Chapter Three - Foundations of Children's Numerical and Mathematical Skills: The Roles of Symbolic and Nonsymbolic Representations of Numerical Magnitude
Introduction
Numerical information informs our everyday behavior. Consider a glance at the alarm clock in the morning, counting change in the line-up at the coffee shop, or reading about the latest election polls—each of these common situations places demands on the ability to process numerical information. Research has shown that the ability to process numbers and use them in mathematical operations (such as calculation) is a critical predictor of an individual's economic and social success (e.g., Bynner & Parsons, 1997). Longitudinal studies investigating the predictors of academic achievement reveal that school-entry numerical and mathematical skills are a strong predictor of later academic achievement. School-entry math skills are a stronger predictor of later achievement than both school-entry reading and attentional skills (e.g., Duncan et al., 2007). Findings such as these demonstrate the critical role that numerical and mathematical knowledge and skills play in children's academic development and outcomes.
What do we know about how numbers are represented in the brain and mind and how such representations change over the course of learning and development? The past three decades have seen a surge in the empirical study of number representation and processing in multiple species and at different levels of analyses (for reviews, see Ansari, 2008, Dehaene, 1997, Nieder and Dehaene, 2009). The aim of this chapter is to provide an overview of this research and to synthesize what is currently known, as well as to discuss open questions and future research directions.
Section snippets
An Approximate System for the Representation of Numerical Magnitude
Much of the research on how we represent and process numerical information has been focused on uncovering the foundational systems that underpin the development of complex numerical and mathematical abilities. In particular, there has been a focus on understanding the representations of numerical magnitude, or the total number of items in a set. The representation of processing numerical magnitude has been investigated from infancy onward at both the behavioral and brain levels of analysis. In
The Symbolic Representation of Numerical Magnitude
The literature just reviewed suggests the existence of an approximate representation of numerical magnitude that humans share with other species and that can be measured very early in human development. All of the findings reviewed thus far relied upon nonsymbolic representations of numerical magnitude (e.g., dot arrays) to glean insights into the representation and processing of numerical magnitude. In contrast to nonhuman primates, however, humans who grow up in literate cultures acquire
The Relationship Between Symbolic and Nonsymbolic Representations of Numerical Magnitude
The mixed evidence concerning the association between nonsymbolic numerical magnitude processing and children's arithmetic achievement casts doubt on the assumption that symbolic number skills are scaffolded on their nonsymbolic counterparts. Specifically, one influential proposal suggests that the very meaning of number symbols is determined by direct reference to the corresponding nonsymbolic magnitude: “When we learn number symbols, we simply attach their arbitrary shapes to the relevant
Summary and Conclusions
Numbers play a critical role in our everyday lives, and acquiring numerical and mathematical skills is one of the central goals of formal education across the globe. Over the past three decades, researchers from the fields of Cognitive Science, Psychology, and Neuroscience have investigated how numbers are represented and processed in the brain and mind. A particular focus of this line of research has been on better understanding the foundations upon which the development of numerical and
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Conceptual foundations of early numeracy: Evidence from infant brain data
2023, Progress in Brain ResearchDevelopmental trajectories of symbolic magnitude and order processing and their relation with arithmetic development
2022, Cognitive DevelopmentCitation Excerpt :Moreover, neuropsychological case studies have reported that processing of numerical magnitude and order can be selectively impaired (Delazer & Butterworth, 1997; Turconi & Seron, 2002). While a large body of evidence suggests that children’s symbolic magnitude processing skills serve as a key foundation for the acquisition of higher-order arithmetic skills (review: De Smedt et al., 2013; meta-analysis: Schneider et al., 2017), the precise role of order processing in arithmetic development is still being debated (Lyons et al., 2014, 2016; Lyons & Ansari, 2015; Orrantia et al., 2019; Sasanguie et al., 2017; Sasanguie & Vos, 2018; Vogel et al., 2015, 2021; Vos et al., 2017; Xu & Lefevre, 2021). Importantly, cross-sectional evidence is suggestive of a fundamental shift in the predictive pattern of arithmetic from dominance of magnitude to order processing between Grades 1 and 2 (Sasanguie & Vos, 2018; Xu & Lefevre, 2021).
Walking another pathway: The inclusion of patterning in the pathways to mathematics model
2022, Journal of Experimental Child PsychologyCitation Excerpt :However, even in Grade 1, children are still in the process of developing conceptual and procedural skills that are related to ordinality (Finke et al., 2021; Hutchison et al., 2022; Xu & LeFevre, 2021). Thus, performance on ordinal tasks, such as number ordering and order judgment tasks (Lyons & Ansari, 2015), taps into a range of individual differences in symbolic number knowledge, decision making, and strategic processes (Hutchison et al., 2022; Muñez, Orrantia, Matilla, & Sanchez, 2022; Vogel, Faulkenberry, & Grabner, 2021; Vos, Gevers, Reynvoet, & Xenidou-Dervou, 2021; Xu & LeFevre, 2021). In the current study, we aimed to identify the cognitive precursors that predict ordinal understanding as measured by number ordering.
Early neurocognitive development of dyscalculia
2021, Heterogeneous Contributions to Numerical Cognition: Learning and Education in Mathematical CognitionThe association between visual attention and arithmetic competence: The mediating role of enumeration
2020, Journal of Experimental Child PsychologyCitation Excerpt :First, given the existence of two different attentional processes (i.e., automatic, stimulus-driven parallel processing vs. effortful, goal-directed serial processing; Wolfe, 1998), it is unclear which attentional process actually drives the relation between visual attention and arithmetic competence. Second, although it has been shown that visual attention is involved in the enumeration process (Simon & Vaishnavi, 1996; Vetter et al., 2008) and that enumeration skills serve as an important precursor of our arithmetic competence (Lyons & Ansari, 2015; Reigosa-Crespo et al., 2012), the issue of whether enumeration skills serve as the mechanism underlying the link between visual attention and arithmetic competence remains unexplored. The current study, therefore, was conducted to address the two aforementioned hypotheses concerning the link between visual attention and arithmetic competence.