# Virtual Reality as an Innovative Tool for Numerosity Perception
## 1 Introduction
The link between math and visual numerosity abilities is also in line with recent imaging studies describing areas in the parietal cortex responding to numerosity [11], digit perception [29], as well as mathematical reasoning [12]. These results highlight the potential of this sensory system to support mathematical learning. With effective training, it could help mitigate the negative effects of low numeracy, including those associated with dyscalculia and math anxiety. Moreover, as numerosity tasks do not require sophisticated language skills, these training activities could be potentially performed relatively early in life, also as a pedagogical strategy for the empowerment of basic non-symbolic prerequisites for later symbolic mathematical learning (for example in pre-school children). Given the potential link between the ANS and math, some studies measured whether and how much this perceptual system can be improved by perceptual training procedures and whether the effect of the training generalizes over mathematical abilities (e.g., improving mental calculation proficiency). Although there are several methodological differences between studies, in general, the results show a relatively high level of plasticity of the ANS, even in adults [30; 31]. At odds with this, the evidence for a potential transfer of perceptual improvements to symbolic mathematical abilities (e.g., calculation) is less clear and still highly debated. For example, [PERSON] and colleagues [30] trained adults to identify whether a set of elements (dots) briefly (to avoid counting, 500 ms) presented on a screen contained more white or black dots. By changing (trial-by-trial) the ratio between black and white dots, they measure sensory thresholds as the difference in numbers of black and white dots necessary to reach a pre-defined correct response rate (e.g., 75%). The results showed a clear improvement in thresholds, with performance continuing to improve even after thousands of trials. Despite the clear sensory improvement, the learning did not transfer to math abilities (arithmetic operations, including addition, subtraction, and multiplication), leaving the performance obtained before and after the perceptual training virtually unchanged. The traditional approach to numerosity estimation typically involves presenting participants with arrays of visual stimuli, such as dots or other shapes, arranged on a 2D display [32]. These arrays can vary in configuration, including regular grids, random distributions, or clustered patterns, with key variables such as item density, size, spacing, and overall arrangement being manipulated [33]. Participants are tasked with estimating the number of items in the display, typically through direct estimation, comparison with other arrays, or magnitude estimation techniques. In addition to accuracy, response time is also often measured [34]. These results can also shed light on perceptual phenomena such as the Weber fraction, which quantifies sensitivity to numerical differences [35]. Other attempts have been made, with different outcomes, sometime showing transfer to math [36; 37; 31], sometimes not [38; 30; 39; 40]. A relatively recent review critically evaluated all published studies that aimed to train the ANS finding no conclusive evidence that ANS training improves symbolic arithmetic [41]. One possible factor behind the lack of generalization of perceptual training in math could reside in the non-ecological quality of the activities used to train this perceptual mechanism. We rarely find ourselves discriminating, for tens of minutes, which set of elements presented on a monitor is the most numerous. These tasks, besides being scarcely ecological, are often monotonous, and are not very suitable for stimulating motivation. The use of virtual reality (VR) in numerosity perception tasks could provide a controlled and immersive environment for presenting numerical stimuli in ways that are difficult or impossible to achieve with traditional methods.