Numerical Cognition

计数、算术、百分比、概率：人们使用象征性的数字，也就是像35这样的数字和像17这样的数字词，来记录和传达关于数量的信息。在数学任务中使用数字的能力是计算机技术、货币系统、工程和医学科学许多方面的基础。我的研究重点是人们在相对简单的数字任务中思考和使用符号数字的方式，例如，当他们解决算术问题时（例如，3 + 4，5 x 8）或估计数额（例如，45 x 96接近4500？）。特别是，我将研究人们在解决数字问题时如何做出战略决策，例如，他们如何在估计任务中简化数字，或将数字放在不寻常的数字线上（例如，如果数字线从0到7000，3421会在哪里？）。这些类型的数字任务的表现，甚至更简单的任务，如快速决定数字3 5 4是否按顺序排列，与成年人在更复杂的数学任务中的表现密切相关。这些相互联系支持了这样一种观点，即大脑中的符号数字处理是数学理解和应用的核心。在这个建议中，我已经制定了一个模型，人们处理数字任务的方式，并概述了一系列实验来测试和改进模型。我也将探讨认知能力的作用，如工作记忆和空间技能的数字性能。我的目标是使用该模型来帮助我们理解符号数字在日常任务中的作用。这项研究的结果将有助于教育工作者和家长对儿童的数字经验和训练的决定。虽然每个人都对数量有基本的理解，但不同的人学习使用数字符号的难易程度有很大的差异。了解人们如何表示和使用数字可以确保每个人都有足够的数字知识，以便在个人和职业生活中取得成功。

Counting, arithmetic, percentage, probabilities: People use symbolic numbers, that is, digits such as 35 and number words such as seventeen, to record and communicate information about quantity. The ability to use numbers in mathematical tasks underlies computer technologies, monetary systems, engineering, and many aspects of medical science. My research is focused on the ways in which people think about and use symbolic numbers in relatively simple number tasks, for example, when they solve arithmetic problems (e.g., 3 + 4, 5 x 8) or estimate amounts (e.g., is 45 x 96 close to 4500?). In particular, I will study how people make strategic decisions when they are solving numerical problems, for example, how they simplify numbers in estimation tasks, or place numbers on unusual number lines (e.g., if the number line goes from 0 – 7000, where would 3421 be located?). Performance on these types of number tasks, and even simpler ones, such as deciding quickly if the numbers 3 5 4 are in order, are closely related to adults’ performance on more complex mathematical tasks. These interconnections support the view that symbolic number processing in the brain is central to mathematical understanding and applications. In this proposal, I have formulated a model of the ways in which people approach numerical tasks and outlined a series of experiments to test and improve the model. I will also explore the role of cognitive abilities such as working memory and spatial skill in numerical performance. My objectives are to use the model to contribute to our understanding of the role of symbolic numbers in everyday tasks. The results of this research will help educators and parents make decisions about children’s numerical experience and training. Although everyone has a fundamental understanding of quantities, the ease with which different people learn to use number symbols varies substantially. Understanding how people represent and use numbers can ensure that everyone has sufficient number knowledge for success in their personal and professional lives.