Numerical Magnitude Representations and Individual Differences in Children's Arithmetic Strategy Use

Abstract

Against the background of neuroimaging studies on how the brain processes numbers, there is now converging evidence that numerical magnitude representations are crucial for successful mathematics achievement. One major drawback of this research is that it mainly investigated mathematics performance as measured through general standardized achievement tests. We extended this research by investigating the association between these numerical magnitude representations and children's strategy use during single-digit arithmetic. Our findings reveal that children's symbolic but not nonsymbolic numerical magnitude processing skills are associated with individual differences in arithmetic. Children with better access to magnitude representations from symbolic digits, retrieve more facts from their memory and are faster in executing fact retrieval as well as procedural strategies. These associations remain even when intellectual ability, digit naming and general mathematics achievement were additionally controlled for. This all indicates that particularly the access to numerical meaning from Arabic symbols is key for children's arithmetic strategy development, which suggests that educators and remedial teachers should focus on connecting Arabic symbols to the quantities they represent.

Symbolic magnitude processing in elementary school children: A group administered paper-and-pencil measure (SYMP Test)

“…Inconsistent results have been reported as some studies found significant associations between children's ability to compare dot arrays and mathematics achievement (Halberda et al, 2008;Mazzocco et al, 2011), while others did not (e.g., De Smedt & Gilmore, 2011;Holloway & Ansari, 2009;Vanbinst, Ghesquière, & De Smedt, 2012). Recently, two meta-analyses have demonstrated that non-symbolic magnitude processing was significantly associated with mathematics achievement, although the correlations tended to be weak (r = .20 in Chen & Li, 2014;r = .22 in Fazio, Bailey, Thompson, & Siegler, 2014), but unfortunately these analyses did not consider measures of symbolic magnitude processing.…”

“…Findings on the symbolic magnitude comparison task have been, in contrast, more robust as most studies showed that the better children are in determining which of two Arabic digits is the largest, the higher their concurrent and future scores on mathematics achievement tests (e.g., De Smedt et al, 2009;Kolkman, Kroesbergen, & Leseman, 2013;Vanbinst et al, 2012). Summarizing the available evidence, De Smedt et al (2013) therefore argued that symbolic magnitude processing might be a more robust predictor of individual differences in mathematics achievement.…”

Profiles of children’s arithmetic fact development: A model-based clustering approach

“…Two recently conducted meta-analyses revealed that children's nonsymbolic numerical magnitude processing skills were significantly associated with their mathematics achievement, although these associations were rather moderate (Chen & Li, 2014;Fazio et al, 2014). There is, however, some debate on associations between nonsymbolic numerical magnitude processing and mathematics achievement (see De Smedt et al, 2013, for a discussion) because some studies failed to find such (longitudinal) associations (e.g., Holloway & Ansari, 2009;Sasanguie, De Smedt, Defever, & Reynvoet, 2012a;Vanbinst, Ghesquière, & De Smedt, 2012;see De Smedt et al, 2013, for a narrative review). In contrast, it has been argued that the results for symbolic numerical magnitude processing are more consistent (e.g., Bugden & Ansari, 2011;De Smedt, Verschaffel, & Ghesquière, 2009;Sasanguie, Van den Bussche, & Reynvoet, 2012b), as indicated by a narrative review by De Smedt et al (2013).…”

“…Furthermore, it is possible that arithmetic facts are stored in long-term memory in a meaningful way, that is, according to their magnitude (e.g., Butterworth, Zorzi, Girelli, & Jonckheere, 2001;Robinson, Menchetti, & Torgesen, 2002). A cross-sectional study by Vanbinst et al (2012) in third-graders investigated the direct associations between numerical magnitude processing and individual differences in arithmetic strategy use. These authors found a significant association between symbolic numerical magnitude comparison and the frequency of arithmetic fact retrieval, indicating that children who were more proficient in discriminating Arabic digits relied more frequently on arithmetic fact retrieval when solving single-digit additions and subtractions.…”

Indexing the approximate number system

“…Finally, some researchers have adopted the Numerical Ratio Effect (NRE), or the closely related Numerical Distance Effect (NDE), to index ANS acuity (e.g., Bugden, Price, McLean & Ansari, 2012;Gilmore et al, 2011;Holloway & Ansari, 2009;Lonnemann, Linkersdorfer, Hasselhorn & Lindberg, 2011;Merkley & Ansari, 2010;Price et al, 2012;Sasanguie, Van den Bussche, & Reynvoet, 2012;Vanbinst, Ghesquière, & De Smedt, 2012). …”