education. To appear in LUMAT-B, International Mathematical Views Conference 2024 – Conference Proceedings

Amico, A. & Doria L. (2023). Is beautiful also transparent? Students learn from graphs about water pollution. In: Proceeding of the 46th Conference of the International Group for the Psychology of Mathematics Education (Vol. 2), University of Haifa, Israel, 35-43.

Bond, M.E., Perkins, S.N., & Ramirez, C. (2012). Students’ perceptions of statistics: An exploration of attitudes, conceptualizations, and content knowledge of statistics. Statistics Education Research Journal, 11(2), 6–25. https://doi.org/10.52041/serj.v11i2.325

Coles, A., Barwell, R., Cotton, T., Winter, J., & Brown, L. (2013). Teaching secondary mathematics as if the planet matters. London: Routledge.

Coles, A. (2023). Teaching in the new climatic regime: steps to a socio-ecology of mathematics education. In: M. Ayalon, B. Koichu, R. Leikin, L. Rubel & M. Tabach (Eds.), Proceedings of the 46th Conference of the International Group for the Psychology of Mathematics Education (Vol. 1, pp. 17-34). Haifa.

Daskalogianni, K. & Simpson, A. (2001). Beliefs overhang: the transition from school to university. Proceedings of the British Society for Research into Learning Mathematics, 21(2), 97–108.

David, A., & Glore, P. (2010). The impact of design and aesthetics on usability, credibility, and learning in an online environment. Online Journal of Distance Learning Administration, 13(4), 43-50.

Doria, L. & Scalvini, C. (2024). Reading mathematical graphs about pollution: exploring the role of mathematical beliefs. LUMAT-B, 9(2), International Mathematical Views Conference 2023 – Conference Proceedings

Duval, R. (2006). A cognitive analysis of problems of comprehension in a learning of mathematics. Educational studies in mathematics, 61, 103-131.

Erens, R., & Eichler, A. (2019). Belief changes in the transition from university studies to school practice. Affect and mathematics education: Fresh perspectives on motivation, engagement, and identity, 345-373.

Fang, L., Kong, J., Chen, R., & Pang, L. (2023). Analysis of the Application of Mathematical Beauty in Middle School Mathematics Teaching. International Journal of Scientific Engineering and Science, 7(11), 21-24.

Fives, H., & Buehl, M. M. (2012). Spring cleaning for the “messy” construct of teachers’ beliefs: What are they? Which have been examined? What can they tell us?.

Furinghetti, F. & Pehkonen, E. (2002). Rethinking characterizations of beliefs. In: G. Leder, E. Pehkonen & G. Törner (Eds.), Beliefs: A hidden variable in mathematics education? (pp. 39-57). Dordrecht/Boston/London: Kluwer Academic Publishers.

Garfield, J., & Ben‐Zvi, D. (2007). How students learn statistics revisited: A current review of research on teaching and learning statistics. International Statistical Review, 75(3), 372–396. https://doi.org/10.1111/j.1751-5823.2007.00029.x

Glazer N.(2011): Challenges with graph interpretation: a review of the literature, Studies in Science Education, 47(2), 183-210

Grainger, S., Mao, F., & Buytaert, W. (2016). Environmental data visualisation for non-scientific contexts: Literature review and design framework. Environmental Modelling & Software, 85, 299-318.

Green, T. F. (1971). The activities of teaching. Tokyo: McGraw-Hill Kogakusha

Grigutsch, S., Raatz, U., & Törner, G. (1998). Einstellungen gegenüber mathematik bei mathematiklehrern. Journal für mathematik-didaktik, 19, 3-45.

Hegel, G. W. F. (1835). Lectures on aesthetics. Newcomb Livraria Press.

Ivanjek, L., Susac, A., Planinic, M., Andrasevic, A., & Milin-Sipus, Z. (2016). Student reasoning about graphs in different contexts. Physical Review Physics Education Research, 12(1), 010106.

Lave, J., & Wenger, E. (1991). Situated learning: Legitimate peripheral participation. Cambridge university press.

Liljedahl, P., Rösken, B., & Rolka, K. (2006, November). Documenting changes in pre-service elementary school teachers beliefs: Attending to different aspects. In Proceedings of the 28th international conference for Psychology of Mathematics Education-North American Chapter (Vol. 2, p. 279Y285).

Kant, I. (2008). Critique of judgment. Newcomb Livraria Press.

Mayring, P. (2015). Qualitative Content Analysis: Theoretical Background and Procedures. In: A. Bikner-Ahsbahs, C. Knipping, & N. Presmeg (Eds.), Approaches to qualitative research in mathematics education (pp. 365–380). Dordrecht: Springer. https://doi.org/10.1007/978-94-017-9181-6_13

O'Leary, Bethan & Ban, Natalie & Fernandez, Miriam & Friedlander, Alan & Borboroglu, Pablo & Golbuu, Yimnang & Guidetti, Paolo & Harris, J. & Hawkins, Julie & Langlois, Tim & Mccauley, Douglas & Pikitch, Ellen & Richmond, Robert & Roberts, Callum. (2018). Addressing Criticisms of Large-Scale Marine Protected Areas. BioScience, 68. 10.1093/biosci/biy021.

Philipp, R. A., Ambrose, R., Lamb, L. L., Sowder, J. T., Schappelle, B. P., Sowder, L., ... & Chauvot, J. (2007). Effects of early field experiences on the mathematical content knowledge and beliefs of prospective elementary school teachers: An experimental study. Journal for Research in Mathematics Education, 38(5), 438-476.

Rosling, H., Rosling, O. & Anna Rosling Rönnlund, A. (2018). Factfulness: Ten reasons we’re wrong about the world – and why things are better than you think. Sceptre.

Roth, W. M. (2003). Toward an anthropology of graphing: Semiotic and activity-theoretic perspectives. Springer Science & Business Media.

Roth, W. M., McGinn, M. K., & Bowen, G. M. (1996). Applications of science and technology studies: Effecting change in science education. Science, Technology, & Human Values, 21(4), 454-484.

Sinclair, N. (2009). Aesthetics as a liberating force in mathematics education?. ZDM, 41(1), 45-60.

Skott, J. (2015). Towards a participatory approach to ‘beliefs’ in mathematics education. In: From beliefs to dynamic affect systems in mathematics education: Exploring a mosaic of relationships and interactions (pp.3-23). Springer

Thielsch, M. T., Scharfen, J., Masoudi, E., & Reuter, M. (2019). Visual aesthetics and performance: A first meta-analysis. In: Proceedings of Mensch und Computer 2019 (pp. 199-210).

Zingarelli, N. (2020). Italian dictionary. Zingarelli.