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Eye Movements During Mathematical Word Problem Solving—Global Measures and Individual Differences

Blickbewegungen beim Lösen mathematischer Textaufgaben – globale Maße und individuelle Unterschiede

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Abstract

In mathematical word problem solving, reading and mathematics interact. Previous research used the method of eye tracking to analyze reading processes but focused on specific elements in prototype word problems. This makes it difficult to compare the role of reading in longer, more complex word problems and between individuals. We used global measures of eye movements that refer to the word problem as a whole, similar to methods used in research on eye movements during reading. Global measures allow comparisons of reading processes of word problems of different structure. To test if these global measures are related to cognitive processes during word problem solving, we analyzed the relation between eye movements and the perceived difficulty of a task and its solution rate. We conducted two experiments with adults and undergraduate students (N = 17 and N = 42), solving challenging mathematical word problems from PISA. Experiment 1 showed that more difficult items were read with shorter fixations, more saccades, more regressions, and slower, with correlations ranging from r = 0.70 to r = 0.86. Multilevel modelling in experiment 2 revealed that for the number of saccades and the proportion of regressions, the relationship was stronger for low-performing students, with performance explaining up to 37% of the variance between students. These two measures are primarily associated with building a problem model. We discuss how this approach enables the use of eye tracking in complex mathematical word problem solving and contributes to our understanding of the role of reading in mathematics.

Zusammenfassung

Beim Lösen mathematischer Textaufgaben interagieren Lesen und Mathematik. Bisherige Forschung verwendet die Methode des Eyetracking, um Leseprozesse zu analysieren, aber fokussiert auf spezifische, lokale Elemente in prototypischen Textaufgaben. Das macht es schwierig, die Bedeutung des Lesens zwischen längeren und komplexeren Textaufgaben sowie zwischen Personen zu vergleichen. Wir verwendeten globale Maße von Blickbewegungen, die sich auf die Textaufgabe als Ganzes beziehen. Diese werden etwa in der Forschung zu Blickbewegungen beim Lesen häufiger verwendet. Globale Maße ermöglichen einen Vergleich der Leseprozesse von Textaufgaben unterschiedlicher Struktur. Um zu prüfen ob diese Maße mit kognitiven Prozessen beim Lösen mathematischer Textaufgaben zusammenhängen, analysieren wir den Zusammenhang zwischen Blickbewegungen und der wahrgenommenen Schwierigkeit einer Aufgabe sowie ihrer Lösungsrate. In zwei Experimenten lösten Erwachsene und Studierende (N = 17 und N = 42) herausfordernde Textaufgaben aus PISA. Experiment 1 zeigte, dass schwierigere Items mit kürzeren Fixationen, mehr Sakkaden, mehr Regressionen und langsamer gelesen wurden, mit Korrelationen im Bereich zwischen r = 0,70 und r = 0,86. Mehrebenenanalysen in Experiment 2 zeigten, dass für die Anzahl der Sakkaden und den Anteil der Regressionen der Zusammenhang für schwächere Studierende anwächst, wobei Leistung bis zu 37 % der Varianz zwischen den Studierenden aufklärt. Diese beiden Maße werden hauptsächlich mit dem Aufbau eines Problemmodells in Verbindung gebracht. Wir diskutieren wie dieser Ansatz die Nutzung von Eyetracking in komplexen Textaufgaben ermöglicht und zum Verständnis der Bedeutung von Lesen in Mathematik beiträgt.

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Authors and Affiliations

  1. Heinz Nixdorf Chair of Mathematics Education, TUM School of Education, Technical University of Munich, Arcisstr. 21, 80333, Munich, Germany

    Anselm R. Strohmaier, Matthias C. Lehner, Jana T. Beitlich & Kristina M. Reiss

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  1. Anselm R. Strohmaier
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  2. Matthias C. Lehner
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  4. Kristina M. Reiss
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Correspondence to Anselm R. Strohmaier.

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Strohmaier, A.R., Lehner, M.C., Beitlich, J.T. et al. Eye Movements During Mathematical Word Problem Solving—Global Measures and Individual Differences. J Math Didakt 40, 255–287 (2019). https://doi.org/10.1007/s13138-019-00144-0

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