Effects of Non-Symbolic Approximate Number Practice on Symbolic Numerical Abilities in Pakistani Children

Abstract

Current theories of numerical cognition posit that uniquely human symbolic number abilities connect to an early developing cognitive system for representing approximate numerical magnitudes, the approximate number system (ANS). In support of this proposal, recent laboratory-based training experiments with U.S. children show enhanced performance on symbolic addition after brief practice comparing or adding arrays of dots without counting: tasks that engage the ANS. Here we explore the nature and generality of this effect through two brief training experiments. In Experiment 1, elementary school children in Pakistan practiced either a non-symbolic numerical addition task or a line-length addition task with no numerical content, and then were tested on symbolic addition. After training, children in the numerical training group completed the symbolic addition test faster than children in the line length training group, suggesting a causal role of brief, non-symbolic numerical training on exact, symbolic addition. These findings replicate and extend the core findings of a recent U.S. laboratory-based study to non-Western children tested in a school setting, attesting to the robustness and generalizability of the observed training effects. Experiment 2 tested whether ANS training would also enhance the consistency of performance on a symbolic number line task. Over several analyses of the data there was some evidence that approximate number training enhanced symbolic number line placements relative to control conditions. Together, the findings suggest that engagement of the ANS through brief training procedures enhances children's immediate attention to number and engagement with symbolic number tasks.

Testing the Efficacy of Training Basic Numerical Cognition and Transfer Effects to Improvement in Children’s Math Ability

“…The results of the present study are in contrast with those reported by some training studies conducted with young children ( Wilson et al, 2009 ; Obersteiner et al, 2013 ; Hyde et al, 2014 ; Khanum et al, 2016 ; Maertens et al, 2016 ; Park et al, 2016 ; Sella et al, 2016 ; Wang et al, 2016 ). In our study, only non-symbolic numerosity comparison performance (but not PAE from symbolic numberline estimation) improved after training without any transfer effects to math achievement.…”

“…In some studies, training on approximate arithmetic (approximate addition and subtraction) using dot arrays improved the training groups’ symbolic addition/subtraction abilities compared to the control group ( Park and Brannon, 2013 , 2014 ; Hyde et al, 2014 ; Khanum et al, 2016 ; Park et al, 2016 ; Au et al, 2018 ; Szkudlarek and Brannon, 2018 ). In contrast, Räsänen et al (2009) did not find any improvement on arithmetic (addition and subtraction) and counting abilities after training with the Number Race program 1 ( Wilson et al, 2006 ) although children’s ANS acuity was improved ( Räsänen et al, 2009 ).…”

From “sense of number” to “sense of magnitude”: The role of continuous magnitudes in numerical cognition

“…The causal evidence comes from two sources. One line of research has found training on ANS tasks leads to improved performance and faster responses on mathematics tests (Hyde et al 2014;Khanum et al 2016;Park & Brannon, 2013;Park et al 2016a). Another has found that manipulating the order in which ANS trials are presented (easy-to-difficult or difficultto-easy) improves mathematics performance (Wang et al 2016).…”

“…Although there has been a debate about the quality of this evidence (e.g., Lindskog & Winman 2016;Merkley et al 2017;Park & Brannon 2016;Wang et al 2017), here we ask whether, taken together at face value, current experimental studies provide sufficient evidence to conclude that there is a causal link between the ANS and mathematics performance. To this end, we performed a p-curve analysis on the set of all studies we are aware of that report a causal link between the ANS and mathematics performance (Hyde et al 2014;Khanum et al 2016;Park & Brannon 2013;Park et al 2016a;Wang et al 2016).…”

Number, time, and space are not singularly represented: Evidence against a common magnitude system beyond early childhood

“…More recent training studies have suggested the possibility of a causal relation between our approximate number and formal math abilities (e.g., Hyde, Khanum, & Spelke, 2014;Khanum, Hanif, Spelke, Berteletti, & Hyde, 2016;Park, Bermudez, Roberts, & Brannon, 2016;Park & Brannon, 2013;Wang, Odic, Halberda, & Feigenson, 2016). In one study, children's performance on a symbolic math task was improved following nonsymbolic addition and nonsymbolic numerical comparison training.…”