Origins of Numerical Competence: Assessment of Number Sense in Piraha

该RAPID项目侧重于数字感觉的三个不同方面的“基础”研究：(1)小精确数系统；(2)大近似数系；(3)基于集合的量化系统。最近的探索性研究表明，数字感觉（特别是大型数值近似系统）与学生在其他数学领域的能力之间存在很强的联系。研究者将研究这三个方面之间的联系，研究的目的是进一步的初步发现（引用上文）。研究人员提出了一项相关研究，他们在一系列认知导向的任务中测试了巴西土著皮拉哈人（一个来自亚马逊地区的小的、孤立的、单语的狩猎采集群体）和美国人样本（每组60人），这些任务测量了不同的核心数字系统以及其他基本认知能力，如短期记忆和面部感知（作为控制任务）。皮拉哈人是理解核心数字系统之间关系的理想测试案例，因为他们的语言中没有数字单词。此外，皮拉哈人在他们的社会中不使用精确的数字，他们也不采用其他文化的文化或语言习俗。快速发展是合理的，因为他们的人口受到迫在眉睫的发展的威胁。这项研究很重要，因为对数字感的概念/认知成分及其相互关系的更深入了解可能会导致对学生如何学习和教师如何教授这一数学领域的理解发生变化。而且，由于数感是数学的基础，并且由于初步研究结果显示它对未来数学学习的潜在重要性，该项目可能会对该领域产生变革性影响。

This RAPID project focuses on "fundamental" research on three distinct aspects of number sense: (1) a small exact number system; (2) a large approximate number system; and (3) a system for set-based quantification. Recent exploratory research suggests a strong linkage between number sense (particularly large numerical approximation systems) and student abilities in other domains of mathematics. The investigators will research the links among these three aspects, and the study is designed to further the preliminary findings (cited above). The investigators propose a correlational study in which they test a population of the indigenous Piraha people of Brazil (a small, isolated, monolingual hunter-gatherer group from the Amazonas) and a sample of Americans (60 in each group) in a battery of cognitively-oriented tasks which measure different core numerical systems as well as other basic cognitive abilities like short-term memory and face perception (as control tasks). The Piraha are an ideal test case for understanding the relationship among core numerical systems because their language is has no words for numbers. In addition, the Piraha do not use exact number in their society and they do not adopt cultural or linguistic conventions from other cultures. A RAPID is justified because their population is threatened by imminent development. This research is important because a deeper understanding of the conceptual/cognitive components of number sense and how they interrelate can lead to perhaps changed understandings of how students learn and teachers teach this area of mathematics. And, because number sense is so foundational to mathematics and because preliminary research results show its potential importance to future mathematics learning, the project may have a transformative impact on the field.