COMPUTER TRAINING OF APPROXIMATE NUMBER SYSTEM COULD IMPROVE MATH ABILITIES

The number of students diagnosed with Specific Learning Disabilities with Math (SLDwM) has been estimated to be 6%. These students face daily challenges related to their disability and as a result have a reduced quality of life. The triple code theory developed by Dehaene (1992) explores the issue of number representation, which is split into three codes: verbal, visual and semantic. The semantic code belongs to the preverbal system in which the Approximate Number System (ANS) plays an important role. In a previous study we have shown that ANS and math disability are causally related. These findings, demonstrated with a short ANS test applied to 50 students (7-11 years old) from three schools in Bucharest, Romania, support the hypothesis of a correlation between low ANS performances and low math ability. However, according to Park & Brannon (2013,) training on approximate addition and subtraction of arrays of dots improves the appropriate symbolic skills. This study describes a computer game with 62 arrays (ratios from 1:2 to 9:10) which can improve appropriate math abilities. Each array of the computer game (i.e., ANS - 62), consists of 4 to 30 images of identical familiar objects (e.g., apples, ice-creams, balloons) of varying sizes. Shrek and Puss in Boots (i.e., two characters well known to children in Romania) divide the objects in ratios from 1:2 to 9:10. Each of the numerosities comparison is presented for 2000 ms and the students indicate the character that has more objects by pressing the key associated with respective character. We hypothesize that the daily use of this game by children at risk for SLDwM, together with other types of interventions directed at memory or visual-spatial orientation, will help improve their ANS. Through this improvement, students can develop their Number Sense and the ability to manipulate symbolic and non-symbolic quantities.据估算，罹患数学特异性学习障碍（Specific Learning Disabilities with Math, SLDwM）的学生占比约为6%。此类学生每日均需应对病症带来的各类阻碍，生活质量因此显著下降。Dehaene于1992年提出的三重编码理论（triple code theory）围绕数字表征问题展开研究，将其划分为言语编码、视觉编码与语义编码三类。语义编码隶属于前言语系统，而近似数字系统（Approximate Number System, ANS）在此系统中扮演核心角色。 在过往一项研究中，我们团队已证实近似数字系统与数学障碍存在因果关联：该研究针对罗马尼亚布加勒斯特3所学校的50名7至11岁学生开展了简短的近似数字系统测试，所得结果支持“低近似数字系统表现与数学能力低下存在相关性”这一假说。不过，Park与Brannon（2013）的研究表明，针对点阵近似加减的训练能够改善相应的符号数学技能。 本研究介绍一款包含62组点阵（比例范围为1:2至9:10）的计算机游戏，该游戏可有效提升学生的数学能力。该游戏的每组点阵（即ANS-62）均由4至30个尺寸不一的相同常见物体图像组成，例如苹果、冰淇淋、气球。游戏中的史莱克与穿靴子的猫——罗马尼亚儿童熟知的两个动画角色——会按照1:2至9:10的比例分配这些物体。每组数量比较任务的展示时长为2000毫秒，学生需按下对应角色的按键，选出拥有更多物体的角色。 我们提出如下假说：若存在数学特异性学习障碍风险的儿童每日使用该游戏，并配合其他针对记忆或视觉空间定向的干预手段，将有助于提升其近似数字系统能力。通过该能力的提升，学生可进一步发展数字感（Number Sense）以及操控符号与非符号数量的能力。