Exploring the nature of proactive interference in an auditory multiplication task

Introduction Multiplication fact retrieval is commonly assumed to rely on verbal memory mechanisms. Beyond the classical problem-size effect, multiplication problems differ substantially in difficulty. A highly influential account proposed by De Visscher and Noël (2014) explains this variability in terms of proactive interference in long-term memory: multiplication facts sharing overlapping features compete during retrieval. For example, 3×4=12 may interfere with 4×6=24 because both facts share the digits 2 and 4. Inspired by classical models of long-term memory, this account assumes that the more a problem overlaps with other problems, indexed by an interference parameter, the poorer the expected performance. While this framework has received strong empirical support, the representational nature of the interference remains unclear. Previous studies focused on visual multiplication tasks implicitly assuming that interference operates at the level of digit features. This approach overlooks the fact that a single digit can be associated with distinct spoken forms. In French, for instance, the digit 2 can be associated to distinct numbers words pronounced “deux” (“two”), “douze” (“twelve”), or “vingt” (“twenty”). Consequently, previous investigations could not disentangle interference driven by shared features from interference arising at a phonological level. Research Aim Building directly on the framework of De Visscher and Noël, this study examines whether proactive interference predicts multiplication performance when presenting the problems auditorily. We also explored whether a description of interference that distinguishes between the different phonological representations of a digit better explains performance than the original interference index that treats different number-words as instances of this digit. Materials and Methods A group of 60 adult native French speakers solved all 36 single-digit multiplication problems from the 2 to the 9 tables, presented auditorily. Participants responded verbally, and reaction times and error rates were recorded. For each problem, a proactive interference index was computed following the original feature-based method proposed by De Visscher and Noël, based on digit overlap across multiplication facts. In parallel, a phonologically informed interference measure was derived by considering overlap between the verbal labels of operands and results. Results Preliminary analyses show that proactive interference predicts both error rates and response latencies, beyond the problem-size effect, when multiplication problems are presented auditorily. Specifically, both response times and error rates increase as the level of interference increases. Conclusion These findings confirm the robustness of proactive interference effects in multiplication while opening a new question regarding their representational basis. They suggest that proactive interference affects multiplication performance even when problems are presented auditorily, motivating further analyses to determine whether phonological overlap contributes additional explanatory power.