Developing Multiplication Fact Fluency

The Moderating Role of Mathematical Skill Level when Using Curricular Methods to Learn Multiplication Tables

“…Our results here coincide with other research in the area of multiplication fluency intervention, which has found greater benefits for interventions based on understanding than for those simply based on memory. For instance, Brendefur et al (2015) employed a form of instruction based on social-interactional and cognitive theories for five weeks, comparing this to one based on behavioristic techniques such as repetition and memorization. They found that the former led to increased multiplication fluency with a greater degree of consistency than the latter.…”

“…Unfortunately, experimental support for curricular methods designed to teach multiplication in the classroom is scarce (e.g., NMAP, 2008). This paucity of evidence stands in clear contrast to the existing literature on intervention, in which either one or a combination of instructional strategies are applied during certain weeks only, sometimes by specialized professionals (e.g., psychologists), and focus on partial results (the learning of a small set of operations) (e.g., Brendefur et al 2015;Kaufmann & Pixner, 2012;Nelson et al, 2013;Woodward, 2006; see also Codding et al, 2011, for a review and meta-analysis on intervention strategies).…”

“…skills benefit from strategies based on memory retrieval, such as conventional ones, which include practicing and modelling at the same time (Codding et al, 2011;Geary, 2004;Nelson et al, 2013) but there is also evidence that methods based on conceptual strategies increase fluency to the same extent (e.g., Gray et al, 2000;Mulligan & Mitchelmore, 2009;Woodward, 2006) and may even provide better outcomes than methods based on drill learning (e.g., Brendefur et al, 2015). Taking into account the principles on which the M&R method is based, we hypothesized that it will be more effective than the conventional one, and that this will be more evident in those children with low mathematical skills, because, together with practice and understanding, it provides easy singlestep rules that should facilitate learning by reducing interference.…”

“…As previously noted, studies in the mathematical field have shown that conceptual instruction provides both understanding and better transfer to novel situations (e.g., see Rittle-Johnson & Alibali, 1999;Rittle-Johnson et al, 2001) and promotes students' success and independence (Miller et al, 1996). Specifically, some data suggest that gains in fluency using memory procedures are not always accompanied by a flexible use of multiplications in other areas, such as problem solving (Brendefur et al, 2015;Geary et al, 2007;Woodward, 2006). On the contrary, it seems that intervention methods that use more conceptual approaches to learning facts, as the M&R does, increase not only fluency but also children's ability to apply these skills to novel situations (e.g., Gray et al, 2000;Mulligan & Mitchelmore, 2009;Woodward, 2006).…”

Αλγοριθμικές Διαδικασίες Ως Κύρια Μαθηματική Γνώση

“…Η αυτοματοποίηση σχετίζεται, συχνά, με τη σχεδόν στιγμιαία ανάκληση των αριθμητικών δεδομένων. Συνεπακόλουθα, ως αυτοματοποίηση μπορεί να οριστεί, λοιπόν, η ικανότητα ανάκλησης γεγονότων, από τη μακροπρόθεσμη μνήμη, με ταχύτητα (κάτω από 3 δευτερόλεπτα, όπως αναφέρεται στο Brendefur et al, 2015), με ακρίβεια αλλά και με καταβολή σχεδόν μηδαμινής γνωστικής προσπάθειας ή προσοχής. Αν τα αριθμητικά δεδομένα δεν μπορούν να ανακληθούν αυτοματοποιημένα, ως δηλωτική μαθηματική γνώση, τότε μπορεί να εξαχθούν ως αποτέλεσμα (χρονοβόρας και απευκταίας) διαδικαστικής μαθηματικής γνώσης (π.χ.…”