How should educational neuroscience conceptualise the relation between cognition and brain function? Mathematical reasoning as a network process

Abstract

Background: There is increasing interest in applying neuroscience findings to topics in education.

Purpose: This application requires a proper conceptualisation of the relation between cognition and brain function. This paper considers two such conceptualisations. The area focus understands each cognitive competency as the product of one (and only one) brain area. The network focus explains each cognitive competency as the product of collaborative processing among multiple brain areas.

Sources of evidence: We first review neuroscience studies of mathematical reasoning–specifically arithmetic problem-solving and magnitude comparison–that exemplify the area focus and network focus. We then review neuroscience findings that illustrate the potential of the network focus for informing three topics in mathematics education: the development of mathematical reasoning, the effects of practice and instruction, and the derailment of mathematical reasoning in dyscalculia.

Main argument: Although the area focus has historically dominated discussions in educational neuroscience, we argue that the network focus offers a complementary perspective on brain function that should not be ignored.

Conclusions: We conclude by describing the current limitations of network-focus theorising and emerging neuroscience methods that promise to make such theorising more tractable in the future.

Keywords:

• educational neuroscience
• mathematics education
• arithmetic; dyscalculia
• magnitude comparison
• large-scale cortical networks

Acknowledgements

We thank the editor and two anonymous reviewers for helpful comments. This material is based upon work supported by the National Science Foundation under grants REC 0337715 and SLC-0354453. Opinions, findings and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.

Notes

1. The use of subtraction has declined over the years as other experimental designs and methods of analysis have been developed. We describe two of these advancements in the ‘Conclusion’ section.

2. Pinel et al. (2004) also had participants compare stimuli along physical dimensions, such as size and luminance. These comparisons also produced SDEs in IPS. Comparisons of numerical magnitude and physical size activated roughly the same peak coordinates in IPS, whereas the comparisons of physical luminance activated different peak coordinates, though in the same area.

3. The dyscalculic patients did show a behavioural problem size effect, but it was exaggerated relative to normal controls, suggesting use of a different strategy (e.g., verbal counting versus magnitude-based processing).

4. Whether the change is an increase or decrease in activation depends on one's conception of what develops (Poldrack 2000). If one believes that representations get richer, then the prediction is increasing activation. If one believes that representations are shaped or tuned (i.e., made more efficient), then the prediction is decreasing activation.

5. There are other ways to interpret this shift. Rivera et al. (2005) favour an attentional interpretation, from more controlled to more automatic processing. Importantly, this interpretation is also a network explanation.

6. The Kucian et al. (2006) results do not strictly compel a network interpretation. It is possible to interpret them from an area focus if one assumes that the dyscalculia is not a homogeneous deficit, but rather is composed of multiple subtypes; and that each subtype is associated with dysfunction of a single competency, and thus a single brain area.