Sources of Mathematical Thinking

拟议的项目继续目前的工作，以检查非人类灵长类动物，儿童和成人，并调查数学思维的基础。过去的研究集中在识别数学思维所基于的三个“积木系统”上：“精确小数系统”、“近似大数系统”以及自然语言的量化和计数功能。拟议的研究继续通过各种灵长类动物和发育研究技术（例如，研究灵长类动物或婴儿可以通过注意力、凝视等方式辨别哪些刺激）。拟议的研究是一个强大的四股研究计划，调查这些基础系统中的每一个：（1）猴子的数字表征，（2）学龄前儿童的数字表征（例如，研究学习第一个数字单词），（3）成年人的数字表征（使用心理加法，乘法等来研究近似大数和精确小数系统的能力，而无需符号操作），以及（4）儿童学习正式数学时语言系统和数字系统之间的映射。这些研究设计得很好，令人兴奋，试图将灵长类动物和发育研究结合起来，构建数学推理所基于的基础系统模型。拟议活动的广泛影响是什么？总的来说，这些研究有可能为数学思维的基础理论做出重要贡献。在过去的工作中，灵长类动物，婴儿和学龄前儿童的发展研究之间的协同作用已经被利用，以促进对数学思维所建立的基本认知机制的理解。研究的第四条链试图将其与教育联系起来，研究学校教授的正式符号数学如何将这些研究中的三个系统结合在一起。

The proposed project continues current work to examine non-human primates, children, and adults and investigate the foundations of mathematical thinking. Past research has converged on the identification of three 'building-block systems' on which mathematical thinking is based: 'exact small number system,' 'approximate large number system,' and the quantification and counting functions of natural language. The proposed studies continue to investigate these three systems in non-human primates, children, and adults through a variety of primate and developmental research techniques (e.g., studies that investigate what stimuli primates or infants can discriminate through measures of attention, gaze, and so on.). The proposed research is a strong program of four strands of research that investigate each of these foundational systems: (1) number representation in monkeys, (2) number representation in preschool children (e.g., examining learning first number words), (3) number representation in adult humans (using mental addition, multiplication etc. to examine the capabilities of the approximate large number and exact small number systems without symbolic manipulation), and (4) mapping between linguistic and number systems in children learning formal mathematics. The studies are well designed and exciting in the attempt to pull together primate and developmental research to construct a model of the foundational systems on which mathematical reasoning is based.What are the broader impacts of the proposed activity?In general, the studies have the potential to provide important contributions to the foundational theories that underlie mathematical thinking. The synergy between the primate, infant, and preschool developmental research has been exploited in past work to advance the state of understanding of the basic cognitive mechanisms on which mathematical thinking is built. The fourth strand of research attempts to make the connection to education, looking at how the formal symbolic mathematics taught in school brings together the three systems in these studies.