There is evidence that early variations in the development of an approximate number system (ANS) and symbolic number understanding are both influences on the later development of formal arithmetic skills. We report a large-scale (N = 552) longitudinal study of the predictors of arithmetic spanning a critical developmental period (the first 3 years of formal education). Variations in early knowledge of symbolic representations of number and the ordinal associations between them are direct predictors of later arithmetic skills. The development of number ordering ability is in turn predicted by earlier variations in arithmetic, the ANS (numerosity judgments), and rapid automatized naming (RAN). These findings have important implications for theories of numerical and arithmetical development and potentially for the teaching of these skills.

有证据表明，近似数系统 (ANS) 发展的早期变化和符号数理解都会影响正式算术技能的后期发展。我们报告了大规模（N = 552) 对跨越关键发展时期（正规教育的前 3 年）的算术预测因素的纵向研究。数字符号表示的早期知识的变化以及它们之间的序数关联是后期算术技能的直接预测因素。数字排序能力的发展反过来又可以通过算术、ANS（数量判断）和快速自动命名 (RAN) 的早期变化来预测。这些发现对数值和算术发展理论以及这些技能的教学具有重要意义。