On the structure of arithmetic facts in memory and its interaction with numerical magnitude representation

虽然基本的数学概念（如乘法）是当代技术社会的基本要求，但大约5%的人口在获得数学技能方面存在困难。这突出了研究认知机制的重要性，这些机制允许发展和理解数学知识。该项目旨在加强对数学认知的核心组成部分之一的理解，即支持简单乘法问题存储的记忆系统（例如，4×3），以及它与数值量级表示的相互作用。数学技能和概念被认为植根于近似数字系统（ANS），这是数值量的模拟大小表示，被概念化为空间导向的心理数轴。然而，目前尚不清楚ANS如何以及在多大程度上影响与算术事实记忆相关的过程。本项目旨在研究(1)算术事实存储器的内部结构和(2)它与ANS的功能关系。为此，我们将测试描述该存储器系统架构的两个并发模型的预测。首先，申请人提出的非对称干扰模型假设算术事实在语义网络架构中表示（关于类似的概念，请参阅Campbell， 1995）。该网络中条目的检索受到ANS及其压缩度量的影响（即，两个相邻数字的表示之间的重叠随着数字的大小增加而增加）。其次，交互邻居模型（Verguts & Fias, 2005）假设算术事实记忆的结构是由文化决定的数字语法特征塑造的。也就是说，在这个存储系统中，问题的结果以组件方式表示，遵循以10为基数系统的语法（例如，数字21表示20年和1个单位）。因此，该模型假定算术事实存储器的内部结构是(a)根据这种（任意的）符号语法组织的，(b)检索不受问题组成部分的语义内容的影响。在一组4个行为和1个脑电图实验中，我们将通过测试这两个模型对行为表现和与乘法问题相关的电生理相关（即事件相关电位）的预测来评估这两个模型的假设。该项目提供的结果将有助于更精确地理解算术事实检索过程，并更准确地描述该记忆系统的内部结构。

Although basic mathematical concepts (e.g., multiplication) are a fundamental requirement in contemporary technological societies, approximately 5% of the population are affected by difficulties in the acquisition of mathematical skills. This highlights the importance of investigating the cognitive mechanisms that allow to develop and understand mathematical knowledge. This project aims at enhancing the comprehension of one of the core components of mathematical cognition, that is the memory system that underpins the storage of simple multiplication problems (e.g., 4×3), and its interaction with the numerical magnitude representation.Mathematical skills and concepts are thought to be rooted in the approximate number system (ANS), that is an analogue magnitude representation of numerical quantities, conceptualized as a spatially oriented mental number line. However, it still remains unclear how and to what extent the ANS actually affects the processes associated with the arithmetic facts memory. This project aims at investigating (1) the internal structure of the arithmetic facts memory and (2) its functional relationship with the ANS. To this end, we will test the predictions of two concurrent models describing the architecture of this memory system. First, the Asymmetric Interference Model, proposed by the applicants, assumes that arithmetic facts are represented in a semantic network architecture (for a similar notion see Campbell, 1995). The retrieval of entries within this network is affected by the ANS and its compressed metric (i.e., the overlap between the representations of two adjacent numbers increases as the magnitude of the numbers increases). Second, the Interacting Neighbors Model (Verguts & Fias, 2005) assumes that the structure of arithmetic facts memory is shaped by the features of the culturally determined number syntax. Namely, within this memory system the result of a problem is represented in a componential fashion, following the syntax of the base-10 system (e.g., the number 21 means 2 decades and 1 unit). This model thus assumes that the internal structure of the arithmetic facts memory is (a) organized according to this (arbitrary) symbolic syntax and (b) retrieval is not affected by the semantic content of the constituents of the problem.In a set of 4 behavioral and 1 electroencephalography experiments, we will evaluate the assumptions of these two models by testing their predictions regarding the behavioral performance and the electrophysiological correlates (i.e., event-related potentials) associated with multiplication problem-solving. The results provided by this project will allow developing a more precise understanding of the processes involved in the retrieval of arithmetic facts and a more accurate description of the internal structure of this memory system.