Sashank Varma

Dyscalculia: From brain to education

Recent research in cognitive and developmental neuroscience is providing a new approach to the understanding of dyscalculia that emphasizes a core deficit in understanding sets and their numerosities, which is fundamental to all aspects of elementary school mathematics. The neural bases of numerosity processing have been investigated in structural and functional neuroimaging studies of adults and children, and neural markers of its impairment in dyscalculia have been identified. New interventions to strengthen numerosity processing, including adaptive software, promise effective evidence-based education for dyscalculic learners.

Autism as a neural systems disorder: a theory of frontal-posterior underconnectivity.

The underconnectivity theory of autism attributes the disorder to lower anatomical and functional systems connectivity between frontal and more posterior cortical processing. Here we review evidence for the theory and present a computational model of an executive functioning task (Tower of London) implementing the assumptions of underconnectivity. We make two modifications to a previous computational account of performance and brain activity in typical individuals in the Tower of London task (Newman et al., 2003): (1) the communication bandwidth between frontal and parietal areas was decreased and (2) the posterior centers were endowed with more executive capability (i.e., more autonomy, an adaptation is proposed to arise in response to the lowered frontal-posterior bandwidth). The autism model succeeds in matching the lower frontal-posterior functional connectivity (lower synchronization of activation) seen in fMRI data, as well as providing insight into behavioral response time results. The theory provides a unified account of how a neural dysfunction can produce a neural systems disorder and a psychological disorder with the widespread and diverse symptoms of autism.

Frontal and parietal participation in problem solving in the Tower of London: fMRI and computational modeling of planning and high-level perception

This study triangulates executive planning and visuo-spatial reasoning in the context of the Tower of London (TOL) task by using a variety of methodological approaches. These approaches include functional magnetic resonance imaging (fMRI), functional connectivity analysis, individual difference analysis, and computational modeling. A graded fMRI paradigm compared the brain activation during the solution of problems with varying path lengths: easy (1 and 2 moves), moderate (3 and 4 moves) and difficult (5 and 6 moves). There were three central findings regarding the prefrontal cortex: (1) while both the left and right prefrontal cortices were equally involved during the solution of moderate and difficult problems, the activation on the right was differentially attenuated during the solution of the easy problems; (2) the activation observed in the right prefrontal cortex was highly correlated with individual differences in working memory (measured independently by the reading span task); and (3) different patterns of functional connectivity were observed in the left and right prefrontal cortices. Results obtained from the superior parietal region also revealed left/right differences; only the left superior parietal region revealed an effect of difficulty. These fMRI results converged upon two hypotheses: (1) the right prefrontal area may be more involved in the generation of a plan, whereas the left prefrontal area may be more involved in plan execution; and (2) the right superior parietal region is more involved in attention processes while the left homologue is more of a visuo-spatial workspace. A 4CAPS computational model of the cognitive processes and brain activation in the TOL task integrated these hypothesized mechanisms, and provided a reasonably good fit to the observed behavioral and brain activation data. The multiple research approaches presented here converge on a deepening understanding of the combination of perceptual and conceptual processes in this type of visual problem solving.

The organization of thinking : What functional brain imaging reveals about the neuroarchitecture of complex cognition

Recent findings in brain imaging, particularly in fMRI, are beginning to reveal some of the fundamental properties of the organization of the cortical systems that underpin complex cognition. We propose an emerging set of operating principles that govern this organization, characterizing the system as a set of collaborating cortical centers that operate as a large-scale cortical network. Two of the network’s critical features are that it is resource constrained and dynamically configured, with resource constraints and demands dynamically shaping the network topology. The operating principles are embodied in a cognitive neuroarchitecture, 4CAPS, consisting of a number of interacting computational centers that correspond to activating cortical areas. Each 4CAPS center is a hybrid production system, possessing both symbolic and connectionist attributes. We describe 4CAPS models of sentence comprehension, spatial problem solving, and complex multitasking and compare the accounts of these models with brain activation and behavioral results. Finally, we compare 4CAPS with other proposed neuroarchitectures.

Scientific and Pragmatic Challenges for Bridging Education and Neuroscience

Educational neuroscience is an emerging effort to integrate neuroscience methods, particularly functional neuroimaging, with behavioral methods to address issues of learning and instruction. This article consolidates common concerns about connecting education and neuroscience. One set of concerns is scientific: in-principle differences in methods, data, theory, and philosophy. The other set of concerns is pragmatic: considerations of costs, timing, locus of control, and likely payoffs. The authors first articulate the concerns and then revisit them, reinterpreting them as potential opportunities. They also provide instances of neuroscience findings and methods that are relevant to education. The goal is to offer education researchers a window into contemporary neuroscience to prepare them to think more specifically about the prospects of educational neuroscience.

Computational Modeling of High-Level Cognition and Brain Function

This article describes a computational modeling architecture, 4CAPS, which is consistent with key properties of cortical function and makes good contact with functional neuroimaging results. Like earlier cognitive models such as SOAR, ACT‐R, 3CAPS, and EPIC, the proposed cognitive model is implemented in a computer simulation that predicts observable variables such as human response times and error patterns. In addition, the proposed 4CAPS model accounts for the functional decomposition of the cognitive system and predicts fMRI activation levels and their localization within specific cortical regions, by incorporating key properties of cortical function into the design of the modeling system. Hum. Brain Mapping 8:128–136, 1999.

A Hybrid Architecture for Working Memory: Reply to MacDonald and Christiansen (2002)

This article responds to M. C. MacDonald and M. H. Christiansen’s 2002 commentary on the capacity theory of working memory (WM) and its computational implementation, the Capacity-Constrained Collaborative Activation–based Production System (3CAPS). The authors also point out several shortcomings in MacDonald and Christiansen’s proposal for the construal of WM, arguing that at some level of description, their model is a variant of a small subset of the 3CAPS theory. The authors go on to describe how the symbolic and connectionist mechanisms within the hybrid 3CAPS architecture combine to produce a processing style that provides a good match to human sentence comprehension and other types of high-level cognition. The properties of 3CAPS are related to the development of other connectionist, symbolic, and hybrid systems.

Infusing Neuroscience Into Teacher Professional Development

Bruer advocated connecting neuroscience and education indirectly through the intermediate discipline of psychology. We argue for a parallel route: The neurobiology of learning, and in particular the core concept of plasticity, have the potential to directly transform teacher preparation and professional development, and ultimately to affect how students think about their own learning. We present a case study of how the core concepts of neuroscience can be brought to in-service teachers—the BrainU workshops. We then discuss how neuroscience can be meaningfully integrated into pre-service teacher preparation, focusing on institutional and cultural barriers.

The mental representation of integers: An abstract-to-concrete shift in the understanding of mathematical concepts

Mathematics has a level of structure that transcends untutored intuition. What is the cognitive representation of abstract mathematical concepts that makes them meaningful? We consider this question in the context of the integers, which extend the natural numbers with zero and negative numbers. Participants made greater and lesser judgments of pairs of integers. Experiment 1 demonstrated an inverse distance effect: When comparing numbers across the zero boundary, people are faster when the numbers are near together (e.g., -1 vs. 2) than when they are far apart (e.g., -1 vs. 7). This result conflicts with a straightforward symbolic or analog magnitude representation of integers. We therefore propose an analog-x hypothesis: Mastering a new symbol system restructures the existing magnitude representation to encode its unique properties. We instantiate analog-x in a reflection model: The mental negative number line is a reflection of the positive number line. Experiment 2 replicated the inverse distance effect and corroborated the model. Experiment 3 confirmed a developmental prediction: Children, who have yet to restructure their magnitude representation to include negative magnitudes, use rules to compare negative numbers. Taken together, the experiments suggest an abstract-to-concrete shift: Symbolic manipulation can transform an existing magnitude representation so that it incorporates additional perceptual-motor structure, in this case symmetry about a boundary. We conclude with a second symbolic-magnitude model that instantiates analog-x using a feature-based representation, and that begins to explain the restructuring process.

How Should Educational Neuroscience Conceptualise the Relation between Cognition and Brain Function? Mathematical Reasoning as a Network Process.

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.