![]() More specifically, multiplication facts are stored in verbal memory (Dehaene, 1992 Dehaene & Cohen, 1995 Dehaene et al., 2003). This aspect is extremely important too: although arithmetic facts have mathematical meaning, and understanding this meaning is a critical stage of learning them, most educated adults eventually come to learn most single-digit arithmetic facts by heart, and they solve them by retrieving a memorized response, and not (at least not only) by applying mathematical rules (Campbell & Beech, 2014). The present study focuses on the second aspect of the knowledge of arithmetic facts, in particular multiplication facts-rote memory. For example, the magnitude of an arithmetic fact affects the difficulty of solving it (Groen & Parkman, 1972 Zbrodoff & Logan, 2005), and solving addition and subtraction facts is associated with the activation of number-line representations (McCrink et al., 2007 Pinheiro-Chagas et al., 2017). ![]() Moreover, several of these truths are not just mathematical, they may also affect the cognitive processing of the arithmetic facts. if we need to solve a problem whose solution we did not learn yet or we forgot. ![]() It can also help compute the result of arithmetic facts-e.g. Learning such mathematical truths is critical to understanding the meaning of arithmetic and being able to use it properly. The mathematical meaning determines the result of each given fact, and it has several consequences-for example, that addition facts are related to counting and to the idea of moving along a number line that a multiplication fact is equivalent to a series of same-operand additions and that for both additions and multiplications, larger operands are correlated with larger results. One aspect pertains to the mathematical meaning of arithmetic facts. Learning arithmetic facts, specifically the multiplication table, has at least two aspects. Given this large memorization challenge, it is perhaps not surprising that many children have difficulties learning the multiplication table and show poor/abnormal performance patterns (Geary, 2004 Gross-Tsur et al., 1996 Noël & De Visscher, 2018 Räsänen & Ahonen, 1995). Other single-digit multiplications are not necessarily learned by heart, as they can be solved using rules, N × 0, N × 1, N × 10 using twin addition, N × 2 or using multi-stage procedures to solve multi-digit multiplication. Children typically learn by heart the single-digit multiplication facts from 3 × 3 to 9 × 9-a challenging quantity of 28 facts to remember. Sadly, learning the multiplication table is not only important, it is also difficult. Mastering the multiplication table is important not only in itself but also for acquiring more advanced mathematical skills: even if not-memorized multiplication facts can be solved by various workarounds (strategies, external devices), automatic knowledge is still advantageous because it can free cognitive resources that can be used for other tasks (Bratina & Krudwig, 2003 Hasselbring, 1988). Learning the basic arithmetic facts, in particular the multiplication table, is a key part of the elementary school mathematics curriculum. Pedagogically, the effectiveness of the low-interference training method, which is dramatically different from currently used pedagogical methods, may pave the way to enhancing how we teach the multiplication table in school. Similarity affected long-term memory-its effect persisted 7 weeks after training has ended and it operated on long-term memory directly, not via the mediation of working memory. Moreover, the interference arose from the similarity between facts in a given week, not from the similarity to previously learned facts. Critically, this similarity effect originated in the specific learning context, i.e., the grouping of facts to weeks, and could not be explained as an intrinsic advantage of certain facts over others. Learning in the low-similarity, low-interference weeks was better than in the high-similarity weeks. In 2 weeks the facts were dissimilar from each other (low interference), and in 2 control weeks the facts were similar (high interference). In a series of 16 short training sessions over 4 weeks, first-grade children learned 16 multiplication facts-4 facts per week. ![]() Here, we examined whether learning would improve if the degree of interference is reduced, and which memory processes are responsible for this improvement. Memorizing the multiplication table is a major challenge for elementary school students: there are many facts to memorize, and they are often similar to each other, which creates interference in memory.
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