Longitudinal development of number line estimation and mathematics performance in primary school children

Abstract

Children's ability to relate number to a continuous quantity abstraction visualized as a number line is widely accepted to be predictive of mathematics achievement. However, a debate has emerged with respect to how children's placements are distributed on this number line across development. In the current study, different models were applied to children's longitudinal number placement data to get more insight into the development of number line representations in kindergarten and early primary school years. In addition, longitudinal developmental relations between number line placements and mathematical achievement, measured with a national test of mathematics, were investigated using cross-lagged panel modeling. A group of 442 children participated in a 3-year longitudinal study (ages 5-8 years) in which they completed a number-to-position task every 6 months. Individual number line placements were fitted to various models, of which a one-anchor power model provided the best fit for many of the placements at a younger age (5 or 6 years) and a two-anchor power model provided better fit for many of the children at an older age (7 or 8 years). The number of children who made linear placements also grew with age. Cross-lagged panel analyses indicated that the best fit was provided with a model in which number line acuity and mathematics performance were mutually predictive of each other rather than models in which one ability predicted the other in a non-reciprocal way. This indicates that number line acuity should not be seen as a predictor of math but that both skills influence each other during the developmental process.

Explaining the relationship between number line estimation and mathematical achievement: The role of visuomotor integration and visuospatial skills

“…Reversing the order by which variables were entered into the hierarchical regression (i.e. by first entering the number line estimation metrics and then entering the visuo-spatial and visuo-motor integration component variable scores; (Booth & Siegler, 2008;Muldoon et al, 2013;Siegler & Opfer, 2008;van den Bos et al, 2015). It was also observed that there were medium to strong significant correlations between all visuo-spatial and visuo-motor integration measures and number line estimation, barring between R 2 LIN and both visuo-spatial working memory and mental rotation.…”

“…A number of tasks have been used to provide an indication of the precision of individuals' numerical representations, of which the number line estimation task is a popular measure (Geary, Hoard, Nugent, & Byrd-Craven, 2008, Siegler & Opfer, 2003van den Bos et al, 2015). In a number line estimation task, participants are generally presented with number lines which include the value of the start and end point of the scale (e.g.…”

“…Performance on the number line estimation task has been related to children's mathematical achievement in a number of studies (e.g., Booth & Siegler, 2008;Siegler & Opfer, 2008;van den Bos et al, 2015) in which participants with more linear and accurate performance demonstrate better mathematical achievement. Moreover, interventions that have focused on improving numerical representations through game-based tasks such as a number line board games or repetitive physical movements along a large-scale number line have noted transfer to arithmetic learning and mathematical performance (Siegler & Ramani, 2008;Fischer, Moeller, Bientzle, Cress & Nuerk, 2011;Link, Moeller, Huber, Fischer & Nuerk, 2013).…”

Early numeracy performance of South African school beginners

“…In general, authors agree that numeracy performance in the early childhood years adequately predicts later mathematics performance (Jordan, Glutting & Ramineni 2010). Especially magnitude comparison, number reading, counting skills, basic arithmetical skills, number line acuity, spontaneous focusing on numerosity and numeracy-related logical knowledge have been found to be relevant for later mathematics performance (Aunio & Niemivirta 2010;Friso-van den Bos et al 2015;HannulaSormunen, Lehtinen & Räsänen 2015;Jordan et al 2010;Krajewski & Schneider 2009;LeFevre et al 2010;Nguyen et al 2016;Passolunghi, Vercelloni & Schadee 2007;Toll et al 2015;Vanbinst, Ghesquière & De Smedt 2015). Related to the development of mathematical skills in early childhood years, there is an agreement among the researchers that children have biologically primary non-verbal number sense which is the base that children start to learn to use their number word sequence skills first in rhymes and then in enumeration tasks and from that follows the basic strategies for addition and subtraction problem solving (Jordan et al 2010;Mazzocco, Feigenson & Halberda 2011).…”

How do different aspects of spatial skills relate to early arithmetic and number line estimation?

“…It is currently debated whether number line estimation tasks tap into children's internal number representation (the mental number line), or whether it reflects proportion judgement strategies (see Dackermann, Huber, Bahnmueller, Nuerk, & Moeller, 2015 for a review on this topic). Nevertheless, performance on the number line estimation task has been consistently related to later mathematical achievement making it a relevant measure of mathematical development (Ashcraft & Moore, 2012;Booth & Siegler, 2008;Friso-van den Bos et al, 2015;LeFevre et al, 2013;Siegler & Opfer, 2003;Simms et al, 2016).…”