NON-SYMBOLIC AND SYMBOLIC NUMERICAL COGNITION: A CROSS-CULTURAL PERSPECTIVE

Abstract

Present study hinges upon a very critical question that is whether approximate number system plays foundational role in symbolic math or not? More specifically in current research it has been tried to explore the causal relationship between non-symbolic and symbolic numerical cognition through a brief training paradigm. Research evidence of past decades has shed light on the relationship between non-symbolic and symbolic numerical cognition through neuroscience, neuropsychological, correlational and indirect research evidences. However there was no research evidence specifying the causal relationship between the two directly. To bridge this gap present study was carried out in an effort to disentangle this relationship through training study with first grade children who are at the very first step of connecting these two systems through class mathematics learning. This research study has been divided in two phases. Phase 1 of the study comprises of four experiments (i.e; experiment 1: N= 48; experiment 2, N=48; experiment 3, N=24; experiment 4, N= 24) conducted with American first grade children. Phase 2 of study comprises of two experiments conducted with Pakistani first grade children (experiment 1, N= 48; experiment 2, N =72). In both, phase1 and 2 children were trained with different training conditions (non-symbolic approximate addition, brightness comparison, line length addition and non-symbolic approximate comparison) and were post tested on symbolic addition (in experiment 1,3,4 of phase 1 and experiment 1 of phase 2), sentence completion task(experiment2 of phase1) and number line placement (experiment 2 of phase 2). Results across different experiments of both phases of study revealed that training with non-symbolic approximate addition and non-symbolic approximate comparison give the children advantage to perform better on symbolic math and number line placement task as compare to control conditions in terms of speed and accuracy. Research evidence indicates that non-symbolic numbers played foundational role in enhancing children performance on symbolic addition, number line placement and that this effect was specific to the domain of mathematics. xi Furthermore, training effect got replicated and extended with Pakistani sample belonging to a totally different cultural context. Results indicate that longitudinal training with nonsymbolic approximate numbers might be helpful to improve children symbolic math and might also be helpful for children with math learning difficulties.