Despite decades of research on the close link between eye movements and human cognitive processes, the exact nature of the link between eye movements and deliberative thinking in problem-solving remains unknown. Thus, this study explored the critical eye-movement indicators of deliberative thinking and investigated whether visual behaviors could predict performance on arithmetic word problems of various difficulties. An eye tracker and test were employed to collect 69 sixth-graders’ eye-movement behaviors and responses. No significant difference was found between the successful and unsuccessful groups on the simple problems, but on the difficult problems, the successful problem-solvers demonstrated significantly greater gaze aversion, longer fixations, and spontaneous reflections. Notably, the model incorporating RT-TFD, NOF of 500 ms, and pupil size indicators could best predict participants’ performance, with an overall hit rate of 74%, rising to 80% when reading comprehension screening test scores were included. These results reveal the solvers’ engagement strategies or show that successful problem-solvers were well aware of problem difficulty and could regulate their cognitive resources efficiently. This study sheds light on the development of an adapted learning system with embedded eye tracking to further predict students’ visual behaviors, provide real-time feedback, and improve their problem-solving performance.
This is a preview of subscription content, log in to check access.
Buy single article
Instant access to the full article PDF.
Price includes VAT for USA
Subscribe to journal
Immediate online access to all issues from 2019. Subscription will auto renew annually.
This is the net price. Taxes to be calculated in checkout.
Abeles, D., & Yuval-Greenberg, S. (2017). Just look away: Gaze aversions as an overt attentional disengagement mechanism. Cognition, 168, 99–109. https://doi.org/10.1016/j.cognition.2017.06.021.
Baird, B., Smallwood, J., Mrazek, M. D., Kam, J. W., Franklin, M. S., & Schooler, J. W. (2012). Inspired by distraction: Mind wandering facilitates creative incubation. Psychological Science, 23(10), 1117–1122. https://doi.org/10.1177/0956797612446024.
Ballard, D. H., Hayhoe, M. M., Pook, P. K., & Rao, R. P. (1997). Deictic codes for the embodiment of cognition. Behavioral and Brain Sciences, 20(4), 723–742. https://doi.org/10.1017/S0140525X97001611.
Belenky, D. M., & Schalk, L. (2014). The effects of idealized and grounded materials on learning, transfer, and interest: An organizing framework for categorizing external knowledge representations. Educational Psychology Review, 26(1), 27–50. https://doi.org/10.1007/s10648-014-9251-9.
Booth, J. L., & Koedinger, K. R. (2012). Are diagrams always helpful tools? Developmental and individual differences in the effect of presentation format on student problem solving. British Journal of Educational Psychology, 82(3), 492–511. https://doi.org/10.1111/j.2044-8279.2011.02041.x.
Chiou, G. L., Hsu, C. Y., & Tsai, M. J. (2019). Exploring how students interact with guidance in a physics simulation: Evidence from eye-movement and log data analyses. Interactive Learning Environments. https://doi.org/10.1080/10494820.2019.1664596.
Doherty-Sneddon, G., Bruce, V., Bonner, L., Longbotham, S., & Doyle, C. (2002). Development of gaze aversion as disengagement from visual information. Developmental Psychology, 38(3), 438–445. https://doi.org/10.1037//0012-16220.127.116.118.
Ehrlichman, H., & Micic, D. (2012). Why do people move their eyes when they think? Current Directions in Psychological Science, 21(2), 96–100. https://doi.org/10.1177/0963721412436810.
Glenberg, A. M., Schroeder, J. L., & Robertson, D. A. (1998). Averting the gaze disengages the environment and facilitates remembering. Memory & Cognition, 26(4), 651–658. https://doi.org/10.3758/BF03211385.
Gredebäck, G., & Melinder, A. M. D. (2010). Infants understanding of everyday social interactions: A dual process account. Cognition, 114, 197–206. https://doi.org/10.3758/BF03211385.
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. https://doi.org/10.1037/0022-0618.104.22.168.
Hegarty, M., Mayer, R. E., & Monk, C. A. (1995). Comprehension of arithmetic word problems: A comparison of successful and unsuccessful problem solvers. Journal of Educational Psychology, 87(1), 18–32. https://doi.org/10.1037//0022-0622.214.171.124.
Horstmann, N., Ahlgrimm, A., & Glöckner, A. (2009). How distinct are intuition and deliberation? An eye-tracking analysis of instruction-induced decision modes. Judgment and Decision making, 4, 335–354. https://doi.org/10.2139/ssrn.1393729.
Hyönä, J., Lorch, R. F., & Rinck, M. (2003). Eye movement measures to study global text processing. In J. Hyönä, R. Radach, & H. Deubel (Eds.), The mind's eye cognitive and applied aspects of eye movement research (pp. 313–334). Elsevier Science BV.
Jackson, I., & Sirois, S. (2009). Infant cognition: Going full factorial with pupil dilation. Developmental Science, 12, 670–679. https://doi.org/10.1111/j.1467-7687.2008.00805.x.
Jian, Y. -C., Chen, M. -L., & Ko, H. -W. (2013). Context effects in processing of Chinese academic words: An eye-tracking investigation. Reading Research Quarterly, 48(4), 403–413. https://doi.org/10.1002/rrq.56.
Just, M. A., & Carpenter, P. A. (1980). A theory of reading: From eye fixations to comprehension. Psychological Review, 87, 329–354. https://doi.org/10.1037//0033-295X.87.4.329.
Just, M. A., & Carpenter, P. A. (1993). The intensity dimension of thought: Pupillometric indices of sentence processing. Canadian Journal of Experimental Psychology, 47(2), 310–339. https://doi.org/10.1037/h0078820.
Kahneman, D. (1973). Attention and effort. Prentice Hall.
Klingner, J., Tversky, B., & Hanrahan, P. (2011). Effects of visual and verbal presentation on cognitive load in vigilance, memory, and arithmetic tasks. Psychophysiology, 48(3), 323–332. https://doi.org/10.1111/j.1469-8986.2010.01069.x.
Knoblich, G., Ohlsson, S., & Raney, G. E. (2001). An eye movement study of insight problem solving. Memory & Cognition, 29(7), 1000–1009. https://doi.org/10.3758/BF03195762.
Ko, H. W. (1999). Reading comprehension-screening test [in Chinese]. Psychological Testing, 46, 1–11.
Krstić, K., Šoškić, A., Ković, V., & Holmqvist, K. (2018). All good readers are the same, but every low-skilled reader is different: An eye-tracking study using PISA data. European Journal of Psychology of Education, 33(3), 511–541. https://doi.org/10.1007/s10212-018-0382-0.
Laeng, B., Sirois, S., & Gredebäck, G. (2012). Pupillometry: A window to the preconscious? Perspectives on Psychological Science, 7(1), 18–27. https://doi.org/10.1177/1745691611427305.
Lin, Y.-T., Wu, C.-C., Hou, T.-Y., Lin, Y.-C., Yang, F.-Y., & Chang, C.-H. (2016). Tracking students’ cognitive processes during program debugging-an eye-movement approach. IEEE Transactions on Education, 59(3), 175–186. https://doi.org/10.1109/TE.2015.2487341.
Liu, T. S. W., Liu, Y. T., & Chen, C. Y. D. (2019). Meaningfulness is in the eye of the reader: Eye-tracking insights of L2 learners reading e-books and their pedagogical implications. Interactive Learning Environments, 27(2), 181–199. https://doi.org/10.1080/10494820.2018.1451901.
Lu, H. I., Chan, Y. C., & Chen, H. C. (2018). Ambiguity and inference processing in verbal jokes: Analyses of eye movement (in Chinese). Bulletin of Educational Psychology, 50(4), 589–609. https://doi.org/10.6251/BEP.201906_50(4).0002.
Micic, D., Ehrlichman, H., & Chen, R. (2010). Why do we move our eyes while trying to remember? The relationship between non-visual gaze patterns and memory. Brain & Cognition, 74(3), 210–224. https://doi.org/10.1016/j.bandc.2010.07.014.
Paas, F., Tuovinen, J. E., Tabbers, H., & Van Gerven, P. W. (2003). Cognitive load measurement as a means to advance cognitive load theory. Educational Psychologist, 38(1), 63–71. https://doi.org/10.1207/S15326985EP3801_8.
Phelps, F. G., Doherty-Sneddon, G., & Warnock, H. (2006). Helping children think: Gaze aversion and teaching. British Journal of Developmental Psychology, 24(3), 577–588. https://doi.org/10.1348/026151005X49872.
Piquado, T., Isaacowitz, D., & Wingfield, A. (2010). Pupillometry as a measure of cognitive effort in younger and older adults. Psychophysiology, 47, 1–10. https://doi.org/10.1111/j.1469-8986.2009.00947.x.
Riley, M. S., & Greeno, J. G. (1988). Developmental analysis of understanding language about quantities and of solving problems. Cognition & Instruction, 5, 49–101. https://doi.org/10.1207/s1532690xci0501_2.
Salvi, C., & Bowden, E. M. (2016). Looking for creativity: Where do we look when we look for new ideas? Frontiers in Psychology, 7, 161. https://doi.org/10.3389/fpsyg.2016.00161.
Schumacher, R. F., & Fuchs, L. S. (2012). Does understanding relational terminology mediate effects of intervention on compare word problems? Journal of Experimental Child Psychology, 111(4), 607–628. https://doi.org/10.1016/j.jecp.2011.12.001.
Siegle, G. J., Ichikawa, N., & Steinhauer, S. (2008). Blink before and after you think: Blinks occur prior to and following cognitive load indexed by pupillary responses. Psychophysiology, 45(5), 679–687. https://doi.org/10.1111/j.1469-8986.2008.00681.x.
Tabachnick, B. G. & Fidell, L. S. (2001). Using Multivariate Statistics. Boston: Allyn and Bacon.
Van der Schoot, M., Arkema, A. H. B., Horsley, T. M., & Van Lieshout, E. C. D. M. (2009). The consistency effect depends on markedness in less successful but not successful problem solvers: An eye movement study in primary school children. Contemporary Educational Psychology, 34, 58–66. https://doi.org/10.1016/j.cedpsych.2008.07.002.
Walcher, S., Körner, C., & Benedek, M. (2017). Looking for ideas: Eye behavior during goal-directed internally focused cognition. Consciousness and Cognition, 53, 165–175. https://doi.org/10.1016/j.concog.2017.06.009.
Wang, C. Y., Tsai, M. J., & Tsai, C. C. (2016). Multimedia recipe reading: Predicting learning outcomes and diagnosing cooking interest using eye-tracking measures. Computers in Human Behavior, 62, 9–18. https://doi.org/10.1016/j.chb.2016.03.064.
Yang, F.-Y., Tsai, M.-J., Chiou, G.-L., Lee, S. W.-Y., Chang, C.-C., & Chen, L.-L. (2018). Instructional suggestions supporting science learning in digital environments based on a review of eye tracking studies. Educational Technology & Society, 21(2), 28–45.
This work was financially supported by the Ministry of Science and Technology, Taiwan under grant number MOST 104-2511-S-003-013-MY3, MOST 108-2511-H-003-014-MY3, MOST108-2636-H-003-003-, and by the “Institute for Research Excellence in Learning Sciences” of National Taiwan Normal University (NTNU) from The Featured Areas Research Center Program within the framework of the Higher Education Sprout Project by the Ministry of Education (MOE) in Taiwan.
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
|1||RT − TFDa||–|
|2||RT − TFDb||.61**||–|
|3||RT − TFDc||.56**||.68**||–|
|4||RT − TFDd||.74**||.69**||.62**||–|
|5||TFD of blanka||.24*||.35**||.30*||−.03||–|
|6||TFD of blankb||.55**||.32**||.43**||.12||.71**||–|
|7||TFD of blankc||.31**||.06||.31**||.34**||.21||.34**||–|
|8||TFD of blankd||.41**||.41**||.63**||.13||.72**||.75**||.26*||–|
|9||NOF of blanka||.29*||.38**||.35**||.01||.70**||.76**||.97**||.27*||–|
|10||NOF of blankb||.61**||.32**||.47**||.17||.98**||.72**||.65**||.26*||.67**||–|
|11||NOF of blankc||.44**||.13||.40**||.42**||.31*||.42**||.24||.92**||.39**||.47**||–|
|12||NOF of blankd||.47**||.41**||.68**||.17||.74**||.98**||.74**||.38**||.75**||.75**||.27*||–|
|13||NOF of 500 msa||.03||.01||−.02||−.17||.06||.05||.02||−.10||.01||.03||−.02||−.16||–|
|14||NOF of 500 msb||.15||−.07||.08||−.13||.17||.10||−.01||.07||.14||.09||−.03||.08||.66**||–|
|15||NOF of 500 msc||−.01||−.12||.03||.07||−.01||−.02||−.06||.14||−.04||−.04||−.06||.08||.56**||.59**||–|
|16||NOF of 500 msd||.04||−.09||.15||−.10||.11||.16||.08||.09||.08||.13||.05||.07||.74**||.59**||.68**||–|
About this article
Cite this article
Wu, C., Liu, C., Yang, C. et al. Eye-movements reveal children’s deliberative thinking and predict performance on arithmetic word problems. Eur J Psychol Educ (2020). https://doi.org/10.1007/s10212-020-00461-w
- Arithmetic word problems
- Eye movements