The difficulty in memorizing arithmetic facts is a general and persistent hallmark of math learning disabilities. It has recently been suggested that hypersensitivity to interference could prevent a person from storing arithmetic facts. The similarity between arithmetic facts would provoke interference, and learners who are hypersensitive to interference would therefore encounter difficulties in storing arithmetic facts in long-term memory. In this study, we created a measure of the interference weight for each multiplication by measuring the overlap of digits between multiplications. First, we tested whether the interference parameter could predict performance across multiplications by analyzing the data from undergraduates published by Campbell (1997). The interference parameter substantially predicted performance across multiplications. Similarly, the performance across multiplications was substantially determined by the interference parameter in 3rd-grade children, 5th-grade children, and undergraduates we tested. Second, we tested whether people with poor arithmetic facts abilities were particularly sensitive to the interference parameter. We tested this hypothesis in typical development by analyzing the data from the 3rd-grade children, 5th-grade children, and undergraduates. We analyzed data with regard to atypical development from a published case study of dyscalculia as well as from 4th-grade children, with either poor or good multiplication skills, tested twice 1 year apart. Results showed that the individual sensitivity to the interference parameter determined part of the individual differences in multiplication performance in all data sets. These findings show that the learning of multiplications is particularly interference prone because of feature overlap and that people who are sensitive to this parameter therefore encounter difficulties in memorizing arithmetic facts.

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Dyscalculia, or mathematics learning disorders, is currently known to be heterogeneous (Wilson & Dehaene, ). While various profiles of dyscalculia coexist, a general and persistent hallmark of this math learning disability is the difficulty in memorizing arithmetic facts (Geary, Hoard & Hamson, ; Jordan & Montani, ; Slade & Russel, ). Arithmetic facts are simple arithmetic problems that are solved by direct retrieval from memory. Recently, De Visscher and Noël () showed hypersensitivity-to-interference in memory in an adult suffering from a specific deficit of arithmetic facts storage. According to the authors, arithmetic facts share many features. The overlapping of these features between arithmetic facts may provoke interference. Consequently, learners who are hypersensitive-to-interference could have considerable difficulties in storing arithmetic facts. The present study aims at testing this new hypothesis on fourth-grade children who are learning multiplication tables. Among 101 children that were assessed, 23 low arithmetic facts learners were selected because of their low score in arithmetic facts fluency (controlling for processing speed). Twenty-three control children were selected, matched for classroom, gender, and age. In addition to a subtest of global reasoning, these participants were given a multiplication production task and a memorization task of low- and high-interference associations. The results show that children with low arithmetic fluencies experience hypersensitivity-to-interference in memory compared with children with typical arithmetic fluencies.

Some multiplication facts share common digits with other, previously learned facts, and as a result, different problems are associated with different levels of interference. The detrimental effect of interference in arithmetic facts knowledge has been recently highlighted in behavioral studies, in children as well as in adults, both in typical and atypical development. The present study investigated the brain regions involved in the interference effect when solving multiplication problems. Twenty healthy adults carried out a multiplication task in an MRI scanner. The event-related design comprised problems whose interference level and problem size were manipulated in a 2×2 factorial design. After each trial, individuals were requested to indicate whether they solved the trial by retrieving the answer from long-term memory. This allowed us to examine which brain areas were sensitive to the interference effect and problem size effect as well as the retrieval strategy. The results highlighted two specific regions: the left angular gyrus was more activated for low interfering than for high interfering problems, and the right intraparietal sulcus was more activated for large problems than for small problems. In both regions, brain activity was not modulated by the other effect. These results suggest that the left angular gyrus is sensitive to the level of interference of the multiplication problems, whereas previously this region was thought to be more activated by small problems or by retrieval strategy. Here, in a design manipulating interference and problem size, while controlling for retrieval strategy, we showed that it rather reflects an automatic mapping between the problem and the answer stored in long-term memory. The right intraparietal sulcus was modulated by the problem size effect, which supports the idea that the problem size effect comes from the higher overlap between magnitude of the answers of large problems compared to small ones. Importantly, neither effects can be reduced to a strategy effect since they were present when analyzing only retrieval trials.