# Virtual Reality as an Innovative Tool for Numerosity Perception
## 1 Introduction  
Math is crucial in modern society. During our daily activities, we often base decisions on numerical information, for example, to organize our diary commitments, to check that we have received the right change, to manage diet and nutrition, to measure medicine doses, to estimate time until our train, and much more. Low numeracy, defined as the inability to understand and use numbers effectively, is a well-known limiting factor for both education (particularly for STEM disciplines) and employment choices, with huge economical costs [1, 2]. Moreover, low numeracy characterizes developmental dyscalculia, a common but still poorly understood learning disorder, impairing children mathematical learning with negative repercussions on quality of life [3]. Numeracy is also often linked to math anxiety (excessive feelings of fear when exposed to mathematical tasks [4]), a relevant clinical condition, which is recently attracting much scientific interest. For these and other reasons, many governments around the world have established activities to continuously track the quality of mathematical learning in children and adolescents, on a large scale. OECD (Organization for Economic Co-operation and Development) director for education and skills defined good numeracy as \"the best protection against unemployment, low wages and poor health\" [5]. Neuroscience can provide significant contributions to this goal. In this regard, it is widely accepted that understanding the basic neurocognitive mechanisms governing the early precursors of mathematical abilities represent a key step to contrast low numeracy, and help dyscalculia and math anxiety [6; 7]. Where does mental math come from? Historically, mathematical skills were considered a paradigmatic example of high-level (human specific) verbal cognitive ability. In recent decades, this idea has radically changed, grounding mental math into a basic sensory mechanism: a visual number sense [8; 9; 10]. This fascinating idea triggered a huge burst of research, also for the implications sketched above, and there is now a huge amount of evidence, coming from different scientific fields, demonstrating that humans have a brain mechanism able to roughly but very quickly estimate the numerosity of objects in the environment [10; 11; 12; 13; 14; 15; 16]. This mechanism, often referred as the \"Approximate Number System (ANS)\" differs from serial counting in that it is faster, much more error-prone [9] and independent of mathematical language [17]. Moreover, whereas symbolic mathematics is a uniquely human function, we share the non-symbolic ANS with many animals' species, including non-human primates [18] but even birds [19; 20], fishes [21], and insects (e.g., bees [22; 23]). Going beyond behavioral results, there is now also clear evidence for the existence of numerosity selective neurons, mainly located in parietal and frontal cortices of both humans and non-human primates [18]. How does math emerge from this sensory mechanism in humans? The rationale is that numerical and mathematical meaning is mapped onto this pre-existing sensory number system, in charge of encoding the numerosity of visual objects. Atypical development of this basic sensory mechanism, should compromise a meaningful mapping between numerical symbols (digits) and their non-symbolic counterpart (the associated numerical quantity), limiting the development of mathematical learning [7]. In line with this idea, a seminal paper by [PERSON] and collaborators [24] reported positive correlations between visual numerosity estimation precision (more blue or yellow dots?) and math performance (e.g., mental calculation) in adolescents and in previous years, back to kindergarten. Moreover, children with dyscalculia often show deficits in visual numerosity tasks, even when the verbal component is eliminated, such as by indicating which of two visual ensembles contains more objects [25; 26; 27; 28].