RESEARCH PAPER
Semiotic analyses of actions on digital and analogue material when sorting data in primary school
 
More details
Hide details
1
Institute for Mathematics and Computer Science Education, Goethe-University Frankfurt, GERMANY
 
 
Publication date: 2022-06-03
 
 
EURASIA J. Math., Sci Tech. Ed 2022;18(7):em2126
 
KEYWORDS
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.
REFERENCES (40)
1.
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....
 
2.
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/10.1007/978-98....
 
3.
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....
 
4.
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-....
 
5.
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/se....
 
6.
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....
 
7.
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-conte....
 
8.
Carey, S. (1988). Conceptual differences between children and adults. Mind and Language, 3(3), 167-181. https://doi.org/10.1111/j.1468....
 
9.
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/10.2307/300349....
 
10.
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/10.1163/978908....
 
11.
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-....
 
12.
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-....
 
13.
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/10.1007/978-98....
 
14.
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.
 
15.
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.....
 
16.
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/10.4324/978131....
 
17.
Gravemeijer, K. (2002). Emergent modeling as the basis for an instructional sequence on data analysis. In B. Phillips (Ed.), Proceedings of the 6th International Conference on Teaching Statistics, Developing a Statistically Literate Society. International Statistical Institute.
 
18.
Harradine, A., & Konold, C. (2006). How representational medium affects the data displays students make [Paper presentation]. The 7th International Conference on Teaching Statistics.
 
19.
Harrison, S. (2018). The impulse to gesture. Where language, minds, and bodies intersect. Cambridge University Press. https://doi.org/10.1017/978110....
 
20.
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....
 
21.
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....
 
22.
Hoffmann, M. (2010). Diagrams as scaffolds for abductive insights. In Proceedings of the 24th AAAI Conference on Artificial Intelligence (pp. 42-49).
 
23.
Huth, M. (2022). Handmade diagrams–Learners doing math by using gestures. In Proceedings of the 12th Congress of the European Society for Research in Mathematics Education.
 
24.
Kadunz, G. (2006). Experiments with diagrams–A semiotic approach. ZMD–Mathematics Education, 38(6), 445-455. https://doi.org/10.1007/BF0265....
 
25.
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....
 
26.
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.
 
27.
Kollosche, D. (2021). Styles of reasoning for mathematics education. Educational Studies in Mathematics, 107, 471-486. https://doi.org/10.1007/s10649....
 
28.
Konold, C., & Miller, C. (2011). TinkerPlots 2.0. Key Curriculum Press.
 
29.
Mayring, P. (2014). Qualitative content analysis: Theoretical foundation, basic procedures and software solutions. Klagenfurt. https://doi.org/10.1007/978-94....
 
30.
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-....
 
31.
Peirce, C. S. (1899-1900[c.]). Notes on topical geometry. MS [R] 142.
 
32.
Peirce, C. S. (1976). The new elements of mathematics (NEM), vol. IV (Ed. C. Eisele). De Gruyter. https://doi.org/10.1515/978311....
 
33.
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.
 
34.
Schreiber, C. (2013). Semiotic processes in chat-based problem-solving situations. Educational Studies Mathematics, 82, 51-73. https://doi.org/10.1007/s10649....
 
35.
Shapiro, S. (1997). Philosophy of mathematics: Structure and ontology. Oxford University Press.
 
36.
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-....
 
37.
Villamor, G., Willis, D., & Wroblewski, L. (2010). Touch gesture reference guide. https://www.lukew.com/ff/entry....
 
38.
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.
 
39.
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-....
 
40.
Wild, C., & Pfannkuch, M. (1999). Statistical thinking in empirical enquiry. International Statistical Review, 67(3), 223-265. https://doi.org/10.1111/j.1751....
 
eISSN:1305-8223
ISSN:1305-8215
Journals System - logo
Scroll to top