Encoding “10ness” improves first-graders’ estimation of numerical magnitudes

Understanding numerical magnitudes is a foundational skill that significantly impacts later learning of mathematics concepts. The current study tested the idea that encoding of “10ness” is crucial to improving children’s estimation of two-digit number magnitudes. We used commercially available base-10 blocks for this purpose. The children in the experimental condition were asked to construct two-digit numbers by laying down the precise combinations of 10- and 1-blocks horizontally (e.g., three 10-blocks and seven 1-blocks for 37). Two control conditions were also included. In one control condition, children used 1-blocks only. In another control condition, children used one 10-block and as many 1-blocks as necessary. After working with the experimenter for only 15 minutes twice, the children in the experimental condition were significantly more accurate on the estimation task than those in the control conditions. The findings confirmed the importance of encoding 10ness as a unit in making accurate estimates of two-digit number magnitudes. The importance of encoding other units in the base-10 system is discussed. peerReviewed publishedVersion

理解数值量级是一项核心基础技能，对后续数学概念的学习具有显著促进作用。本研究验证了如下假设：对‘十性（10ness）’的编码，是提升儿童两位数数值量级估计能力的关键所在。为此，本研究采用了市售的十进制积木（base-10 blocks）。实验组儿童需通过横向摆放精确组合的10单位积木（10-blocks）与1单位积木（1-blocks），来构建两位数（例如，用3块10单位积木加7块1单位积木表示37）。本研究同时设置了两组对照组：其一，儿童仅使用1单位积木；其二，儿童使用1块10单位积木与按需取用的1单位积木。在仅与实验者进行两次、每次15分钟的操作训练后，实验组儿童在数值估计任务中的准确率显著高于对照组儿童。本研究结果证实，将‘十性’作为单位进行编码，对准确估计两位数数值量级具有重要意义。本研究还讨论了十进制系统中其他单位编码的重要性。经同行评审的正式发表版本（peerReviewed publishedVersion）