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1. Schneider, R.M., & Barner, D. (2020). Children use one-to-one correspondence to establish equality after learning to count. 42nd Annual Meeting of the Cognitive Science Society.

   Schneider, R.M. (January 2020, 42nd Annual Meeting of the Cognitive Science Society.)

   null (Ed.)

   Humans make frequent and powerful use of external symbols to express number exactly, leading some to question whether exact number concepts are only available through the acquisition of symbolic number systems. Although prior work has addressed this longstanding debate on the relationship between language and thought in innumerate populations and seminumerate children, it has frequently produced conflicting results, leaving the origin of exact number concepts unclear. Here, we return to this question by replicating methods previously used to assess exact number knowledge in innumerate groups, such as the Piraha, with a large sample of semi- numerate US toddlers. We replicate previous findings from both innumerate cultures and developmental studies showing that numeracy is linked to the concept of exact number. However, we also find evidence that this knowledge is surprisingly fragile even amongst numerate children, suggesting that numeracy alone does not guarantee a full understanding of exactness. 

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2. Counting and the ontogenetic origins of exact equality

   https://doi.org/10.1016/j.cognition.2021.104952  

   Schneider, R. M. (January 2022, Cognition)

   Humans are unique in their capacity to both represent number exactly and to express these representations symbolically. This correlation has prompted debate regarding whether symbolic number systems are necessary to represent large exact number. Previous work addressing this question in innumerate adults and semi-numerate children has been limited by conflicting results and differing methodologies, and has not yielded a clear answer. We address this debate by adapting methods used with innumerate populations (a “set-matching” task) for 3- to 5-year-old US children at varying stages of symbolic number acquisition. In five studies we find that children’s ability to match sets exactly is related not simply to knowing the meanings of a few number words, but also to understanding how counting is used to generate sets (i.e., the cardinal principle). However, while children were more likely to match sets after acquiring the cardinal principle, they nevertheless demonstrated failures, compatible with the hypothesis that the ability to reason about exact equality emerges sometime later. These findings provide important data on the origin of exact number concepts, and point to knowledge of a counting system, rather than number language in general, as a key ingredient in the ability to reason about large exact number. 

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3. The causal impact of objective numeracy on judgments: Improving numeracy via symbolic and non-symbolic approximate arithmetic training yields more consistent risk judgments

   https://doi.org/10.5964/jnc.6925  

   Chesney, Dana L.; Shoots-Reinhard, Brittany; Peters, Ellen (January 2021, Journal of Numerical Cognition)

   Park and Brannon (2013, https://doi.org/10.1177/0956797613482944) found that practicing non-symbolic approximate arithmetic increased performance on an objective numeracy task, specifically symbolic arithmetic. Manipulating objective numeracy would be useful for many researchers, particularly those who wish to investigate causal effects of objective numeracy on performance. Objective numeracy has been linked to performance in multiple areas, such as judgment-and-decision-making (JDM) competence, but most existing studies are correlational. Here, we expanded upon Park and Brannon’s method to experimentally manipulate objective numeracy and we investigated whether numeracy’s link with JDM performance was causal. Experimental participants drawn from a diverse internet sample trained on approximate-arithmetic tasks whereas active control participants trained on a spatial working-memory task. Numeracy training followed a 2 × 2 design: Experimental participants quickly estimated the sum of OR difference between presented numeric stimuli, using symbolic numbers (i.e., Arabic numbers) OR non-symbolic numeric stimuli (i.e., dot arrays). We partially replicated Park and Brannon’s findings: The numeracy training improved objective-numeracy performance more than control training, but this improvement was evidenced by performance on the Objective Numeracy Scale, not the symbolic arithmetic task. Subsequently, we found that experimental participants also perceived risks more consistently than active control participants, and this risk-consistency benefit was mediated by objective numeracy. These results provide the first known experimental evidence of a causal link between objective numeracy and the consistency of risk judgments. 

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4. Money matters (especially if you are good at math): Numeracy, verbal intelligence, education, and income in satisfaction judgments

   https://doi.org/10.1371/journal.pone.0259331  

   Bjälkebring, Pär; Peters, Ellen (November 2021, PLOS ONE)

   Luciano, Michelle (Ed.)

   Objective numeracy, the ability to understand and use mathematical concepts, has been related to superior decisions and life outcomes. Unknown is whether it relates to greater satisfaction in life. We investigated numeracy’s relations with income satisfaction and overall life satisfaction in a diverse sample of 5,525 American adults. First, more numerate individuals had higher incomes; for every one point higher on the eight-item numeracy test, individuals reported $4,062 more in annual income, controlling for education and verbal intelligence. Combined, numeracy, education, and verbal intelligence explained 25% of the variance in income while Big-5 personality traits explained less than 4%. Further, the higher incomes associated with greater numeracy were related to more positive life evaluations (income and life satisfaction). Second, extant research also has indicated that the highly numerate compare numbers more than the less numerate. Consistent with numeracy-related income comparisons, numeracy moderated the relation between income and life evaluations, meaning that the same income was valued differently by those better and worse at math. Specifically, among those with lower incomes, the highly numerate were less satisfied than the less numerate; this effect reversed among those with higher incomes as if the highly numerate were aware of and made comparisons to others’ incomes. Further, no clear income satiation point was seen among those highest in numeracy, and satiation among the least numerate appeared to occur at a point below $50,000. Third, both education and verbal intelligence related to income evaluations in similar ways, and numeracy’s relations held when controlling for these other relations. Although causal claims cannot be made from cross-sectional data, these novel results indicate that numeracy may be an important factor underlying life evaluations and especially for evaluations concerning numbers such as incomes. Finally, this study adds to our understanding of education and intelligence effects in life satisfaction and happiness. 

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5. Unique and combined effects of quantitative mathematical language and numeracy instruction within a picture book intervention: A registered report.

   https://doi.org/10.1037/edu0000820  

   Purpura, David J; O'Rear, Connor D; Ellis, Alexa; Logan, Jessica_A R; Westerberg, Lauren; Ehrman, Patrick; King, Yemimah A; Vander_Tuin, Mackenna; Nordgren, Inga; Anderson, Kirsten; et al (January 2024, Journal of Educational Psychology)

   Children’s early understanding of mathematics provides a foundation for later success in school. Identifying ways to enhance mathematical instruction is crucial to understanding the ideal ways to promote academic success. Previous work has identified mathematical language (i.e., the words and concepts related to early mathematical development such as more, same, or similar) as a key mechanism that can be targeted to improve children’s development of early numeracy skills (e.g., counting, cardinality, and addition). Current recommendations suggest a combination of numeracy instruction and quantitative language instruction to promote numeracy skills. However, there is limited direct support of this recommendation. The goal of the proposed study is to compare the unique and combined effects of each type of instruction on children’s numeracy skills in the context of picture book reading. We randomly assigned 234 children (ages 3–5) to one of four conditions where they worked with trained project staff who read picture books targeting: (a) quantitative language only (e.g., more or less), (b) numeracy only (e.g., cardinality, addition), (c) combined [quantitative language + numeracy], or (d) nonnumerical (active control) picture books. Results revealed no significant effects of the quantitative language only or numeracy only conditions, but mixed effects of the combined condition. These findings indicate that more work is needed on how mathematical language and numeracy instruction should best be delivered to preschool children. 

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