Characterizing exact arithmetic abilities before formal schooling

Children appear to have some arithmetic abilities before formal instruction in school, but the extent of these abilities as well as the mechanisms underlying them are poorly understood. Over two studies, an initial exploratory study of preschool children in the U.S. (N = 207; Age = 2.89-4.30 years) and a pre-registered replication of preschool children in Italy (N = 130; Age = 3-6.33 years), we documented some basic behavioral signatures of exact arithmetic using a non-symbolic subtraction task. Furthermore, we investigated the underlying mechanisms by analyzing the relationship between individual differences in exact subtraction and assessments of other numerical and non-numerical abilities. Across both studies, children performed above chance on the exact non-symbolic arithmetic task, generally showing better performance on problems involving smaller quantities compared to those involving larger quantities. Furthermore, individual differences in non-verbal approximate numerical abilities and exact cardinal number knowledge were related to different aspects of subtraction performance. Specifically, non-verbal approximate numerical abilities were related to subtraction performance in older but not younger children. Across both studies we found evidence that cardinal number knowledge was related to performance on subtraction problems where the answer was zero (i.e., subtractive negation problems). Moreover, subtractive negation problems were only solved above chance by children who had a basic understanding of cardinality. Together these finding suggest that core non-verbal numerical abilities, as well as emerging knowledge of symbolic numbers provide a basis for some, albeit limited, exact arithmetic abilities before formal schooling.

Number symbols are processed more automatically than nonsymbolic numerical magnitudes: Findings from a Symbolic-Nonsymbolic Stroop task

Are number symbols (e.g., 3) and numerically equivalent quantities (e.g., •••) processed similarly or distinctly? If symbols and quantities are processed similarly then processing one format should activate the processing of the other. To experimentally probe this prediction, we assessed the processing of symbols and quantities using a Stroop-like paradigm. Participants (N_Study1 = 80, N_Study2 = 63) compared adjacent arrays of symbols (e.g., 4444 vs 333) and were instructed to indicate the side containing either the greater quantity of symbols (nonsymbolic task) or the numerically larger symbol (symbolic task). The tasks included congruent trials, where the greater symbol and quantity appeared on the same side (e.g. 333 vs. 4444), incongruent trials, where the greater symbol and quantity appeared on opposite sides (e.g. 3333 vs. 444), and neutral trials, where the irrelevant dimension was the same across both sides (e.g. 3333 vs. 333 for nonsymbolic; 333 vs. 444 for symbolic). The numerical distance between stimuli was systematically varied, and quantities in the subitizing and counting range were analyzed together and independently. Participants were more efficient comparing symbols and ignoring quantities, than comparing quantities and ignoring symbols. Similarly, while both symbols and quantities influenced each other as the irrelevant dimension, symbols influenced the processing of quantities more than quantities influenced the processing of symbols, especially for quantities in the counting rage. Additionally, symbols were less influenced by numerical distance than quantities, when acting as the relevant and irrelevant dimension. These findings suggest that symbols are processed differently and more automatically than quantities.

Learning disabilities: Developmental dyscalculia

Developmental dyscalculia (DD) is a developmental learning disability that manifests as a persistent difficulty in comprehending even the most basic numeric and arithmetic concepts, despite normal intelligence and schooling opportunities. Given the predominant use of numbers in modern society, this condition can pose major challenges in the sufferer's everyday life, both in personal and professional development. Since, to date, we still lack a universally recognized and psychometrically driven definition of DD, its diagnosis has been applied to a wide variety of cognitive profiles. In this chapter, we review the behavioral and neural characterization of DD as well as the different neurocognitive and etiologic accounts of this neurodevelopmental disorder. We underline the multicomponential nature of this heterogeneous disability: different aspects of mathematical competence can be affected by both the suboptimal recruitment of general cognitive functions supporting mathematical cognition (such as attention, memory, and cognitive control) and specific deficits in mastering numeric concepts and operations. Accordingly, both intervention paradigms focused on core numeric abilities and more comprehensive protocols targeting multiple neurocognitive systems have provided evidence for effective positive outcomes.

The Relational SNARC: Spatial Representation of Nonsymbolic Ratios

Recent research in numerical cognition has begun to systematically detail the ability of humans and nonhuman animals to perceive the magnitudes of nonsymbolic ratios. These relationally defined analogs to rational numbers offer new potential insights into the nature of human numerical processing. However, research into their similarities with and connections to symbolic numbers remains in its infancy. The current research aims to further explore these similarities by investigating whether the magnitudes of nonsymbolic ratios are associated with space just as symbolic numbers are. In two experiments, we found that responses were faster on the left for smaller nonsymbolic ratio magnitudes and faster on the right for larger nonsymbolic ratio magnitudes. These results further elucidate the nature of nonsymbolic ratio processing, extending the literature of spatial-numerical associations to nonsymbolic relative magnitudes. We discuss potential implications of these findings for theories of human magnitude processing in general and how this general processing relates to numerical processing.