Constructing shared mathematical meanings in the classroom with digital artifacts that simulate real-world phenomena

Mathematics Education Research Journal (2021)Cite this article

Abstract

This paper describes and examines students’ shared construction of meanings while learning about quadratic functions via digital artifacts that simulate real-world phenomena, like the motion of a ball on an inclined plane, focusing specifically on the role of the teacher in that construction process. The study follows the interactions of twenty 15-year-old students and their teacher during the completion of three sequential digital tasks, analyzing how these interactions promote the students’ ability to construct the mathematical meanings of the quadratic function. The study was guided by the theory of semiotic mediation, which treats artifacts as fundamental to cognition and views learning as the evolution from meanings connected to the use of a certain artifact to those recognizable as mathematical. The data analysis showed students progressing from the description of the real-world phenomenon toward a construction of the meaning of the quadratic function that models the phenomenon. While marking the “critical moments” in this progress, we analyze the communication strategies used by the teacher to facilitate it. Our research findings showed evidence that certain types of questions and the strategy “re-voicing” can be particularly effective in prompting students’ construction of mathematical meanings.

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References

  1. Artigue, M. (2002). Learning mathematics in a CAS environment: the genesis of a reflection about instrumentation and the dialectics between technical and conceptual work. International Journal of Computers for Mathematical Learning, 7, 245–274.

    Article  Google Scholar 

  2. Arzarello, F., & Robutti, O. (2010). Multimodality in multi-representational environments. ZDM, 42(7), 715–731.

    Article  Google Scholar 

  3. Arzarello, F., & Sabena, C. (2011). Semiotic and theoretic control in argumentation and proof activities. Educational Studies in Mathematics, 77(2–3), 189–206.

    Article  Google Scholar 

  4. Arzarello, F., Paola, D., Robutti, O., & Sabena, C. (2009). Gestures as semiotic resources in the mathematics classroom. Educational Studies in Mathematics, 70(2), 97–109.

    Article  Google Scholar 

  5. Bartolini Bussi, M. G., & Mariotti, M. A. (2008). Semiotic mediation in the mathematics classroom: Artifacts and signs after a Vygotskian perspective (pp. 746–783). New York: Handbook of international research in mathematics education.

    Google Scholar 

  6. Bray, A., & Tangney, B. (2016). Enhancing student engagement through the affordances of mobile technology: a 21st century learning perspective on realistic mathematics education. Mathematics Education Research Journal, 28(1), 173–197.

    Article  Google Scholar 

  7. Chapin, S. H., O'Connor, C., O'Connor, M. C., & Anderson, N. C. (2009). Classroom discussions: Using math talk to help students learn, grades K-6. Sausalito: Math Solutions.

    Google Scholar 

  8. D’Angelo, C. M., Rutstein, D., & Harris, C. J. (2016). Learning with STEM simulations in the classroom: Findings and trends from a meta-analysis. Educational Technology, 56(3), 58–61.

    Google Scholar 

  9. Duval, R. (2006). A cognitive analysis of problems of comprehension in a learning of mathematics. Educational Studies in Mathematics, 61(1–2), 103–131.

    Article  Google Scholar 

  10. Enyedy, N., Rubel, L., Castellón, V., Mukhopadhyay, S., Esmonde, I., & Secada, W. (2008). Revoicing in a multilingual classroom. Mathematical Thinking and Learning, 10(2), 134–162.

    Article  Google Scholar 

  11. Faggiano, E., Montone, A., & Rossi, P. G. (2017). The synergy between manipulative and digital artefacts in a mathematics teaching activity: a codisciplinary perspective. JE-LKS, 13, 33–45.

  12. Faggiano, E., Montone, A., & Mariotti M. A. (2018). Synergy between manipulative and digital artefacts: a teaching experiment on axial symmetry at primary school. International Journal of Mathematical Education in Science and Technology, 49(8), 1165–1180.

  13. Falcade, R., Laborde, C., & Mariotti, M. A. (2007). Approaching functions: Cabri tools as instruments of semiotic mediation. Educational Studies in Mathematics, 66(3), 317–333.

    Article  Google Scholar 

  14. Forman, E. A., Larreamendy-Joerns, J., Stein, M. K., & Brown, C. A. (1998). “You’re going to want to find out which and prove it”: collective argumentation in a mathematics classroom. Learning and Instruction, 8(6), 527–548.

    Article  Google Scholar 

  15. Fraivillig, J., Murphy, L., & Fuson, K. (1999). Advancing children’s mathematical thinking in everyday mathematics classrooms. Journal for Research in Mathematics Education, 30(2), 148–170.

    Article  Google Scholar 

  16. Geiger, V., Faragher, R., & Goos, M. (2010). Cas-enabled technologies as ‘agents provocateurs’ in teaching and learning mathematical modelling in secondary school classrooms. Mathematics Education Research Journal, 22(2), 48–68.

    Article  Google Scholar 

  17. Goos, M., & Bennison, A. (2008). Surveying the technology landscape: teachers’ use of technology in secondary mathematics classrooms. Mathematics Education Research Journal, 20(3), 102–130.

    Article  Google Scholar 

  18. Harel, G. (1998). Two dual assertions: the first on learning and the second on teaching (or vice versa). The American Mathematical Monthly, 105(6), 497–507.

    Article  Google Scholar 

  19. Herbel-Eisenmann, B. A., & Breyfogle, M. L. (2005). Questioning our patterns of questioning. Mathematics Teaching in the Middle School, 10(9), 484–489.

    Article  Google Scholar 

  20. Hoyles, C. (2018). Transforming the mathematical practices of learners and teachers through digital technology. Research in Mathematics Education, 20(3), 209–228.

    Article  Google Scholar 

  21. Johnson, H. L. (2012). Reasoning about variation in the intensity of change in covarying quantities involved in rate of change. The Journal of Mathematical Behavior, 31(3), 313–330.

    Article  Google Scholar 

  22. Larkin, K., & Calder, N. (2016). Mathematics education and mobile technologies. Mathematics Education Research Journal, 28(1), 1–7.

    Article  Google Scholar 

  23. Lynch, J. (2006). Assessing effects of technology usage on mathematics learning. Mathematics Education Research Journal, 18(3), 29–43.

    Article  Google Scholar 

  24. Mariotti, M. A. (2009). Artifacts and signs after a Vygotskian perspective: the role of the teacher. ZDM, 41(4), 427–440.

    Article  Google Scholar 

  25. Mariotti, M. A. (2013). Introducing students to geometric theorems: how the teacher can exploit the semiotic potential of a DGS. ZDM, 45(3), 441–452.

    Article  Google Scholar 

  26. National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston: Author.

    Google Scholar 

  27. Radford, L. (2008). The ethics of being and knowing: towards a cultural theory of learning. In L. Radford, G. Schubring, & F. Seeger (Eds.), Semiotics in mathematics education: epistemology, history, classroom, and culture (pp. 215–234). Rotterdam: Sense Publishers.

    Google Scholar 

  28. Sokolowski, A., Yalvac, B., & Loving, C. (2011). Science modelling in pre-calculus: how to make mathematics problems contextually meaningful. International Journal of Mathematical Education in Science and Technology, 42(3), 283–297.

    Article  Google Scholar 

  29. Soldano, C., & Arzarello, F. (2016). Learning with touchscreen devices: game strategies to improve geometric thinking. Mathematics Education Research Journal, 28(1), 9–30.

    Article  Google Scholar 

  30. Stein, M., Engle, R., Smith, M., & Hughes, E. (2008). Orchestrating productive mathematical discussions: five practices for helping teachers move beyond show and tell. Mathematical Thinking and Learning, 10(4), 313–340.

    Article  Google Scholar 

  31. Swidan, O. (2019). Construction of the mathematical meaning of the function–derivative relationship using dynamic digital artifacts: a case study. Digital Experiences in Mathematics Education, 1–20. https://doi.org/10.1007/s40751-019-00053-4.

  32. Swidan, O., & Yerushalmy, M. (2014). Learning the indefinite integral in a dynamic and interactive technological environment. ZDM, 46(4), 517–531.

  33. Thompson, P. W. (1994). Images of rate and operational understanding of the fundamental theorem of calculus. Educational Studies in Mathematics, 26(2–3), 229–274.

    Article  Google Scholar 

  34. Trouche, L. (2004). Managing complexity of human/machine interactions in computerized learning environments: guiding students’ command process through instrumental orchestrations. International Journal of Computers for Mathematical Learning, 9(3), 281–307.

    Article  Google Scholar 

  35. Wood, T. (1998). Alternative patterns of communication in mathematics classes: funneling or focusing? In H. Steinbring, M. G. Bartolini Bussi, & A. Sierpinska (Eds.), Language and communication in the mathematics classroom (pp. 167–178). Reston: NCTM.

    Google Scholar 

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Acknowledgments

The authors would like to thank the teacher of the class Mrs. Silvia Beltramino and Prof. Ferdinando Arzarello for his fruitful comments and suggestions.

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Author notes

  1. Osama Swidan and Eleonora Faggiano contributed equally to this work.

Affiliations

  1. Graduate Program for Science & Technology Education, Ben Gurion University of the Negev, Be’er Sheva, Israel

    Osama Swidan

  2. Department of Mathematics, Università di Bari Aldo Moro, Bari, Italy

    Osama Swidan & Eleonora Faggiano

Authors
  1. Osama Swidan
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  2. Eleonora Faggiano
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Correspondence to Osama Swidan.

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Swidan, O., Faggiano, E. Constructing shared mathematical meanings in the classroom with digital artifacts that simulate real-world phenomena. Math Ed Res J (2021). https://doi.org/10.1007/s13394-020-00362-7

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Keywords

  • Quadratic function
  • Shared construction of meanings
  • Digital artifact
  • Simulation of real-world phenomena
  • Semiotic mediation
  • Teacher intervention