Abstract
This study explores the coordination of several semiotic presentations in the process of the objectification of Cartesian coordinates by first grade children. By means of novel dual eye-tracking technology, I investigated the micro-dynamics of a child’s and her parent’s attentions as they were involved in the teaching-learning process. The analysis of the synchronized data that were retrieved from two eye-trackers and from an external video camera showed ambiguity, not only of verbal terms and visual inscriptions, but also of pointing gestures. It brought out the joint attention moments as crucial for acquiring the culturally adequate meaning of the Cartesian plane. The active disclosure of different presentations’ complementarity determined the moment when the child acquired some meaning, yet not always the cultural one. The joint attention (or the absence of it) allowed the adult to keep track of the understanding that was emerging in the child’s mind, to compare it with her own perception of the cultural representation, and to rectify the child’s perception.
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- 1.
These and following figures represent the paths of the eye-movements on the Cartesian coordinates (only the fragments are shown). The red arrows point at the positions of the gazes at these very moments. The green line represents the eye-movements of the child; the violet line represents the eye-movements of the adult. The pictures on the left show where the adult was pointing (the end of the pointing stick is marked by a red circle).
References
Abrahamson, D., Shayan, S., Bakker, A., & Van der Schaaf, M. F. (2016). Exposing Piaget’s scheme: Empirical evidence for the ontogenesis of coordination in learning a mathematical concept. In C.-K. Looi, J. L. Polman, U. Cress, & P. Reimann (Eds.), Transforming learning, empowering learners. Proceedings of the International Conference of the Learning Sciences (ICLS 2016) (pp. 466–473). Singapore: International Society of the Learning Sciences.
Andrá, C., Arzarello, F., Ferrara, F., Holmqvist, K., Lindstroem, P., Robutti, O., & Sabena, C. (2009). How students read mathematical representations: An eye tracking study. In M. Tzekaki, M. Kaldrimidou, & C. Sakonidis (Eds.), Proceedings of the 33rd Conference of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 49–56). Thessaloniki, Greece: PME.
Andrá, C., Lindström, P., Arzarello, F., Holmqvist, K., Robutti, O., & Sabena, C. (2015). Reading mathematics representations: An eye-tracking study. International Journal of Science and Mathematics Education, 13(2), 237–259. http://doi.org/10.1007/s10763-013-9484-y.
Aspinwall, L., Shaw, K. L., & Presmeg, N. C. (1996). Uncontrollable mental imagery: Graphical connections between a function and its derivative. Educational Studies in Mathematics, 33(3), 301–317. http://doi.org/10.1023/A:1002976729261.
Belenky, D., Ringenberg, M., Olsen, J., Aleven, V., & Rummel, N. (2014). Using dual eye-tracking to evaluate students’ collaboration with an intelligent tutoring system for elementary-level fractions. In CogSci 2014 (pp. 176–181). Quebec City, Canada.
Chesney, D. L., McNeil, N. M., Brockmole, J. R., & Kelley, K. (2013). An eye for relations: Eye-tracking indicates long-term negative effects of operational thinking on understanding of math equivalence. Memory & Cognition, 41(7), 1079–1095. http://doi.org/10.3758/s13421-013-0315-8.
de Koning, B. B., Tabbers, H. K., Rikers, R. M. J. P., & Paas, F. (2010). Attention guidance in learning from a complex animation: Seeing is understanding? Learning and Instruction, 20(2), 111–122. http://doi.org/10.1016/j.learninstruc.2009.02.010.
Duval, R. (2006, February 28). A cognitive analysis of problems of comprehension in a learning of mathematics. Educational Studies in Mathematics. Springer. http://doi.org/10.1007/s10649-006-0400-z.
Epelboim, J., & Suppes, P. (2001). A model of eye movements and visual working memory during problem solving in geometry. Vision Research, 41(12), 1561–1574. http://doi.org/10.1016/S0042-6989(00)00256-X.
Froese, T., & Fuchs, T. (2012). The extended body: A case study in the neurophenomenology of social interaction. Phenomenology and the cognitive sciences (Vol. 11). http://doi.org/10.1007/s11097-012-9254-2.
Gallagher, S. (2011). Interactive coordination in joint attention. In A. Seemann (Ed.), Joint attention: New developments in psychology, philosophy of mind, and social neuroscience (pp. 293–305). Boston, United States: MIT Press.
Gegenfurtner, A., Lehtinen, E., & Säljö, R. (2011). Expertise differences in the comprehension of visualizations: A meta-analysis of eye-tracking research in professional domains. Educational Psychology Review, 23(4), 523–552. http://doi.org/10.1007/s10648-011-9174-7.
Guo, J., & Feng, G. (2013). How eye gaze feedback changes parent-child joint attention in shared storybook reading? In Eye gaze in intelligent user interfaces (pp. 9–21). London: Springer. http://doi.org/10.1007/978-1-4471-4784-8_2.
Hutto, D. D. (2011). Elementary mind minding, enactivist-style. Joint attention: New developments in psychology, philosophy of mind, and social neuroscience (pp. 307–341). United States: MIT Press.
Jarodzka, H., Van Gog, T., Dorr, M., Scheiter, K., & Gerjets, P. (2013). Learning to see: Guiding students’ attention via a model’s eye movements fosters learning. Learning and Instruction, 25, 62–70. http://doi.org/10.1016/j.learninstruc.2012.11.004.
Jornet, A., & Roth, W.-M. (2015). The joint work of connecting multiple (re)presentations in science classrooms. Science Education, 99(2), 378–403. http://doi.org/10.1002/sce.21150.
Krichevets, A. N. (2014). Vygotsky and intersubjectivity. Psychology in Russia: State of the Art, 7(3), 13–23. http://doi.org/10.11621/pir.2014.0302.
Krichevets, A., Shvarts, A., & Chumachenko, D. (2014). Perceptual action of novices and experts in operating visual representations of a mathematical concept. Psychology. Journal of Higher School of. Economics, 11(3), 55–78.
Leont’ev, A. N. (1978). Activity, consciousness, and personality. Englewood Cliffs, NJ: Prentice-Hall.
Peters, M. (2010). Parsing mathematical constructs: Results from a preliminary eye tracking study. In Proceedings of the British Society for Research into Learning Mathematics (Vol. 30, pp. 47–52).
Pfeiffer, T., & Renner, P. (2014). EyeSee3D: A low-cost approach for analyzing mobile 3D eye tracking data using computer vision and augmented reality technology. In Proceedings of the Symposium on Eye Tracking Research and Applications—ETRA’14 (pp. 195–202). New York, NY: ACM Press. http://doi.org/10.1145/2578153.2578183.
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 (pp. 215–234). Rotterdam: Sense.
Radford, L. (2010). The eye as a theoretician: Seeing structures in generalizing activities. For the Learning of Mathematics, 30(2), 2–7. Retrieved from http://www.jstor.org/stable/20749442.
Radford, L., & Sabena, C. (2015). The question of method in a Vygotskian semiotic approach. In Approaches to qualitative research in mathematics education (pp. 157–182). Utrecht: Springer. http://doi.org/10.1007/978-94-017-9181-6_7.
Radford, L., Demers, S., Guzmán, J., & Cerulli, M. (2003). Calculators, graphs, gestures, and the production meaning. In N. Pateman, B. Dougherty, & J. Zilliox (Eds.), 27 Conference of the international group for the psychology of mathematics education (Vol. 4, pp. 55–62). Honolulu, United States.
Richardson, D. C., & Dale, R. (2005). Looking to understand: the coupling between speakers’ and listeners’ eye movements and its relationship to discourse comprehension. Cognitive Science, 29(6), 1045–1060. http://doi.org/10.1207/s15516709cog0000_29.
Roth, W.-M. (2008). The dawning of signs in graph interpretation. In L. Radford, G. Schubring, & F. Seeger (Eds.), Semiotics in mathematics education (pp. 83–102). Rotterdam: Sense.
Roth, W.-M., & Radford, L. (2011). A cultural-historical perspective on mathematics teaching and learning. Rotterdam: Sense.
Rouinfar, A., Agra, E., Larson, A. M., Rebello, N. S., & Loschky, L. C. (2014). Linking attentional processes and conceptual problem solving: Visual cues facilitate the automaticity of extracting relevant information from diagrams. Frontiers in Psychology, 5, 1094. http://doi.org/10.3389/fpsyg.2014.01094.
San Diego, J. P., Aczel, J., Hodgson, B., & Scanlon, E. (2006). “There’s more than meets the eye”: Analysing verbal protocols, gazes and sketches on external mathematical representations. In J. Novotná, H. Moraová, M. Krátká, & N. Stehlíková (Eds.), Proceedings of the 30th Conference of the International Group for the Psychology of Mathematics Education (Vol. 5, pp. 17–24). Prague: PME.
Scheiter, K., & Eitel, A. (2010). The effects of signals on learning from text and diagrams: How looking at diagrams earlier and more frequently improves understanding (pp. 264–270). Berlin, Heidelberg: Springer. http://doi.org/10.1007/978-3-642-14600-8_26.
Seeger, F. (2008). Intentionality and sign. In L. Radford, G. Schubring, & F. Seeger (Eds.), Semiotics in mathematics education: Epistemology, history, classroom, and culture (pp. 1–18). Rotterdam: Sense.
Sharma, K., Caballero, D., Verma, H., Jermann, P., & Dillenbourg, P. (2015). Looking AT versus looking THROUGH: A dual eye-tracking study in MOOC context. In Computer Supported Collaborative Learning. Retrieved from https://www.isls.org/cscl2015/papers/MC-0250-FullPaper-Sharma.pdf.
Sharma, K., Jermann, P., & Dillenbourg, P. (2014). “With-me-ness”: A gaze-measure for students’ attention in MOOCs. In International conference of the learning sciences. Retrieved from https://pdfs.semanticscholar.org/bf6d/bd6e7b1ccf2ea60cdf04eb437043154e81b2.pdf.
Sharma, K., Jermann, P., Nüssli, M.-A., & Dillenbourg, P. (2013). Understanding collaborative program comprehension: Interlacing gaze and dialogues. In Computer Supported Collaborative Learning (CSCL 2013). Madison, Wisconsin, USA.
Sierpinska, A. (1994). Understanding in mathematics. New York: Falmer.
Tomasello, M., & Farrar, M. J. (1986). Joint attention and early language. Child Development, 57(6), 1454. https://doi.org/10.2307/1130423.
van Gog, T., Jarodzka, H., Scheiter, K., Gerjets, P., & Paas, F. (2009). Attention guidance during example study via the model’s eye movements. Computers in Human Behavior, 25(3), 785–791. https://doi.org/10.1016/j.chb.2009.02.007.
van Gog, T., & Scheiter, K. (2010). Eye tracking as a tool to study and enhance multimedia learning. Learning and Instruction, 20(2), 95–99. https://doi.org/10.1016/j.learninstruc.2009.02.009.
van Marlen, T., van Wermeskerken, M., Jarodzka, H., & van Gog, T. (2016). Showing a model’s eye movements in examples does not improve learning of problem-solving tasks. Computers in Human Behavior, 65, 448–459. https://doi.org/10.1016/j.chb.2016.08.041.
Vygotsky, L. S. (2004). The essential Vygotsky. New York, NY: Kluwer Academic, Plenum Publishers.
Vygotsky, L. S. (2001). Lektsii po pedologii [Lectures on pedology]. Izhevsk: Izdatel’kii dom Udmurtskii universitet. (Original work published 1934).
Yu, C., & Smith, L. B. (2016). The social origins of sustained attention in one-year-old human infants. Current Biology: CB, 26(9), 1235–1240. https://doi.org/10.1016/j.cub.2016.03.026.
Acknowledgements
I would like to thank Anatoly Krichevets for his efforts in creating the technological dual eye-tracking solution and to acknowledge Andonis Zagorianakos for productive discussions of the data and for sharing his insightful vision of the phenomena from a Husserlian phenomenology point of view. This research was supported by RFBR research grant No. 15-06-06319.
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Shvarts, A. (2018). Joint Attention in Resolving the Ambiguity of Different Presentations: A Dual Eye-Tracking Study of the Teaching-Learning Process. In: Presmeg, N., Radford, L., Roth, WM., Kadunz, G. (eds) Signs of Signification. ICME-13 Monographs. Springer, Cham. https://doi.org/10.1007/978-3-319-70287-2_5
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