Educational Measurement and Applied Cognitive Science, Université du Luxembourg Walferdange, Luxembourg.
Front Psychol. 2013 Aug 29;4:518. doi: 10.3389/fpsyg.2013.00518. eCollection 2013.
The approximate number system (ANS) is thought to be a building block for the elaboration of formal mathematics. However, little is known about how this core system develops and if it can be influenced by external factors at a young age (before the child enters formal numeracy education). The purpose of this study was to examine numerical magnitude representations of 5-6 year old children at 2 different moments of Kindergarten considering children's early number competence as well as schools' socio-economic index (SEI). This study investigated estimation abilities of large numerosities using symbolic and non-symbolic output formats (8-64). In addition, we assessed symbolic and non-symbolic early number competence (1-12) at the end of the 2nd (N = 42) and the 3rd (N = 32) Kindergarten grade. By letting children freely produce estimates we observed surprising estimation abilities at a very young age (from 5 year on) extending far beyond children's symbolic explicit knowledge. Moreover, the time of testing has an impact on the ANS accuracy since 3rd Kindergarteners were more precise in both estimation tasks. Additionally, children who presented better exact symbolic knowledge were also those with the most refined ANS. However, this was true only for 3rd Kindergarteners who were a few months from receiving math instructions. In a similar vein, higher SEI positively impacted only the oldest children's estimation abilities whereas it played a role for exact early number competences already in 2nd and 3rd graders. Our results support the view that approximate numerical representations are linked to exact number competence in young children before the start of formal math education and might thus serve as building blocks for mathematical knowledge. Since this core number system was also sensitive to external components such as the SEI this implies that it can most probably be targeted and refined through specific educational strategies from preschool on.
近似数量系统（ANS）被认为是形式数学发展的基础。然而，对于这个核心系统是如何发展的，以及它是否可以在儿童进入正式数学教育之前（在幼儿时期）受到外部因素的影响，我们知之甚少。本研究的目的是在两个不同的时间点（幼儿园阶段的 2 年级和 3 年级）考察 5-6 岁儿童的数值大小表示，同时考虑儿童早期的数字能力和学校的社会经济指数（SEI）。本研究使用符号和非符号输出格式（8-64）调查了大数量的估计能力。此外，我们在 2 年级末（N = 42）和 3 年级末（N = 32）评估了符号和非符号的早期数字能力（1-12）。通过让孩子们自由地进行估计，我们在非常年幼的时候（从 5 岁开始）观察到了令人惊讶的估计能力，这种能力远远超出了儿童的符号显性知识。此外，测试时间对 ANS 的准确性有影响，因为 3 年级的儿童在两个估计任务中都更精确。此外，具有更好的精确符号知识的儿童也具有更精细的 ANS。然而，这仅适用于即将接受数学指导的 3 年级儿童。同样，较高的 SEI 仅对年龄较大的儿童的估计能力产生积极影响，而在 2 年级和 3 年级的儿童中，SEI 对精确的早期数字能力产生影响。我们的研究结果支持这样一种观点，即在正式的数学教育开始之前，年幼的儿童的近似数值表示与精确的数字能力有关，并且可能是数学知识的基础。由于这个核心数字系统也对外界因素（如 SEI）敏感，这意味着它可以通过从学前教育开始的具体教育策略来进行目标设定和改进。
