Mechanisms Underlying Numerical and Mathematical Cognition

随着世界经济越来越依赖于科技创新，了解影响科学、技术、工程和数学（STEM）领域成功的因素变得越来越重要。熟练掌握空间处理和数值/数学处理是STEM的重要组成部分，在空间任务中表现较好的人也具有较高的数学能力（例如，Lubinski & Benbow, 1992）。然而，尽管对这一联系进行了深入的调查，但并没有很好地解释它（Mix & Cheng, 2012）。毫无疑问，空间处理与数学有很多联系。在本提案中，我提出了一个新的理论，解释了为什么空间处理与数值处理相关的一个组成部分，更具体地说，空间处理涉及哪些元素。利用这一理论框架，我推导并验证了具体的预测。******在这项拟议的研究中发展和测试的理论的核心是，数字是沿着内部心理数轴表示的，左边是小数，右边是大数（例如，Dehaene, 2011）。这里采用的理论框架将心理数轴视为任务的函数，并保存在工作记忆（WM）中，其中人们系统地将数字映射到WM中保存的内部心理数轴上（Van Dijck & Fias, 2011）。重要的是，一个人的数轴越精确，他们的数学能力就越高（Holloway & Ansari, 2009; Siegler & Ramani, 2009）。提出的研究考察了这种映射过程至少部分地负责观察到的空间处理和数值处理之间的关系的新观点，认为空间资源参与了心理数轴的创建（例如，Gunderson, Ramirez, Beilock, & Levine, 2012）。******本提案中的研究旨在检查空间处理在需要和不需要数值量级比较的数值和数学任务中的作用，测试空间处理涉及线性表征的生成这一假设，并研究不同类型空间能力的个体差异与在需要和不需要数值量级比较的数值和数学任务中的表现之间的关系。这项工作不仅有可能深入了解数字和数学认知的基本认知机制，而且还可以为基于空间处理的干预提供信息，旨在提高数学成绩，增加有资格进入STEM职业并取得成功的候选人数量。*****

As world economies are becoming increasingly more reliant on scientific and technological innovation, understanding the factors that influence success in science, technology, engineering, and mathematics (STEM) fields is becoming increasingly more important. Proficiency in spatial processing and numerical/mathematical processing are important components of STEM and people who perform better on spatial tasks also have higher mathematical ability (e.g., Lubinski & Benbow, 1992). However, despite the thorough investigation of this link, there are not well-articulated explanations for it (Mix & Cheng, 2012). There are undoubtedly many ways that spatial processing can be related to mathematics. In this proposal, I present a novel theory explaining one component of why spatial processing is related to numerical processing and, more specifically, which elements of spatial processing are involved. Using this theoretical framework, I derive and test specific predictions.****** Central to the theory developed and tested within this proposed research is the idea that numbers are represented along an internal mental number line with small numbers on the left and large numbers on the right (e.g., Dehaene, 2011). The theoretical framework adopted here views the mental number line as being constructed as a function of the task and held in working memory (WM) wherein people systematically map the numbers onto an internal mental number line that is held in WM (Van Dijck & Fias, 2011). Importantly, the more precise one's number lines are, the higher their mathematical ability tends to be (Holloway & Ansari, 2009; Siegler & Ramani, 2009). The proposed research examines the novel idea that this mapping process is, at least partially, responsible for the observed relation between spatial processing and numerical processing, arguing that spatial resources are engaged in the creation of the mental number line (e.g., Gunderson, Ramirez, Beilock, & Levine, 2012).****** The research within this proposal serves to examine the role of spatial processing in numerical and mathematical tasks that do and do not require comparisons of numerical magnitude, test the hypothesis that spatial processing is involved in the generation of a linear representation onto which constructs are mapped and examine how individual differences in various types of spatial abilities relate to performance on numerical and mathematical tasks that do and do not require the comparisons of numerical magnitude. This work has the potential to not only garner insights into the basic cognitive mechanisms underlying numerical and mathematical cognition, but also to inform spatial-processing-based interventions aimed at improving achievement in mathematics and increasing the number of candidates qualified to enter and succeed in STEM careers.*****