Chapter 7 - Memory and cognitive control circuits in mathematical cognition and learning
Introduction
Knowledge of numerical magnitude and manipulations of symbolic and nonsymbolic quantity (number sense) are critical building blocks from which all mathematical knowledge is constructed. These basic building blocks rely on visual and auditory association cortices which help decode the visual form and phonological features of numerical stimuli, and the parietal attention system (Dehaene et al., 2003) which helps to build semantic representations of quantity (Ansari, 2008) from visuospatial primitives including object identification, spatial attention, eye gaze, and pointing (Simon et al., 2002). With increased proficiency, these functions are subserved by a “core” visuospatial number system anchored in the fusiform gyrus (FG) and intraparietal sulcus (IPS).
The IPS subdivision of the posterior parietal cortex has been the focus of most neurobiological research on mathematical cognition and learning (Ansari, 2008, Butterworth, 1999, Dehaene et al., 2003). The IPS and FG form core building blocks from which number form and quantity representations are constructed in the brain (Ansari, 2008). But these regions do not function in isolation. They receive input from multiple brain regions and send outputs to several others. Furthermore, the development of core systems is supported by its engagement with multiple brain systems. Recent research is beginning to emphasize a multisystem approach (Arsalidou and Taylor, 2011, Fias et al., 2013, Qin et al., 2014). Multiple distributed neural processes involved in number form, magnitude and quantity representations, working memory, and declarative memory have been identified as being important for numerical problem solving and mathematical learning (Fig. 1). This chapter synthesizes emerging findings on multiple memory and cognitive control systems which play a critical, but heretofore underappreciated, role in mathematical cognition in adults, as well as in scaffolding children's mathematics learning and skill development.
We focus on two memory systems—working memory and declarative memory—that play distinct roles in mathematical cognition and learning. The working memory system anchored in parietal–frontal circuits creates short-term representations that allow manipulation of multiple discrete quantities over several seconds. In contrast, declarative memory systems anchored in hippocampal–frontal circuits play an important role in formation of associative memories and binding of new and old information, contributing to long-term memory and generalization beyond individual problem attributes. Both these processes require flexible integration of functional circuits anchored in prefrontal cognitive control systems. We describe cognitive control systems which guide allocation of attention resources and retrieval of facts from memory in the service of goal-directed numerical problem solving.
The roles of the two memory systems are greatly amplified during key developmental stages of learning, and their involvement in mathematical cognition and learning is best studied in the context of cognitive development. There is now growing evidence to suggest that functional circuits engaged by children are not the same as those engaged by adults who have evolved multiple strategies for learning and cognitive skill acquisition. Studies comparing children with adults are therefore likely to be insensitive to major changes that occur during specific stages of development. A number of scaffolding systems are likely to be engaged during development, and new studies are beginning to investigate the role of parietal–frontal and hippocampal–frontal circuits that might otherwise be missed in studies involving adults. The precise nature of this engagement is a function of developmental stage, domain knowledge, problem complexity, and individual proficiency in use of efficient problem-solving strategies. Accordingly, this review has a strong focus on both typical and atypical neurodevelopmental processes associated with the two memory systems and their associated prefrontal cognitive control systems.
The next sections are organized as follows. In Section 2, we first consider the relation between core systems and working memory and describe multiple parietal–frontal working memory circuits anchored in different subdivisions of the posterior parietal cortex, with a specific focus on functional circuits associated with the IPS and supramarginal gyrus. The role of parietal–frontal working memory circuits in the typical and atypical development of mathematical cognition is then discussed. In Section 3, we turn to the declarative memory system highlighting key hippocampal–prefrontal circuits. Emerging findings on the role of the hippocampal memory system in mathematical learning and development are then described. In Section 4, we consider how distinct prefrontal cortex (PFC) control systems facilitate mathematical cognition and learning. Section 5 summarizes the main points of this review. This chapter builds on related topical reviews (Menon, 2015, Menon, 2016) and attempts an integrative view of distinct, but overlapping, memory and cognitive control circuits involved in mathematical cognition and learning.
Section snippets
Core and Noncore Parietal Systems Overlap in the IPS
Parietal–frontal circuits play a prominent role in mathematical cognition. Functional neuroimaging research has revealed significant overlap in multiple parietal and prefrontal cortical regions involved in working memory and numerical problem solving (Arsalidou and Taylor, 2011, Metcalfe et al., 2013, Rottschy et al., 2012). Common patterns of coactivation have most prominently been detected in the IPS, supramarginal gyrus, premotor cortex, and ventral and dorsal aspects of the lateral PFC.
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The Medial Temporal Lobe: A System for Associative Learning
Over the past few years, evidence has been accumulating for the differential involvement of the declarative memory system in mathematical learning, especially during key stages of skill acquisition in children (Qin et al., 2014). The importance of the medial temporal lobe, particularly its hippocampal subdivision, in learning and memory for events in space and time is well known (Davachi, 2006, Davachi et al., 2003, Diana et al., 2007, Eichenbaum et al., 2007, Tulving, 1983). Theories of memory
Flexible Hubs for Cognitive Control
Prefrontal control processes are important for virtually every complex cognitive task, including mathematical cognition. The role of both working memory and declarative memory systems in mathematical cognition must therefore be considered in the context of cognitive control processes that support flexible problem solving and learning. Prefrontal control processes serve several functions in numerical cognition including maintenance of attention on goal-relevant numerical representations,
Summary and Conclusions
Multiple lines of evidence affirm that numerical cognition relies on interactions within and between multiple functional brain circuits, including those underlying numerical quantity representations (FG–IPS), working memory (IPS–SMG–ventrolateral and dorsolateral PFC), declarative memory (hippocampus–ventrolateral and dorsolateral PFC), and cognitive control (anterior insula–ventrolateral and dorsolateral PFC) (Fig. 1). We have highlighted the role of distinct memory and cognitive control
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