ABSTRACT

It has become increasingly clear that the early use of decomposition for addition is associated with later mathematical achievement. This study examined how younger children execute a base-10 decomposition strategy to solve complex arithmetic (e.g. two-digit addition). 24 addition problems in two modalities (WA: Written Arithmetic; OA: Oral Arithmetic) with sums less than 100 were administered to 22 Japanese and 22 Singaporean 6-year-old kindergarteners. Our findings reveal that they were able to solve complex addition. For instance, Japanese kindergarteners tended to solve complex arithmetic using base-10 decomposition across the modality, whereas Singaporean kindergarteners used standard algorithms and basic counting to solve complex WA and OA problems, respectively. We speculate that Japanese kindergarteners might have a clearer understanding of the base-10 concept and were able to use this knowledge more readily than Singaporean kindergarteners. Mathematical experiences in kindergarten and number-naming systems have been put forward as two of the crucial contributors for such cross-cultural differences. This study also provides new directions for future research on the understanding of the base-10 concept and its application among young children.

摘要

越来越清楚的是，早期使用分解进行加法与后来的数学成就有关。这项研究调查了年幼的孩子如何执行以 10 为基数的分解策略来解决复杂的算术（例如两位数加法）。对 22 名日本和 22 名新加坡 6 岁幼儿园儿童进行了 24 道总和小于 100 的两种形式的加法题（WA：书面算术；OA：口算）。我们的发现表明他们能够解决复杂的加法问题。例如，日本幼儿园儿童倾向于使用以 10 为底的跨模态分解来解决复杂算术，而新加坡幼儿园儿童则分别使用标准算法和基本计数来解决复杂的 WA 和 OA 问题。我们推测日本幼儿园儿童可能比新加坡幼儿园儿童对以 10 为底的概念有更清晰的理解，并且能够更容易地使用这些知识。幼儿园的数学经验和数字命名系统被认为是造成这种跨文化差异的两个重要因素。本研究也为今后幼儿对十进制概念的理解及其应用的研究提供了新的方向。