Semiotic analyses of actions on digital and analogue material when sorting data in primary school

Lara Kristina Billion

doi:10.29333/ejmste/12138

Full Text (PDF)

Lara Kristina Billion ¹ ^*

More Detail

¹ Institute for Mathematics and Computer Science Education, Goethe-University Frankfurt, GERMANY^* Corresponding Author

Abstract

This paper focuses on the actions of learners on digital and analogue materials while dealing with a statistical problem. To investigate the learners’ actions, a semiotic perspective of mathematical learning according to C. S. Peirce is used, since in this perspective learning mathematics is described as visible activities on diagrams. Through a qualitative semiotic analysis of the actions of two third-graders working with given data, the statistical diagram interpretations of the learners can be reconstructed. A comparison of the reconstructed diagram interpretations reveals whether different movements lead to similar diagram interpretations. In addition, it is of interest whether the diagram interpretations are the same when acting on digital and analogue diagrams because the same mathematical relationships have to be observed. Through this comparison, conclusions can be drawn about the similarities and differences in working with digital and analogue materials and how these materials may be used profitably in statistical learning.

Keywords

diagrammatic reasoning
mathematical actions
primary school children
semiotic perspective on learning mathematics
statistical learning

License

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

EURASIA J Math Sci Tech Ed, 2022, Volume 18, Issue 7, Article No: em2126

https://doi.org/10.29333/ejmste/12138

Publication date: 03 Jun 2022

Article Views: 1317

Article Downloads: 621

Open Access Disclosures References How to cite this article

Disclosure

Declaration of Conflict of Interest: No conflict of interest is declared by author(s).

Data sharing statement: Data supporting the findings and conclusions are available upon request from the corresponding author(s).

References

Bakker, A., & Hoffmann, M. (2005). Diagrammatic reasoning as the basis for developing concepts: A semiotic analysis of students’ learning about statistical distribution. Educational Studies in Mathematics, 60, 333-358. https://doi.org/10.1007/s10649-005-5536-8
Ben-Zvi, D. (2018). Foreword. In A. Leavy, M. Meletiou-Mavrotheris, & E. Paparistodemou (Eds.), Statistics in early childhood and primary education. Supporting early statistical and probabilistic thinking (pp. vii-viii). Springer. https://doi.org/10.1007/978-981-13-1044-7
Ben-Zvi, D., & Garfield, J. (2004). Statistical literacy, reasoning, and thinking: Goals, definitions, and challenges. In D. Ben-Zvi, & J. Garfield (Eds.), The challenge of developing statistical literacy, reasoning and thinking (pp. 3-15). Kluwer Academic Publisher. https://doi.org/10.1007/1-4020-2278-6
Biehler, R., Ben-Zvi, D., Bakker, A., & Makar, K. (2013). Technology for enhancing statistical reasoning at the school level. In M. A. Clements, A. J. Bishop, C. Keitel, J. Kilpatrick, & F. S. K. Leung (Eds.), Third international handbook of mathematics education. Springer international handbooks of education (pp. 643-689). Springer. https://doi.org/10.1007/978-1-4614-4684-2_21
Billion, L. (2021a). The usage of inscriptions – mathematical experiences of learners working with diagrams. In J. Novotná & H. Moravá (Eds.), Proceedings of the International Symposium Elementary Mathematics Teaching. Broadening experiences in elementary school mathematics (pp. 82-92). https://semt.cz/proceedings/semt-21.pdf
Billion, L. (2021b). Reconstruction of the interpretation of geometric diagrams of primary school children based on actions on various materials – a semiotic perspective on actions. International Electronic Journal of Mathematics Education, 16(3), em0650. https://doi.org/10.29333/iejme/11068
Billion, L., & Vogel, R. (2021). Material as an impulse for mathematical actions in primary school – A semiotic perspective on a geometric example. In M. Inprasitha, N. Changsri, & N. Boonsena (Eds.), Proceedings of the 44th Conference of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 81-88). PME. https://www.igpme.org/wp-content/uploads/2022/04/Volume-2_final.pdf
Carey, S. (1988). Conceptual differences between children and adults. Mind and Language, 3(3), 167-181. https://doi.org/10.1111/j.1468-0017.1988.tb00141.x
Doerr, H., & English, L. (2003). A modeling perspective on students’ mathematical reasoning about data. Journal for Research in Mathematics Education, 34(2), 110-136. https://doi.org/10.2307/30034902
Dörfler, W. (2006). Inscriptions as objects of mathematical activities. In J. Maaz, & W. Schlögelmann (Eds.), New mathematics education research and practice (pp. 97-111). Sense Publishers. https://doi.org/10.1163/9789087903510_011
Dörfler, W. (2015). Abstrakte Objekte in der Mathematik [Abstract objects in mathematics]. In G. Kadunz (Ed.), Semiotische Perspektiven auf das Lernen von Mathematik [Semiotic perspectives on learning mathematics] (pp. 33-49). Springer-Verlag. https://doi.org/10.1007/978-3-642-55177-2
Dörfler, W. (2016). Signs and their use: Peirce and Wittgenstein. In A. Bikner-Ahsbahs, A. Vohns, R. Bruder, O. Schmitt, & W. Dörfler (Eds.), Theories in and of mathematics education (pp. 21-31). Springer. https://doi.org/10.1007/978-3-319-42589-4
English, L. D. (2018). Young children’s statistical literacy in modelling with data and chance. In A. Leavy, M. Meletiou-Mavrotheris, & E. Paparistodemou (Eds.), Statistics in early childhood and primary education. Supporting early statistical and probabilistic thinking (pp. 295-313). Springer. https://doi.org/10.1007/978-981-13-1044-7_17
Friel, S., Curcio, R., & Bright, G. (2001). Making sense of graphs: Critical factors influencing comprehension of instructional implications. Journal of Research in Mathematics Education, 32(2), 124-158. https://doi.org/10.2307/749671
Frischemeier, D. (2020). Building statisticians at an early age–Statistical projects exploring meaningful data in primary school. Statistics Education Research Journal, 19(1), 39-56. https://doi.org/10.52041/serj.v19i1.118
Graesser, A., Swamer, S., Baggett, W., & Sell, M. (1996). New models of deep comprehension. In B. Britton, & A. Graesser (Eds.), Models of understanding text (pp. 1-32). Erlbaum. https://doi.org/10.4324/9781315806143
Gravemeijer, K. (2002). Emergent modeling as the basis for an instructional sequence on data analysis. In B. Phillips (Ed.), Proceedings of the 6^th International Conference on Teaching Statistics, Developing a Statistically Literate Society. International Statistical Institute.
Harradine, A., & Konold, C. (2006). How representational medium affects the data displays students make [Paper presentation]. The 7^th International Conference on Teaching Statistics.
Harrison, S. (2018). The impulse to gesture. Where language, minds, and bodies intersect. Cambridge University Press. https://doi.org/10.1017/9781108265065.002
Hestenes, D. (2013). Modeling theory for math and science education. In R. Lesh, P. L. Galbraith, C. R. Haines, & A. Hurford (Eds.), Modeling students’ mathematical modeling competencies (pp. 13-42). Springer. https://doi.org/10.1007/978-94-007-6271-8_3
Hoffmann, M. (2006). What is a “semiotic perspective”, and what could it be? Some comments on the contributions to this special issue. Educational Studies in Mathematics, 61, 279-291. https://doi.org/10.1007/s10649-006-1456-5
Hoffmann, M. (2010). Diagrams as scaffolds for abductive insights. In Proceedings of the 24^th AAAI Conference on Artificial Intelligence (pp. 42-49).
Huth, M. (2022). Handmade diagrams–Learners doing math by using gestures. In Proceedings of the 12^th Congress of the European Society for Research in Mathematics Education.
Kadunz, G. (2006). Experiments with diagrams–A semiotic approach. ZMD–Mathematics Education, 38(6), 445-455. https://doi.org/10.1007/BF02652781
Kadunz, G. (2016). Geometry, a means of argumentation. In A. Sáenz-Ludloy, & G. Kadunz (Eds.), Semiotics as a tool for learning mathematics. How to describe the construction, visualisation, and communication of mathematical concepts (pp. 25-42). Sense Publishers. https://doi.org/10.1007/978-94-6300-337-7
Kendon, A. (1984). Did gesture have the happiness to escape the curse at the confusion of babel? In A. Wolfgang (Ed.), Nonverbal behaviour. Perspectives applications intercultural insights (pp. 75-114). Hogrefe.
Kollosche, D. (2021). Styles of reasoning for mathematics education. Educational Studies in Mathematics, 107, 471-486. https://doi.org/10.1007/s10649-021-10046-z
Konold, C., & Miller, C. (2011). TinkerPlots 2.0. Key Curriculum Press.
Mayring, P. (2014). Qualitative content analysis: Theoretical foundation, basic procedures and software solutions. Klagenfurt. https://doi.org/10.1007/978-94-017-9181-6_13
Moreno-Armella, L., & Sriraman, B. (2010). Symbols and mediation in mathematics education. In B. Sriraman, & L. English (Eds.), Theories of mathematics education (pp. 213-232). Springer. https://doi.org/10.1007/978-3-642-00742-2_22
Peirce, C. S. (1899-1900[c.]). Notes on topical geometry. MS [R] 142.
Peirce, C. S. (1976). The new elements of mathematics (NEM), vol. IV (Ed. C. Eisele). De Gruyter. https://doi.org/10.1515/9783110805888
Peirce, C. S. (CP). Collected papers of Charles Sanders Peirce (Volumes I-VI, ed. by C. Hartshorne and P. Weiss, 1931-1935, Volumes VII-VIII, ed. by A.W. Burks, 1958). Harvard UP.
Schreiber, C. (2013). Semiotic processes in chat-based problem-solving situations. Educational Studies Mathematics, 82, 51-73. https://doi.org/10.1007/s10649-012-9417-7
Shapiro, S. (1997). Philosophy of mathematics: Structure and ontology. Oxford University Press.
Sriraman, B., & Chernoff, E. J. (2020). Probabilistic and statistical thinking. In S. Lerman (Ed.), Encyclopedia of mathematics education (pp. 675-681). Springer. https://doi.org/10.1007/978-3-030-15789-0_100003
Villamor, G., Willis, D., & Wroblewski, L. (2010). Touch gesture reference guide. https://www.lukew.com/ff/entry.asp?1071
Vogel, R. (2017). “wenn man da von oben guckt sieht das aus als ob…”–Die, Dimensionslücke’ zwischen zweidimensionaler Darstellung dreidimensionaler Objekte im multimodalen Austausch [“when you look from above it looks as if...” –The ‘dimensional gap’ between two-dimensional representation of three-dimensional objects in multimodal exchange]. In M. Beck, & R. Vogel (Eds.), Geometrische Aktivitäten und Gespräche von Kindern im Blick qualitativen Forschens Mehrperspektivische Ergebnisse aus den Projekten erStMaL und MaKreKi [Geometric activities and conversations of children in the perspective of qualitative research Multi-perspective results from the projects erStMaL and MaKreKi] (pp. 61-75). Waxmann.
Vogel, R., & Huth, M. (2020). Modusschnittstellen in mathematischen Lernprozessen. Handlungen am Material und Gesten als diagrammatische Tätigkeit [Mode interfaces in mathematical learning processes. Actions on the material and gestures as a diagrammatic activity]. In G. Kadunz (Ed.), Zeichen und Sprache im Mathematikunterricht–Semiotik in Theorie und Praxis [Signs and language in mathematics lessons–Semiotics in theory and practice]. Springer. https://doi.org/10.1007/978-3-662-61194-4
Wild, C., & Pfannkuch, M. (1999). Statistical thinking in empirical enquiry. International Statistical Review, 67(3), 223-265. https://doi.org/10.1111/j.1751-5823.1999.tb00442.x

How to cite this article

APA

Billion, L. K. (2022). Semiotic analyses of actions on digital and analogue material when sorting data in primary school. Eurasia Journal of Mathematics, Science and Technology Education, 18(7), em2126. https://doi.org/10.29333/ejmste/12138

Vancouver

Billion LK. Semiotic analyses of actions on digital and analogue material when sorting data in primary school. EURASIA J Math Sci Tech Ed. 2022;18(7):em2126. https://doi.org/10.29333/ejmste/12138

AMA

Billion LK. Semiotic analyses of actions on digital and analogue material when sorting data in primary school. EURASIA J Math Sci Tech Ed. 2022;18(7), em2126. https://doi.org/10.29333/ejmste/12138

Chicago

Billion, Lara Kristina. "Semiotic analyses of actions on digital and analogue material when sorting data in primary school". Eurasia Journal of Mathematics, Science and Technology Education 2022 18 no. 7 (2022): em2126. https://doi.org/10.29333/ejmste/12138

Harvard

Billion, L. K. (2022). Semiotic analyses of actions on digital and analogue material when sorting data in primary school. Eurasia Journal of Mathematics, Science and Technology Education, 18(7), em2126. https://doi.org/10.29333/ejmste/12138

MLA

Billion, Lara Kristina "Semiotic analyses of actions on digital and analogue material when sorting data in primary school". Eurasia Journal of Mathematics, Science and Technology Education, vol. 18, no. 7, 2022, em2126. https://doi.org/10.29333/ejmste/12138