Determining the foundational properties of numerical development

该项目由罗切斯特大学的一组研究人员领导，旨在回答有关数字学习基础认知能力的重要问题。研究小组将通过研究提斯曼人（Tsimane'）的数学学习能力来检验主流理论所假定的普遍能力。提斯曼人是一个独特的农业-觅食人群。他们接受正规教育的极端差异将为研究人员提供一个评估教育、年龄、成熟度和核心认知系统在推动早期数学发展中的作用的机会。该项目将涉及多种方法，从Tsimane生活中数字使用的民族志研究，到基本认知资源（如工作记忆）的评估，再到数学知识的测试。该团队将对美国2至12岁儿童的匹配样本进行研究，这些儿童在贫困的学习环境中长大。目标是确定数字能力的哪些认知成分应该成为未来干预的目标，以改善生活在贫困中或面临学习迟缓的美国儿童的学习。该项目由EHR核心研究（ECR）项目资助，该项目支持推进STEM学习基础研究文献的工作。许多能力与计算能力和数字感有关，包括集合知识、数字单词、计数、1-1对应、空间关系和近似数字估计。然而，目前尚不清楚这些能力中哪些是早期数量增长的基础，哪些是数量获取或其他文化因素的结果。该提案将寻求发现土著居民Tsimane对数字的认知基础。这一人口的关键科学相关特征是其正规教育体系的极端差异——有些孩子没有接受过正规教育——并且他们在漫长的时间尺度上通过数字学习阶段的进步，花费的时间是该地区其他儿童和美国儿童的3-4倍。其他孩子则接受了更长时间的正规教育。在这一群体中，教育程度、年龄和父母计算能力的高度可变性将使许多与数量增长相关的因素在不同寻常的程度上作为因果因素被解开。研究小组将使用人类学的方法来记录数字的文化背景和使用，以便了解哪些做法有助于数字的获取，并预测儿童的知识。他们还将使用一系列从数学教育和认知科学文献中提取的简单实验任务来评估数字的发展，并详细绘制Tsimane数字学习的轨迹。我们的目标是开发一个统一的数字学习计算模型，该模型可以快速用于预测哪些未来的干预措施将最有希望帮助改善美国儿童的学习，特别是那些生活在不利学习环境中的儿童。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

Award AbstractThe goal of this project, led by a team of researchers at the University of Rochester, is to answer important questions about fundamental cognitive capacities underlying number learning. The team will examine abilities assumed by prevailing theories to be universal by studying mathematical learning in the Tsimane', a unique population of farming-foragers. The extreme variability in their exposure to formal education will provide the researchers with an opportunity to evaluate the roles of education, age, maturity, and core cognitive systems in driving early mathematical development. The project will involve multiple methodologies from ethnographic studies of number use in Tsimane' life, to assessments of basic cognitive resources such as working memory, to tests of mathematical knowledge. The team will conduct studies of matched samples of children from 2 to 12 years of age in the US who grow up in impoverished learning environments. The goal is to identify which cognitive components of number competence ought to be targeted by future interventions so as to improve learning in US children living in poverty or who face learning delays. The project is funded by the EHR Core Research (ECR) program, which supports work that advances the fundamental research literature on STEM learning. Many abilities are related to numeracy and number sense, including knowledge of sets, the number words, counting, 1-1 correspondence, spatial relations, and approximate number estimation. Yet, it is not known which of these capacities are the foundations of early number growth and which are the consequence of number acquisition or other cultural factors. This proposal will seek to discover the cognitive underpinnings of number in an indigenous population, the Tsimane'. The key scientifically-relevant features of this population are the extreme variability in their formal educational system -- some children receive no formal education -- and that they progress through the stages of number learning at a protracted timescale, taking 3-4 times as long other children in the locale and children in the United States. Other children have longer, formal education. The high variability in education, age, and parental numeracy in this population will allow many of the components related to number growth to be disentangled as causal factors to an unusual extent. The team will use anthropological methods to document the cultural context and use of number in order to understand what practices support its acquisition and predict children's knowledge. They will also use a series of simple experimental tasks drawn from the mathematics education and cognitive science literatures to assess numerical development and chart the trajectory of Tsimane' number learning in detail. The goal is to develop a unifying computational model of number learning that can be used rapidly to predict which future interventions will be most promising in helping to improve learning in US children, especially those living in disadvantaged learning environments.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.