Why numerical symbols count in the development of mathematical skills: evidence from brain and behaviour

Numerical skills measured prior to school entry are predictive of mathematics achievement longitudinally. It is therefore important that young children start school with strong mathematical foundations. Here we review evidence from behavior and neuroimaging that highlights numerical symbol knowledge as a key mediator between informal and formal mathematical competencies. We argue that future research should aim to elucidate cognitive and neuronal mechanisms underpinning the acquisition of symbolic knowledge. Furthermore, multiple aspects of numerical symbol knowledge, such as identification, cardinality, and ordinality, should be emphasized in preschool childcare environment

Investigating the visual number form area: A replication study

© 2019 The Authors. Published by the Royal Society The influential triple-code model of number representation proposed that there are three distinct brain regions for three different numerical representations: verbal words, visual digits and abstract magnitudes. It was hypothesized that the region for visual digits, known as the number form area, would be in ventral occipitotemporal cortex (vOTC), near other visual category-specific regions, such as the visual word form area. However, neuroimaging investigations searching for a region that responds in a category-specific manner to the visual presentation of number symbols have yielded inconsistent results. Price & Ansari (Price, Ansari 2011 Neuroimage 57, 1205–1211) investigated whether any regions activated more in response to passively viewing digits in contrast with letters and visually similar nonsense symbols and identified a region in the left angular gyrus. By contrast, Grotheer et al. (Grotheer, Herrmann, Kovács 2016 J. Neurosci. 36, 88–97) found bilateral regions in vOTC which were more activated in response to digits than other stimuli categories while performing a one-back task. In the current study, we aimed to replicate the findings reported in Grotheer et al. with Price & Ansari’s passive viewing task as this is the most stringent test of bottom-up, sensory-driven, category-specific perception. Moreover, we used the contrasts reported in both papers in order to test whether the discrepancy in findings could be attributed to the difference in analysis

The Inferior Temporal Numeral Area distinguishes numerals from other character categories during passive viewing: A representational similarity analysis

A region in the posterior inferior temporal gyrus (pITG) is thought to be specialized for processing Arabic numerals, but fMRI studies that compared passive viewing of numerals to other character types (e.g., letters and novel characters) have not found evidence of numeral preference in the pITG. However, recent studies showed that the engagement of the pITG is modulated by attention and task contexts, suggesting that passive viewing paradigms may be ill-suited for examining numeral specialization in the pITG. It is possible, however, that even if the strengths of responses to different category types are similar, the distributed response patterns (i.e., neural representations) in a candidate numeral-preferring pITG region ( pITG-numerals ) may reveal categorical distinctions, even during passive viewing. Using representational similarity analyses with three datasets that share the same task paradigm and stimulus sets (total N = 88), we tested whether the neural representations of digits, letters, and novel characters in pITG-numerals were organized according to visual form and/or conceptual categories (e.g., familiar versus novel, numbers versus others). Small-scale frequentist and Bayesian meta-analyses of our dataset-specific findings revealed that the organization of neural representations in pITG-numerals is unlikely to be described by differences in abstract shape, but can be described by a categorical digits versus letters distinction, or even a digits versus others distinction (suggesting greater numeral sensitivity). Evidence of greater numeral sensitivity during passive viewing suggest that pITG-numerals is likely part of a neural pathway that has been developed for automatic processing of objects with potential numerical relevance. Given that numerals and letters do not differ categorically in terms of shape, categorical distinction in pITG-numerals during passive viewing must reflect ontogenetic differentiation of symbol set representations based on repeated usage of numbers and letters in differing task contexts

Making the Executive ‘Function’ for the Foundations of Mathematics: the Need for Explicit Theories of Change for Early Interventions

A vast body of work highlights executive functions (EFs) as robust correlates of mathematics achievement over the primary and preschool years. Yet, despite such correlational evidence, there is limited evidence that EF interventions yield improvements in early years mathematics. As intervention studies are a powerful tool to move beyond correlation to causality, failures of transfer from executive functions interventions are, we argue, highly problematic for both applied and theoretical reasons. We review the existing correlational and intervention literature at complementary neuroscientific, cognitive, developmental and educational levels. We appraise distinct theories of change underpinning the correlations between EF and early mathematics, as well as explicit or implicit theories of change for different types of EF interventions. We find that isolated EF interventions are less likely to transfer to improvements in mathematics than integrated interventions. Via this conceptual piece, we highlight that the field of EF development is in need of (1) a clearer framework for the mechanisms underpinning the relationships between early EF and other developing domains, such as mathematical cognition; (2) clearer putative theories of change for how interventions of different kinds operate in the context of EF and such domains; (3) and greater clarity on the developmental and educational contexts that influence these causal associations. Our synthesis of the evidence emphasises the need to consider the dynamic development of EFs with co-developing cognitive functions, such as early math skills, when designing education environments

Executive functioning skills and their environmental predictors among pre-school aged children in South Africa and The Gambia

Executive functions (EFs) in early childhood are predictors of later developmental outcomes and school readiness. Much of the research on EFs and their psychosocial correlates has been conducted in high-income, minority world countries, which represent a small and biased portion of children globally. The aim of this study is to examine EFs among children aged 3–5 years in two African countries, South Africa (SA) and The Gambia (GM), and to explore shared and distinct predictors of EFs in these settings. The SA sample (N = 243, 51.9% female) was recruited from low-income communities within the Cape Town Metropolitan area. In GM, participants (N = 171, 49.7% female) were recruited from the rural West Kiang region. EFs, working memory (WM), inhibitory control (IC) and cognitive flexibility (CF), were measured using tablet-based tasks. Associations between EF task performance and indicators of socioeconomic status (household assets, caregiver education) and family enrichment factors (enrichment activities, diversity of caregivers) were assessed. Participants in SA scored higher on all EF tasks, but children in both sites predominantly scored within the expected range for their age. There were no associations between EFs and household or familial variables in SA, except for a trend-level association between caregiver education and CF. Patterns were similar in GM, where there was a trend-level association between WM and enrichment activities but no other relationships. We challenge the postulation that children in low-income settings have poorer EFs, simply due to lower socioeconomic status, but highlight the need to identify predictors of EFs in diverse, global settings. Research Highlights: Assessed Executive Functioning (EF) skills and their psychosocial predictors among pre-school aged children (aged 3–5 years) in two African settings (The Gambia and South Africa). On average, children within each setting performed within the expected range for their age, although children in South Africa had higher scores across tasks. There was little evidence of any association between socioeconomic variables and EFs in either site. Enrichment activities were marginally associated with better working memory in The Gambia, and caregiver education with cognitive flexibility in South Africa, both associations were trend-level significance

Guidelines for the use and interpretation of assays for monitoring autophagy (4th edition)1.

In 2008, we published the first set of guidelines for standardizing research in autophagy. Since then, this topic has received increasing attention, and many scientists have entered the field. Our knowledge base and relevant new technologies have also been expanding. Thus, it is important to formulate on a regular basis updated guidelines for monitoring autophagy in different organisms. Despite numerous reviews, there continues to be confusion regarding acceptable methods to evaluate autophagy, especially in multicellular eukaryotes. Here, we present a set of guidelines for investigators to select and interpret methods to examine autophagy and related processes, and for reviewers to provide realistic and reasonable critiques of reports that are focused on these processes. These guidelines are not meant to be a dogmatic set of rules, because the appropriateness of any assay largely depends on the question being asked and the system being used. Moreover, no individual assay is perfect for every situation, calling for the use of multiple techniques to properly monitor autophagy in each experimental setting. Finally, several core components of the autophagy machinery have been implicated in distinct autophagic processes (canonical and noncanonical autophagy), implying that genetic approaches to block autophagy should rely on targeting two or more autophagy-related genes that ideally participate in distinct steps of the pathway. Along similar lines, because multiple proteins involved in autophagy also regulate other cellular pathways including apoptosis, not all of them can be used as a specific marker for bona fide autophagic responses. Here, we critically discuss current methods of assessing autophagy and the information they can, or cannot, provide. Our ultimate goal is to encourage intellectual and technical innovation in the field

Beyond number sense: Contributions of domain-general processes to the development of numeracy in early childhood

A large proportion of recent research on the development of numerical cognition has focused on the foundational role of approximate number sense, yet number sense alone cannot fully explain how young children acquire numeracy skills. This thesis aims to investigate how other domain-specific processes and domain-general cognitive processes relate to numeracy in early childhood and whether they play a role in learning about mathematics. The experiments presented in Chapter 2 explored how domain-general processes relate to young children’s attention to discrete number in non-symbolic representations through a correlational approach. Results supported the role for inhibitory control in selecting numerosity as the relevant stimulus dimension. In order to investigate causal relationships in emerging maths performance, Chapter 3 reports a cognitive training study aimed at contrasting transfer effects of domain-general and domain-specific training in pre- schoolers. Findings suggested caution in interpreting published transfer effects without the highest level of control. The latter chapters targeted learning mechanisms by tackling a specific process in mathematical cognition: acquiring the meaning of numerical symbols. Specifically, the experiments presented in Chapter 4 employed an artificial learning paradigm to test factors influencing adults' and children’s formation of novel symbolic numerical representations. Congruency between discrete and continuous non-symbolic quantity influenced novel representations and numerical order information facilitated learning, especially in children. In order to explore symbolic representations of real numbers, Chapter 5 focuses on associations between different representational formats of real numbers in young children and how this relates to both domain-specific and domain-general factors. Children had stronger mappings between symbols and precise non-symbolic representations for numbers smaller than four, than between larger numbers and approximate non-symbolic representations. Taken together, results from the experiments presented in this thesis highlight the need to incorporate factors beyond number sense in theories of numeracy development.</p

What is the precise role of cognitive control in the development of a sense of number?

The theory put forward by Leibovich et al. of how children acquire a sense of number does not specify the mechanisms through which cognitive control plays a role in this process. We argue that visual attention and number word knowledge influence each other over development and contribute to the development of the concept of number