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Space and numbers are closely linked to each other in the human mind and brain. These bidirectional links may be the end product of innate biases and/or developmental, educational, and acculturation processes. Whatever their origin may be, there is no doubt that space-number relationships are influenced by linguistic and other cognitive determinants in adults. Biological development, refinement of domain-general abilities like inhibition, working memory capacity, reasoning skills, embodied representations underlying spatial and/or numerical processes may create a basis for formation or restructuring of the links between space and numbers. In modern societies, all this happens in parallel to enculturation encompassing linguistic factors (e.g., reading / writing direction; grammatical number forms), cognitive factors that are not or only partially related to language (e.g., working memory, inhibition) and those that are explicitly related to formal math education and culture (e.g., teaching a number line, individually, culturally or religiously (dys-)preferred numbers like 3, 8, 12, or 13). However, such processes neither begin nor end with adulthood, but continue developing through the lifespan. The associations between space and numbers seems to vary across lifetime development: some space-number relationships become weaker with age so that it is easier to inhibit processing of irrelevant spatial / numerical features in conflicting stimuli. On the other hand, some space number associations are strengthened in lifetime development, possibly due to longer exposure to cultural factors, as well as due to decrease in efficiency of inhibition mechanism. A better theoretical distinction is needed to differentiate the development of different types of space-number relationships over the lifetime. For instance, an important distinction in such models is the distinction between directionality of space-number relations (e.g., SNARC effect) and extension of spatial and numerical magnitudes, such as conflicts between spatial and numerical codes in Approximate Number System (ANS) tasks, where different numerosities (and hence different visually corresponding aspects) have to be compared.

Science: general issues --- Psychology --- Spatial-numerical association --- number processing --- spatial biases --- cognitive development --- Spatial-numerical association taxonomy --- Spatial-numerical association --- number processing --- spatial biases --- cognitive development --- Spatial-numerical association taxonomy

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Living at the beginning of the 21st century requires being numerate, because numerical abilities not only essential for life prospects of individuals but also for economic interests of post-industrial knowledge societies. Thus, numerical development is at the core of both individual as well as societal interests. There is the notion that we are already born with a very basic ability to deal with small numerosities. Yet, this often called “number sense” seems to be very restricted, approximate, and driven by perceptual constraints. During our numerical development in formal (e.g., school) but also informal contexts (e.g., family, street) we acquire culturally developed abstract symbol systems to represent exact numerosities – in particular number words and Arabic digits – refining our numerical capabilities. In recent years, numerical development has gained increasing research interest documented in a growing number of behavioural, neuro-scientific, educational, cross-cultural, and neuropsychological studies addressing this issue. Additionally, our understanding of how numerical competencies develop has also benefitted considerably from the advent of different neuro-imaging techniques allowing for an evaluation of developmental changes in the human brain. In sum, we are now starting to put together a more and more coherent picture of how numerical competencies develop and how this development is associated with neural changes as well. In the end, this knowledge might also lead to a better understanding of the reasons for atypical numerical development which often has grieve consequences for those who suffer from developmental dyscalculia. Therefore, this Research Topic deals with all aspects of numerical development: findings from behavioural performance to underlying neural substrates, from cross-sectional to longitudinal evaluations, from healthy to clinical populations. To this end, we encourage empirical contributions using different experimental methodologies but also welcome theoretical contributions, review articles, or opinion papers. We hope that in this Research Topic the expertise of researchers from different backgrounds will be brought together to advance a topic with both scientific and every-day relevance.

Calculus --- Mathematics --- Physical Sciences & Mathematics --- developmental dyscalculia --- mathematics learning disability --- approximate number system --- language development --- spatial-numerical association --- numerical development