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

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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.