Editorial: Individual Differences in Arithmetical Development

Does Multi-Component Strategy Training Improve Calculation Fluency Among Poor Performing Elementary School Children?

“…This could explain why spontaneous transfer did not happen across the arithmetic operations, although children started to make more frequent use of retrieval and derived fact/decomposition strategies in addition. Moreover, even typically achieving children often fail to extend their knowledge of addition principles appropriately to subtraction principles ( Dowker, 1998 , 2014 ). For example, they find the addition/subtraction inverse principle far more difficult to recognize and use than addition-specific principles, such as commutativity, and often overextend addition principles to subtraction, e.g., saying that if 14 − 5 = 9, 14 − 6 must be 10 “because 6 is one more than 5.” Thus, explicit instruction and intensive practice are likely to be required to learn to use derived fact/decomposition strategies for subtraction, rather than expecting them to spontaneously extend their strategic knowledge in addition also to subtraction.…”

“…The differences in math performance between typically performing children and children with MDs can be striking. Even young primary school children can often retrieve answers from memory or derive and predict unknown arithmetical facts from known facts without direct teaching ( Dowker, 1998 , 2014 ; Canobi, 2005 ), whereas children with difficulties may not learn to use these more advanced strategies despite practicing arithmetic at school for several years and despite having a normal cognitive capacity. Previous intervention research aimed at enhancing calculation fluency in children with MDs has generally focused either on training fact retrieval itself or more efficient counting-based strategies, such as counting on from the largest number, (e.g., Christensen and Gerber, 1990 ; Tournaki, 2003 ; Fuchs et al, 2006 ), and thus the effectiveness of training MD children in derived fact and decomposition strategies remains unclear.…”

“…The main principle of both studies was that rather than training children in arithmetical facts by rote learning, the aim was to enable them to use conceptual and procedural knowledge to construct calculation strategies based on meaningful relationships between the known and unknown arithmetical facts. This is important, both because derived fact strategies are themselves an important aspect of arithmetical reasoning ( Dowker, 1998 , 2014 ; Canobi, 2005 ; Star and Rittle-Johnson, 2008 ) and because children with difficulties in fact retrieval may be able to use such strategies to compensate. Although rigid counting-based strategy use characterizes many children with MDs, some studies suggest that the ability to use derived fact strategies is a relative strength for some low attainers in arithmetic ( Russell and Ginsburg, 1984 ; Dowker, 2009 ); it may be possible to capitalize on this in enabling them to develop and use compensatory strategies.…”

Conceptual Understanding, Procedural Knowledge and Problem-Solving Skills in Mathematics: High School Graduates Work Analysis and Standpoints

“…and Operations (Canobi and Bethune, 2008;Jordan et al, 2009) fractions and decimals (Reimer and Moyer, 2005;Hallett et al, 2010) estimation (Dowker, 1998;Star and Rittle-Johnson, 2009) and equation solving (Durkin et al, 2011).…”

The contribution of attentional processes to calculation skills in second and third grade in a typically developing sample

“…Calculation and mathematical performance rely on a number of components, such as basic knowledge of numbers, retrieval of arithmetical facts, understanding of mathematical concepts, and the ability to follow procedures (Dowker, 1998;Gersten et al, 2005;Tobia et al, 2016). Early numerical abilities emerge and manifest very early on in development, already in the first months of life in humans, and this evidence is confirmed in populations from various cultural backgrounds (e.g., Gordon 2004;Wynn 1992;Xu et al 2005).…”