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Mathematical cognition: individual differences in resource allocation

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Abstract

Individuals scoring higher in tests of general cognitive abilities tend to perform better on novel and familiar mathematical tasks. It has been scarcely investigated how this superior mathematical performance relates to the amount of cognitive resources that is invested to solve a given task. In this study we propose that, on novel tasks, individuals with high cognitive abilities outperform less able individuals, because they allocate a higher amount of resources. On familiar tasks, however, individuals with higher abilities profit from more efficient processes compared to individuals of lower cognitive abilities. We tested this hypothesis by administering to 11th graders a geometric analogy task not practiced at school and an algebraic transformation task comprising operations that are routinely required during mathematical courses. General cognitive abilities were measured with Ravens Advanced Progressive matrices (fluid intelligence), the d2 (focused attention) and KAI-N (working memory capacity). Resource allocation was measured by assessing pupil diameter during the problem-solving process. Performance on both the analogy and the algebra task was correlated with general cognitive abilities, especially fluid intelligence. In line with our assumptions, a positive correlation between fluid intelligence and resource allocation was observed in the novel geometric analogy task, whereas the correlation was not significant in the more familiar algebra task.

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Notes

  1. This uneven gender ratio in our sample roughly reflects the gender ratio in these schools.

  2. Replaced data in choice reaction time task 4.9% (SD 9.7); analogy task 5.8% (SD 8.7); algebra task 5.3% (SD 9.1).

  3. This was done to allow for the redilation of the pupil. As the pupil responds with a certain delay to cognitive work (cf. Loewenfeld 1993), processes active during solving the task might be visible in pupillary response shortly after the trial ends.

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Acknowledgments

This research was supported by grants from the German Federal Ministry for Education and Research (BMBF, Programme: Neuroscience-Instruction-Learning). IW was funded by the Stifterverband fuer die Deutsche Wissenschaft, Claussen-Simon-Stiftung.

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Authors and Affiliations

  1. Department of Psychology, Humboldt University Berlin, Rudower Chaussee 18, 12489, Berlin, Germany

    Boris Bornemann, Manja Foth, Judith Horn, Jan Ries & Elke van der Meer

  2. Department of Mathematics, Humboldt University Berlin, Berlin, Germany

    Elke Warmuth

  3. Department of Neurology Charité Berlin, Berlin NeuroImaging Center, Berlin, Germany

    Isabell Wartenburger

  4. Department of Linguistics, University of Potsdam, Berlin, Germany

    Isabell Wartenburger

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  1. Boris Bornemann
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  2. Manja Foth
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Correspondence to Boris Bornemann.

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Bornemann, B., Foth, M., Horn, J. et al. Mathematical cognition: individual differences in resource allocation. ZDM Mathematics Education 42, 555–567 (2010). https://doi.org/10.1007/s11858-010-0253-x

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