As a full-blown research topic, numerical cognition is investigated by a variety of disciplines including cognitive science, developmental and educational psychology, linguistics, anthropology and, more recently, biology and neuroscience. However, despite the great progress achieved by such a broad and diversified scientific inquiry, we are still lacking a comprehensive theory that could explain how numerical concepts are learned by the human brain. In this perspective, I argue that computer simulation should have a primary role in filling this gap because it (...) allows identifying the finer-grained computational mechanisms underlying complex behavior and cognition. Modeling efforts will be most effective if carried out at cross-disciplinary intersections, as attested by the recent success in simulating human cognition using techniques developed in the fields of artificial intelligence and machine learning. In this respect, deep learning models have provided valuable insights into our most basic quantification abilities, showing how numerosity perception could emerge in multi-layered neural networks that learn the statistical structure of their visual environment. Nevertheless, this modeling approach has not yet scaled to more sophisticated cognitive skills that are foundational to higher-level mathematical thinking, such as those involving the use of symbolic numbers and arithmetic principles. I will discuss promising directions to push deep learning into this uncharted territory. If successful, such endeavor would allow simulating the acquisition of numerical concepts in its full complexity, guiding empirical investigation on the richest soil and possibly offering far-reaching implications for educational practice. (shrink)

The basic human ability to treat quantitative information can be divided into two parts. With proto-arithmetical ability, based on the core cognitive abilities for subitizing and estimation, numerosities can be treated in a limited and/or approximate manner. With arithmetical ability, numerosities are processed (counted, operated on) systematically in a discrete, linear, and unbounded manner. In this paper, I study the theory of enculturation as presented by Menary (2015) as a possible explanation of how we make the move from the proto-arithmetical (...) ability to arithmetic proper. I argue that enculturation based on neural reuse provides a theoretically sound and fruitful framework for explaining this development. However, I show that a comprehensive explanation must be based on valid theoretical distinctions and involve several stages in the development of arithmetical knowledge. I provide an account that meets these challenges and thus leads to a better understanding of the subject of enculturation. (shrink)

Children learn and use various strategies to solve math problems. One way children's math learning can be supported is through their use of and exposure to hand gestures. Children's self-produced gestures can reveal unique, math-relevant knowledge that is not contained in their speech. Additionally, these gestures can assist with their math learning and problem solving by supporting their cognitive processes, such as executive function. The gestures that children observe during math instructions are also linked to supporting cognition. Specifically, children are (...) better able to learn, retain, and generalize knowledge about math when that information is presented within the gestures that accompany an instructor's speech. To date, no conceptual model provides an outline regarding how these gestures and the math environment are connected, nor how they may interact with children's underlying cognitive capacities such as their executive function. In this review, we propose a new model based on an integration of the information processing approach and theory of embodied cognition. We provide an in-depth review of the related literature and consider how prior research aligns with each link within the proposed model. Finally, we discuss the utility of the proposed model as it pertains to future research endeavors. (shrink)