The association between children's numerical magnitude processing and mental multi-digit subtraction

Abstract

Children apply various strategies to mentally solve multi-digit subtraction problems and the efficient use of some of them may depend more or less on numerical magnitude processing. For example, the indirect addition strategy (solving 72-67 as "how much do I have to add up to 67 to get 72?"), which is particularly efficient when the two given numbers are close to each other, requires to determine the proximity of these two numbers, a process that may depend on numerical magnitude processing. In the present study, children completed a numerical magnitude comparison task and a number line estimation task, both in a symbolic and nonsymbolic format, to measure their numerical magnitude processing. We administered a multi-digit subtraction task, in which half of the items were specifically designed to elicit indirect addition. Partial correlational analyses, controlling for intellectual ability and motor speed, revealed significant associations between numerical magnitude processing and mental multi-digit subtraction. Additional analyses indicated that numerical magnitude processing was particularly important for those items for which the use of indirect addition is expected to be most efficient. Although this association was observed for both symbolic and nonsymbolic tasks, the strongest associations were found for the symbolic format, and they seemed to be more prominent on numerical magnitude comparison than on number line estimation.

Strategies for written additions in adults

“…In later years, the application of the written algorithm could be less systematic and more adaptively selected as a function of the characteristics of the problems. One argument for this scenario is the fact that the ability to represent the magnitude of numbers, a central aspect of basic number sense which sharpens through development (Halberda & Feigenson, 2008), is particularly linked to the flexible use of mental calculations (Linsen, Verschaffel, Reynvoet, & De Smedt, 2014, 2015.…”

Does numerical processing uniquely predict first graders’ future development of single-digit arithmetic?

“…These tests reflect performance averaged across various mathematical skills and it has been observed that numerical processing impacts more on some specific mathematical skills compared to others. For example, Linsen, Verschaffel, Reynvoet, and De Smedt (2014) showed that in multi-digit subtraction, the use of the flexible subtraction-by-addition strategy relied more on numerical processing than the more common direct subtraction strategy (see also Fuchs, Geary, Fuchs, Compton, & Hamlett, 2014;Jordan, Mulhern, & Wylie, 2009).…”

How number line estimation skills relate to neural activations in single digit subtraction problems

“…Linearity is initially acquired for smaller ranges and progressively, with age and increasing number knowledge, linearity is extended to larger ranges (Berteletti et al, 2010; Siegler and Booth, 2004; Siegler et al, 2009). Performance on the NL task correlates with other estimation tasks (Booth & Siegler, 2006; Laski & Siegler, 2007), improves following interventions on children's linear and cardinal understanding of the numerical sequence (Ramani and Siegler, 2008; Siegler and Ramani, 2008), and is correlated with and is predictive of arithmetic learning and mathematical achievement (Booth & Siegler, 2008; Link, Nuerk, & Moeller, 2014; Linsen, Verschaffel, Reynvoet, & De Smedt, 2014; Ostergren & Träff, 2013; Sasanguie, Göbel, Moll, Smets, & Reynvoet, 2013; Schneider, Grabner, & Paetsch, 2009). Performance is also impaired or delayed in children with math learning difficulty (Geary et al, 2008; Landerl, 2013).…”

“…Importantly, improving children's performance on the NL task enhances performance in numerical magnitude processing tasks as well as facilitates learning of multi-digit addition problems (Booth and Siegler, 2008; Kucian et al, 2011). Because the NL task has been shown to be a strong and unique predictor of arithmetical ability in grades 1 and 2 over and above other non-symbolic and symbolic tasks (Lyons et al, 2014), and because the NL tasks were correlated to mental multi-digit subtraction performance (Linsen et al, 2014), it can be argued that the NL task is specifically calling upon numerical processes that are crucial for later acquisition of mathematical competences. Two types of functional processes involved in the number line task might explain the relationship with mathematical performance and in particular with subtraction problems.…”