Improving With Practice: A Neural Model of Mathematical Development

Abstract

The ability to improve in speed and accuracy as a result of repeating some task is an important hallmark of intelligent biological systems. Although gradual behavioral improvements from practice have been modeled in spiking neural networks, few such models have attempted to explain cognitive development of a task as complex as addition. In this work, we model the progression from a counting-based strategy for addition to a recall-based strategy. The model consists of two networks working in parallel: a slower basal ganglia loop and a faster cortical network. The slow network methodically computes the count from one digit given another, corresponding to the addition of two digits, whereas the fast network gradually "memorizes" the output from the slow network. The faster network eventually learns how to add the same digits that initially drove the behavior of the slower network. Performance of this model is demonstrated by simulating a fully spiking neural network that includes basal ganglia, thalamus, and various cortical areas. Consequently, the model incorporates various neuroanatomical data, in terms of brain areas used for calculation and makes psychologically testable predictions related to frequency of rehearsal. Furthermore, the model replicates developmental progression through addition strategies in terms of reaction times and accuracy, and naturally explains observed symptoms of dyscalculia.

Developmental Dyscalculia and Automatic Magnitudes Processing: Investigating Interference Effects between Area and Perimeter

“…This pattern is compatible with inhibition deficits often associated with DD ( Wang et al, 2012 ; Szucs et al, 2013a ; Bugden and Ansari, 2015 ). As suggested by Aubin et al (2016) , individuals with DD might fail to consolidate magnitude knowledge and to produce the shift from the “slow” computing neural network to the “fast” retrieval network. Hence, they must invest more cognitive efforts in order to ignore irrelevant magnitude information.…”

“…The cognitive method as well as the statistical analysis of the current study enabled us not only to study the differences between automatic processing of area vs. perimeter (i.e., investigating magnitude sense in DD), but also to investigate whether DD participants indeed perform poorly or differently on continuous magnitude processing tasks in initial vs. proficiency stages of learning (i.e., to investigate learning functions in DD). Earlier studies showed that even a small number of rehearsals of numerical problems led to automatic processing and to changes in brain functions ( Ischebeck et al, 2007 ; Aubin et al, 2016 ). For instance, Ischebeck et al (2007) found that very short training (eight repetitions) in multiplication problems led to a decrease in the activity of fronto-parietal brain areas related to calculation and numerical processing ( Menon et al, 2000 ; Dehaene et al, 2003 ).…”

“…On the other hand, the training also resulted in increased activity in temporo-parietal regions known to be involved in arithmetic fact retrieval ( Dehaene et al, 2003 ). Recently, it was proposed that DDs’ deficits in inhibition of irrelevant numerical information can also represent difficulties with consolidating learned information and with performing the shift from initial computing based processing to automatic retrieval based processing ( Ischebeck et al, 2007 ; Aubin et al, 2016 ). Indeed, Aubin et al (2016) suggested that people with DD may be less able to consolidate a numerical task within the frontal-parietal region and must instead rely on their working memory.…”

“…Recently, it was proposed that DDs’ deficits in inhibition of irrelevant numerical information can also represent difficulties with consolidating learned information and with performing the shift from initial computing based processing to automatic retrieval based processing ( Ischebeck et al, 2007 ; Aubin et al, 2016 ). Indeed, Aubin et al (2016) suggested that people with DD may be less able to consolidate a numerical task within the frontal-parietal region and must instead rely on their working memory. Consequently, there would be limited progression to recalling numerical information and a continued dependence on working memory.…”

Structured sequence processing and combinatorial binding: neurobiologically and computationally informed hypotheses

“…R. Soc. B 375: 20190304 may be investigated further by instantiating a dynamic neural implementation of the model via the NEF [83], where learning algorithms employing, for instance, spike-timing-dependent plasticity can be applied to learn functions over time [116].…”