# READING MATHEMATICS REPRESENTATIONS: AN EYE-TRACKING STUDY

Article

First Online:

- 1.2k Downloads
- 14 Citations

## Abstract

We use eye tracking as a method to examine how different mathematical representations of the same mathematical object are attended to by students. The results of this study show that there is a meaningful difference in the eye movements between formulas and graphs. This difference can be understood in terms of the cultural and social shaping of human perception, as well as in terms of differences between the symbolic and graphical registers.

## Key words

Eye tracking Mathematical representations Semiotics Visual perception## Preview

Unable to display preview. Download preview PDF.

## Supplementary material

10763_2013_9484_MOESM1_ESM.pdf (945 kb)

## References

- Ainsworth, S. (2006). DeFT: a conceptual framework for considering learning with multiple representations.
*Learning and Instruction, 16*, 183–198.CrossRefGoogle Scholar - Andrà, C., Arzarello, F., Ferrara, F., Holmqvist, K., Lindström, P., Robutti, O. & Sabena, C. (2009). How students read mathematical representations: an eye tracking study.
*Proceedings of the XXXIII conference of the psychology of math education*. Thessaloniki, GR.Google Scholar - Arcavi, A. (1994). Symbol sense: informal sense-making in formal mathematics.
*For the Learning of Mathematics, 14*(3), 24–35.Google Scholar - Arzarello, F., Ascari, M., Thomas, M. & Yoon, C. (2011). Teaching practice: a comparison of two teachers’ decision making in the mathematics classroom. In: B. Ubuz (Ed.),
*Proceedings of the 35th conference of the international group for the psychology of mathematics education*(Vol. 2, pp. 65–72). Ankara, Turkey: PME.Google Scholar - Brousseau, G. (1997).
*Theory of didactical situations in mathematics*. Dordrecht: Kluver.Google Scholar - Bushwell, G. T. (1935).
*How people look at pictures*. Chicago: University of Chicago Press.Google Scholar - Carpenter, P. A. & Shah, P. (1998). A model of the perceptual and conceptual processes in graph comprehension.
*Journal of Experimental Psychology: Applied, 4*(2), 75–100.Google Scholar - Chandler, P. & Sweller, J. (1991). Cognitive load theory and the format of instruction.
*Cognition and Instruction, 8*(4), 293–332.CrossRefGoogle Scholar - De Freitas, E. & Sinclair, N. (2012). Diagram, gesture, agency: theorizing embodiment in the mathematics classroom.
*Educational Studies in Mathematics, 80*.Google Scholar - Duval, R. (2006). A cognitive analysis of problems of comprehension in a learning of mathematics.
*Educational Studies in Mathematics, 61*, 103–131.CrossRefGoogle Scholar - Gray, E. & Tall, D. (1994). Duality, ambiguity, and flexibility: a “proceptual” view of simple arithmetic.
*Journal for Research in Mathematics Education, 25*(2), 116–140.CrossRefGoogle Scholar - Hegarty, M., Mayer, R. E. & Green, C. E. (1992). Comprehension of arithmetic word problems: evidence from students' eye fixations.
*Journal of Educational Psychology, 84*(1), 76–84.CrossRefGoogle Scholar - Henderson, J. M., Weeks, P. A., Jr. & Hollingworth, A. (1999). The effects of semantic consistency on eye movements during complex scene viewing.
*Journal of Experimental Psychology: Human Perception and Performance, 25*(1), 210–228.Google Scholar - Holmqvist, K., Andrá, C., Lindström, P., Arzarello, F., Ferrara, F., Robutti, O. & Sabena C. (2011). A method for quantifying focussed versus overview behaviour in AOI sequences.
*Behavior Research Method, 43*(4), 987–998.Google Scholar - Husserl, E. (1931). In: W.R. Boyce Gibson, trans., 3rd [1958] (eds.),
*Ideas. General introduction to pure phenomenology.*London, UK: George Allen and Unwin.Google Scholar - Johnson-Laird, P. N. (1983).
*Mental models: towards a cognitive science of language, interference and consciousness*. Cambridge: Cambridge University Press.Google Scholar - Just, M. A. & Carpenter, P. A. (1980). A theory of reading: from eye fixations to comprehension.
*Psychological Review, 87*(4), 329–354.CrossRefGoogle Scholar - Kintsch, W. (1998).
*Comprehension: a paradigm for cognition*. New York: Cambridge University Press.Google Scholar - Kieran, C. (1988). Two different approaches among algebra learners. In A. F. Coxford (Ed.),
*The ideas of algebras. Yearbook 1988, K-12*. Reston: NCTM.Google Scholar - Knoblich, G., Ohlsson, S. & Raney, G. E. (2001). An eye movement study of insight problem solving.
*Memory and Cognition, 29*(7), 1000–1009.CrossRefGoogle Scholar - Lakoff, G. & Núñez, R. (2000).
*Where does mathematics come from*. New York: Basic Books.Google Scholar - Latour, P. L. (1962). Visual threshold during eye movements.
*Vision Research, 2*, 261–262.CrossRefGoogle Scholar - Leung, F. K. S., Graf, K. & Lopez-Real, F. (2006).
*Mathematics Education in Different Cultural Traditions- A Comparative Study of East Asia and the West: The 13th ICMI Study*. SpringerGoogle Scholar - Levinas, E. (1989). In: Sean Hand (ed),
*The Levinas reader*, Oxford, UK: Blackwell.Google Scholar - Lindamood, P., Bell, N. & Lindamood, P. (1997). Sensory-cognitive factors in the controversy over reading instruction.
*Journal of Developmental Disorders, 1*, 143–182.Google Scholar - Loftus, G. T. & Macworth, N. H. (1978). Cognitive determinants of fixation location during picture viewing.
*Journal of Experimental Psychology: Human Perception and Performance, 4*(4), 565–572.Google Scholar - Mason, J. (2008). Being mathematical with and in front of learners: attention, awareness, and attitude as sources of differences between teacher educators, teachers and learners. In T. Wood & B. Jaworski (Eds.),
*International handbook of mathematics teacher education: the mathematics teacher educator as a developing professional*(Vol. 4, pp. 31–56). Rotterdam: Sense publishers.Google Scholar - Nemirovsky, R. & Monk, S. (2000). “If you look at it the other way…” an exploration into the nature of symbolizing. In P. Cobb, E. Yackel & K. McClain (Eds.),
*Symbolizing and communicating in mathematics classrooms*(pp. 177–221). Hillsdale: Lawrence Erlbaum.Google Scholar - Paivio, A. (1971).
*Imagery and verbal processes*. New York: Holt, Rinehart, and Winston.Google Scholar - Radford, L. (2002). The seen, the spoken and the written. A semiotic approach to the problem of objectification of mathematical knowledge.
*For the Learning of Mathematics, 22*(2), 14–23.Google Scholar - Radford, L. (2010). The eye as a theoretician: seeing structures in generalizing activities.
*For the Learning of Mathematics, 30*(2), 2–7.Google Scholar - Rayner, K. (1998). Eye movements in reading and information processing: 20 years of research.
*Psychological Bulletin, 124*(3), 372–422.CrossRefGoogle Scholar - Robutti, O. (2006). Motion, technology, gesture in interpreting graphs.
*The International Journal for Technology in Mathematics Education, 13*(3), 117–126.Google Scholar - Roth, W. M. (2003).
*Toward an anthropology of graphing: semiotic and activity-theoretic perspective*. Dordrecht: Kluwer.CrossRefGoogle Scholar - Scheiter, K. & van Gog, T. (2009). Using eye tracking in applied research to study and stimulate the process of information from multi-representational sources.
*Applied Cognitive Psychology, 23*, 1209–1214.CrossRefGoogle Scholar - Schoenfeld, A. H. (2010). How we think: a theory of goal-oriented decision making and its educational applications. Routledge, New York.Google Scholar
- Sfard, A. (1991). On the dual nature of mathematical conceptions: reflections on processes and objects as different sides of the same coin.
*Educational Studies in Mathematics, 22*, 1–36.CrossRefGoogle Scholar - Sfard, A. (2000). Symbolizing mathematical reality into being: how mathematical discourse and mathematical objects create each other. In P. Cobb, K. E. Yackel & K. McClain (Eds.),
*Symbolizing and communicating: perspectives on mathematical discourse, tools, and instructional design*(pp. 37–98). Mahwah: Erlbaum.Google Scholar - Tall, D. (2002). Using Technology to Support an Embodied Approach to Learning Concepts in Mathematics. First
*Coloquio do Historia e Tecnologia no Ensino de Matematica at Universidade do Estrado do Rio de Janeiro*, Rio de Janeiro, BR.Google Scholar - Tarmizi, R. & Sweller, J. (1988). Guidance during mathematical problem solving.
*Journal of Educational Psychology, 80*, 424–436.CrossRefGoogle Scholar - van Gog, T. & Scheiter, K. (2010). Eye tracking as a tool to study and enhance multimedia learning.
*Learning and Instruction, 20*, 95–99.CrossRefGoogle Scholar - Verschaffel, L., De Corte, E. & Pauwels, A. (1992). Solving compare problems: an eye movement test of Lewis and Mayers consistency hypothesis.
*Journal of Educational Psychology, 84*(1), 85–94.CrossRefGoogle Scholar - Volkman, F. C. (1976). Sacadic suppression: a brief review. In R. A. Monty & J. W. Senders (Eds.),
*Eye movements and psychological processes*. Hilsdale: Earlbaum.Google Scholar - Yarbus, A. L. (1967).
*Eye movements and vision*. New York: Plenum.CrossRefGoogle Scholar

## Copyright information

© National Science Council, Taiwan 2013