Making sense of a ”misleading” graph

Authors

Oduor Olande

Abstract

Given the importance of a critical-analytical disposition in the case of graphical artefacts, this paper explores graphicacy based on students’ answers to an item from PISA survey test. Primarily, results from the written test were analyzed using PISA’s doubledigit rubrics or coding. In evaluating these categories, it is observed that just a small percentage of students are able to produce answers that reflect a critical-analytical approach with respect to the use of statistical/mathematical operators and forms of expressions. Secondly, video observation shows that students tend to employ what is perceived as an ”identification approach” while discussing the task. Whereas elements of mathematical and statistical ideas can be identified in the students’ discussion, these are not explicitly stated and are largely submerged in everyday concerns and forms of expression.

References

Adjiage, R. & Pluvinage, F. (2007). An experiment in teaching ratio and proportion. Educational Studies in Mathematics, 65, 149-175. https://doi.org/10.1007/s10649-006-9049-x

Allerup, P., Lindenskov, L. & Weng, P. (2006). "Growing up" - the story behind two items in PISA 2003. In J. Mejding & A. Roe (Eds.), Northern lights on PISA 2003 - a reflection from the Nordic countries (pp. 59-72). Copenhagen: Nordic Council of Ministers.

Arcavi, A. (2003). The role of visual representations in the learning of mathematics. Educational Studies in Mathematics, 52, 215-241. https://doi.org/10.1023/A:1024312321077

Balchin, W. G. V. & Coleman, A. M. (1965, November, 5). Graphicacy should be the fourth ace in the pack. Times educational supplement, p. 947.

BBC. (2010). Misleading graphs. Retrieved April 17, 2013 from http://www.bbc. co.uk/schools/gcsebitesize/maths/statistics/representingdata2rev5.shtml

Ben-Zvi, D. & Arcavi, A. (2001). Junior high school students' construction of global views of data and data representations. Educational Studies in Mathematics, 45, 35-65. https://doi.org/10.1023/A:1013809201228

Bertin, J. (1983). Semiology of graphics: diagrams networks maps (W. J. Berg, Trans.) Madison: The University of Wisconsin Press (Original work published in 1967).

Bloch, I. (2003). Teaching functions in a graphic milieu: What forms of knowledge enable students to conjecture and prove? Educational Studies in Mathematics, 52, 3-28. https://doi.org/10.1023/A:1023696731950

Curcio, F. R. (1987). Comprehension of mathematical relationships expressed in graphs. Journal for Research in Mathematics Education, 18, 382-393. https://doi.org/10.5951/jresematheduc.18.5.0382

De Lange, J. (2006). Mathematical literacy for living from OECD-PISA perspective. Retrieved April 17, 2013 from http://www.criced.tsukuba.ac.jp/ math/sympo_2006/lange.pdf

Diezmann, C. M. (2009). The role of fluency in a mathematics item with an embedded graphic: interpreting a pie chart. ZDM: The International Journal on Mathematics Education, 41, 651-662. https://doi.org/10.1007/s11858-009-0212-6

Dossey, J. A., Jones, C. O. & Martin, T. S. (2002). Analyzing student responses in mathematics using two-digit rubrics. In D. F. Robitaille & A. E. Beaton (Eds.), Secondary analysis of the TIMSS data (pp. 21-45). Dordrecht: Kluwer Academic Publishers. https://doi.org/10.1007/0-306-47642-8_3

Friel, S. N., Curcio, F. R. & Bright, G. W. (2001). Making sense of graphs: critical factors influencing comprehension and instructional implications. Journal for Research in Mathematics Education, 32, 124-158. https://doi.org/10.2307/749671

Gal, I. (1998). Assessing statistical knowledge as it relates to students' interpretation of data. In S. P. Lajoie (Ed.), Reflections on statistics: learning, teaching and assessment in grades K-12 (pp. 275-295). Mahwah: Lawrence Erlbaum Associates.

Gal, I. (2002). Adults' statistical literacy: meanings, components, responsibilities. International Statistical Review, 70, 1-25. https://doi.org/10.1111/j.1751-5823.2002.tb00336.x

Gal, I. (2003). Teaching for statistical literacy and services of statistics agencies. The American Statistician, 57, 80-84. https://doi.org/10.1198/0003130031469

Garfield, J. & Gal, I. (1999). Assessment and statistics education: current challenges and directions. International Statistical Review, 67, 1-12. https://doi.org/10.1111/j.1751-5823.1999.tb00377.x

Jones, G. W. (2005). Exploring probability in schools: the challenges for teaching and learning. New York: Springer.

Lie, S., Taylor, A. & Harmon, M. (1996). Scoring techniques and criteria. In M. O. Martin & D. Kelly (Eds.), Third international mathematics and science study, technical report. Vol. 1: Design and development. Boston College.

Limberg, L. B. (2008). Phenomenography. In L. M. Given (Ed.), The SAGE encyclopedia of qualitative research methods (Vol. 2, pp. 612-615). Thousand Oaks: Sage Publications.

Marton, F. (1981). Phenomenology - describing conceptions of the world around us. Instructional Science, 10, 177-200. https://doi.org/10.1007/BF00132516

Monteiro, C. & Ainley, J. (2007). Investigating the interpretation of media graphs among student teachers. International Electronic Journal of Mathematics Education, 2, 188-207. https://doi.org/10.29333/iejme/183

Monteiro, C. & Ainley, J. (2004) Developing critical sense in graphing. In M. A. Mariotti (Ed.), Proceedings of the third conference of the European society for research in mathematics education. Bellaria, Italy: ERME. Retrieved April 17, 2013 from http://www.dm.unipi.it/~didattica/CERME3/proceedings/Groups/TG5/TG5_list3.html

NCTM. (2000). Principles and standards for school mathematics. Reston: Author.

OECD. (2003). PISA assessment framework: mathematics, reading, science and problem solving knowledge and skills. Paris: Author.

OECD. (2005). PISA 2003: technical report. Paris: Author.

OECD. (2006). Assessing scientific, reading and mathematics literacy: a framework for PISA 2006. Paris: Author.

OECD. (2009). Take the sample test: sample questions from OECD's PISA assessments. Paris: Author.

OECD. (2010). Database-PISA 2003. Retrieved April 17, 2013 from http://pisa2003.acer.edu.au/downloads.php

Pantziara, M. & Philippou, G. (2011). Levels of students' "conception" of fractions. Educational Studies in Mathematics, 79, 61-83. https://doi.org/10.1007/s10649-011-9338-x

Person, R. S (2006). VSAIEEDC-a cognition-based generic model for qualitative data analysis in gifted and talented research. Gifted and Talented International, 21, 29-37. https://doi.org/10.1080/15332276.2006.11673473

Postigo, Y. & Pozo, J. I. (2004). On the road to graphicacy: the learning of graphical representation systems. Educational Psychology, 24, 623-644. https://doi.org/10.1080/0144341042000262944

Roth, W.-M. (2009). Embodied mathematical communication and the visibility of graphical features. In W.-M. Roth (Ed.), Mathematical representation at the interface of body and culture (pp. 95-121). Charlotte: Information Age Publishing.

Roth, W.-M., Pozzer-Ardenghi, L. & Han, J. Y. (2005). Critical graphicacy: understanding visual representation practice in school science. Dordrecht: Springer.

Rumsey, D. J. (2002). Statistical literacy as a goal for introductory statistics courses. Journal of Statistics Education, 10. Retrieved April 17, 2013 from http://www.amstat.org/publications/jse/v10n3/rumsey2.html https://doi.org/10.1080/10691898.2002.11910678

Skolverket. (2009). Syllabuses for the compulsory school. Stockholm: Skolverket & Fritzes.

Tufte, E. R. (2001). The visual display of quantitative information. Chesire: Graphics Press.

Walls, F. (2009). Mathematical subjects: Children talk about their mathematics lives. Dordrecht: Springer. https://doi.org/10.1007/978-1-4419-0597-0

Watson, J. M. (1997). Assessing statistical thinking using the media. In I. Gal & J. Garfield (Eds.), The assessment challenge in statistics education (pp. 107- 121). Amsterdam: IOS Press and International Statistical Institute.

Watson, J. M. (2006). Statistical literacy at school: growth and goals. Mahwah: Lawrence Erlbaum Associates.

Watson, J. M. & Kelly, B. A. (2008). Sample, random and variation: the vocabulary of statistical literacy. International Journal of Science and Mathematics Education, 6, 741-767. https://doi.org/10.1007/s10763-007-9083-x

Downloads

Published

2024-11-19

How to Cite

Olande, O. (2024). Making sense of a ”misleading” graph. NOMAD Nordic Studies in Mathematics Education, 18(1), 5–30. Retrieved from https://tidsskrift.dk/NOMAD/article/view/148495