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We investigate number and arithmetic learning among a Bolivian indigenous people, the Tsimane', for whom formal schooling is comparatively recent in history and variable in both extent and consistency. We first present a large-scale meta-analysis on child number development involving over 800 Tsimane' children. The results emphasize the impact of formal schooling: Children are only found to be full counters when they have attended school, suggesting the importance of cultural support for early mathematics. We then test especially remote Tsimane' communities and document the development of specialized arithmetical knowledge in the absence of direct formal education. Specifically, we describe individuals who succeed on arithmetic problems involving the number five-which has a distinct role in the local economy-even though they do not succeed on some lower numbers. Some of these participants can perform multiplication with fives at greater accuracy than addition by one. These results highlight the importance of cultural factors in early mathematics and suggest that psychological theories of number where quantities are derived from lower numbers via repeated addition (e.g., a successor function) are unlikely to explain the diversity of human mathematical ability.

The scope of human learning and development poses a radical challenge for cognitive science. We propose that developmental theories can address this challenge by adopting perspectives from computer science. Many of our best models treat learning as analogous to computer programming because symbolic programs provide the most compelling account of sophisticated mental representations. We specifically propose that children's learning is analogous to a particular style of programming called hacking, making code better along many dimensions through an open-ended set of goals and activities. By contrast to existing theories, which depend primarily on local search and simple metrics, this view highlights the many features of good mental representations and the multiple complementary processes children use to create them., (Copyright © 2020 The Authors. Published by Elsevier Ltd.. All rights reserved.)

Background: Seasons affect many social, economic, and biological outcomes, particularly in low-resource settings, and some studies suggest that birth season affects child growth., Aim: To study a predictor of stunting that has received limited attention: birth season., Subjects and Methods: This study uses cross-sectional data collected during 2008 in a low-resource society of horticulturists-foragers in the Bolivian Amazon, Tsimane'. It estimates the associations between birth months and height-for-age Z-scores (HAZ) for 562 girls and 546 boys separately, from birth until age 11 years or pre-puberty, which in this society occurs ∼13-14 years., Results: Children born during the rainy season (February-May) were shorter, while children born during the end of the dry season and the start of the rainy season (August-November) were taller, both compared with their age-sex peers born during the rest of the year. The correlations of birth season with HAZ were stronger for boys than for girls. Controlling for birth season, there is some evidence of eventual partial catch-up growth, with the HAZ of girls or boys worsening until ∼ age 4-5 years, but improving thereafter. By age 6 years, many girls and boys had ceased to be stunted, irrespective of birth season., Conclusion: The results suggest that redressing stunting will require attention to conditions in utero, infancy and late childhood.

Objectives: We assessed associations between child stunting, recovery, and faltering with schooling and human capital skills in a native Amazonian society of horticulturalists-foragers (Tsimane')., Methods: We used cross-sectional data (2008) from 1262 children aged 6 to 16 years in 53 villages to assess contemporaneous associations between three height categories: stunted (height-for-age Z score, HAZ<-2), moderately stunted (-2 ≤ HAZ≤-1), and nonstunted (HAZ>-1), and three categories of human capital: completed grades of schooling, test-based academic skills (math, reading, writing), and local plant knowledge. We used annual longitudinal data (2002-2010) from all children (n = 853) in 13 villages to estimate the association between changes in height categories between the first and last years of measure and schooling and academic skills., Results: Stunting was associated with 0.4 fewer completed grades of schooling (∼24% less) and with 13-15% lower probability of showing any writing or math skills. Moderate stunting was associated with ∼20% lower scores in local plant knowledge and 9% lower probability of showing writing skills, but was not associated with schooling or math and writing skills. Compared with nonstunted children, children who became stunted had 18-21% and 15-21% lower probabilities of showing math and writing skills, and stunted children had 0.4 fewer completed grades of schooling. Stunted children who recovered showed human capital outcomes that were indistinguishable from nonstunted children., Conclusions: The results confirm adverse associations between child stunting and human capital skills. Predictors of growth recovery and faltering can affect human capital outcomes, even in a remote, economically self-sufficient society., (© 2017 Wiley Periodicals, Inc.)

Human infants, like immature members of any species, must be highly selective in sampling information from their environment to learn efficiently. Failure to be selective would waste precious computational resources on material that is already known (too simple) or unknowable (too complex). In two experiments with 7- and 8-month-olds, we measure infants' visual attention to sequences of events varying in complexity, as determined by an ideal learner model. Infants' probability of looking away was greatest on stimulus items whose complexity (negative log probability) according to the model was either very low or very high. These results suggest a principle of infant attention that may have broad applicability: infants implicitly seek to maintain intermediate rates of information absorption and avoid wasting cognitive resources on overly simple or overly complex events.

The study of how children learn numbers has yielded one of the most productive research programs in cognitive development, spanning empirical and computational methods, as well as nativist and empiricist philosophies. This paper provides a tutorial on how to think computationally about learning models in a domain like number, where learners take finite data and go far beyond what they directly observe or perceive. To illustrate, this paper then outlines a model which acquires a counting procedure using observations of sets and words, extending the proposal of Piantadosi et al. (2012). This new version of the model responds to several critiques of the original work and outlines an approach which is likely appropriate for acquiring further aspects of mathematics.

We show that children in the Tsimane', a farming-foraging group in the Bolivian rain-forest, learn number words along a similar developmental trajectory to children from industrialized countries. Tsimane' children successively acquire the first three or four number words before fully learning how counting works. However, their learning is substantially delayed relative to children from the United States, Russia, and Japan. The presence of a similar developmental trajectory likely indicates that the incremental stages of numerical knowledge--but not their timing--reflect a fundamental property of number concept acquisition which is relatively independent of language, culture, age, and early education.