Mathematical cognition: individual differences in resource allocation

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.

Promises and potential pitfalls of a ‘cognitive neuroscience of mathematics learning’

“…The contributions by Bornemann et al (2010) as well as Landgraf et al (2010) provide first evidence of its sensitivity to mathematical processes and the link to regional cortical activity. This inexpensive methodology may also help to provide some biological constraints on existing cognitive accounts of mathematics learning.…”

“…This special issue also comprises investigations using transcranial near-infrared spectroscopy (NIRS) and pupillometry (Bornemann et al 2010;Landgraf et al 2010;Obersteiner et al 2010), which are both easily applicable in younger age groups. NIRS, on the one hand, measures cortical activity by detecting activation-related changes in the absorption and reflection of near-infrared light that is emitted into the scalp.…”

“…Therefore, in most mathematical neuroimaging studies, participants respond by button press, verifying a given answer (e.g., Bornemann, et al 2010;Preusse et al 2010) or choosing between different answer options (e.g., Landgraf, et al 2010;Lee, et al 2010;Obersteiner, et al 2010). An objection that is frequently raised concerning the use of verification tasks is that they may engage different cognitive processes compared to tasks in which the answer has to be actively produced and thereby use a response modality that is not ecologically valid.…”

Traveling down the road: from cognitive neuroscience to mathematics education … and back

“…A similar potential of cognitive neuroscience in relation to atypical development has been expressed in the field of reading as well (Gabrieli, 2009). Looking at the opposite side of the spectrum of individual differences, researchers are trying to unravel which cognitive factors contribute to proficiency with mathematics, as exemplified in this issue by Bornemann et al (2010) and Preusse et al (2010). They both investigated geometrical reasoning in high-intelligent individuals by combining behavioral data and neuroscientific measures, such as pupil dilatation and fMRI.…”

“…It is the first special issue containing a collection of studies that use neuroscientific methods to examine mathematics learning that is published in a leading mathematics education journal. Moreover, this issue is not restricted to elementary number processing, but addresses explicitly arithmetical and mathematical skills that are formally taught in school, such as arithmetic (Menon, 2010), word problem solving (Lee et al, 2010;Obersteiner et al, 2010), geometry (Stavy & Babai, 2010;Bornemann et al, 2010), algebra (Thomas et al, 2010), and connecting, at least in terms of the mathematics subjects that are investigated, clearly to school mathematics.…”