Arithmetic facts storage deficit : the hypersensitivity-to-interference in memory hypothesis

While different profiles of dyscalculia are suggested, the difficulty to memorize arithmetic facts (use a retrieval strategy) is a general and persistent hallmark of this math learning disability. The studies reported in this thesis aim to explore the typical and atypical development of the arithmetic facts network. The theoretical introduction starts with a review of the literature about the acquired arithmetic facts network, its characteristics and its sensitivity to certain factors. The second section reports the major theoretical advances about the developmental arithmetic facts deficit. The last section depicts memory models forming the theoretical basis of the theory developed in the experimental part of this manuscript. In the second chapter, we present a case study of an adult woman (DB) with very good cognitive capacities suffering from a specific and developmental arithmetic fact retrieval deficit. We showed that DB suffered from heightened sensitivity to interference that prevented her from memorizing arithmetic facts. We suggested that the high features overlap between arithmetic facts may provoke interference and that consequently, learners who are hypersensitive-to-interference have considerable difficulties in storing arithmetic facts. In the third chapter, we tested this new hypothesis on fourth-grade children who are learning multiplication tables. The results show that children with low arithmetic fluencies experience hypersensitivity-to-interference in memory compared with children with typical arithmetic fluencies. The fourth chapter aims to link features of mathematical difficulties to certain potential etiologies. First, we wanted to test the hypothesis of a serial-order learning deficit in adults with dyscalculia. Second, we wanted to test the hypersensitivity-to-interference hypothesis and explore whether it leads to a particular profile of dyscalculia (De Visscher & Noël, 2013; in press). We observed that people with dyscalculia who show good conceptual knowledge in mathematics but impaired arithmetic fluency suffer from increased sensitivity-to-interference compared with controls. Secondly, people with dyscalculia who show a deficit in a global mathematical test suffer from a serial-order learning deficit characterized by a quick degradation of the sequence’s memory trace. In the last chapter, based on the features-overlap forgetting theory of Oberauer and Lange (2008), we created a measure of the interference weight of each multiplication according to the usual learning order. This interference parameter was used to test two main questions on the case study DB, on third-, fourth-, fifth-grade children and on adults. The first question asks whether the interference parameter can predict the performance across multiplication problems, beyond the problem-size. The second question concerns the individual differences in multiplication performance. Results showed that the interference parameter predicts a substantial part of the performance (mostly speed) across multiplications. Moreover, the individual sensitivity to the interference parameter determines a part of the inter-individual differences in multiplication performance and is significantly larger in the patient DB than in controls or in children with poor arithmetic facts fluency than in controls. Furthermore, we showed that the sensitivity to the interference parameter is linked to a general sensitivity to interference, but not to inhibition of proponent response or general verbal memory capacities. Studies collected in this thesis bring evidence of the influence of similarity-based interference in arithmetic facts learning. First, the performance across arithmetic facts is shown to depend on the feature-overlap across problems, indicating that the feature-overlap makes the arithmetic facts learning an interference-prone situation. Second, we show that people who are sensitive to interference encounter difficulties in arithmetic facts learning. More precisely, we demonstrate that the interference coming from the arithmetic problems will hamper people who are sensitive to interference to store the arithmetic facts in memory, and then hinder them from using a retrieval strategy.