Xenidou-Dervou Iro, Gilmore Camilla, van der Schoot Menno, van Lieshout Ernest C D M
Department of Educational Neuroscience and LEARN! Research Institute for Learning and Education, Faculty of Psychology and Education, VU University Amsterdam Amsterdam, Netherlands.
Mathematics Education Centre, Loughborough University Loughborough, UK.
Front Psychol. 2015 Apr 29;6:487. doi: 10.3389/fpsyg.2015.00487. eCollection 2015.
Symbolic (i.e., with Arabic numerals) approximate arithmetic with large numerosities is an important predictor of mathematics. It was previously evidenced to onset before formal schooling at the kindergarten age (Gilmore et al., 2007) and was assumed to map onto pre-existing nonsymbolic (i.e., abstract magnitudes) representations. With a longitudinal study (Experiment 1), we show, for the first time, that nonsymbolic and symbolic arithmetic demonstrate different developmental trajectories. In contrast to Gilmore et al.'s (2007) findings, Experiment 1 showed that symbolic arithmetic onsets in grade 1, with the start of formal schooling, not earlier. Gilmore et al. (2007) had examined English-speaking children, whereas we assessed a large Dutch-speaking sample. The Dutch language for numbers can be cognitively more demanding, for example, due to the inversion property in numbers above 20. Thus, for instance, the number 48 is named in Dutch "achtenveertig" (eight and forty) instead of "forty eight." To examine the effect of the language of numbers, we conducted a cross-cultural study with English- and Dutch-speaking children that had similar SES and math achievement skills (Experiment 2). Results demonstrated that Dutch-speaking kindergarteners lagged behind English-speaking children in symbolic arithmetic, not nonsymbolic and demonstrated a working memory overload in symbolic arithmetic, not nonsymbolic. Also, we show for the first time that the ability to name two-digit numbers highly correlates with symbolic approximate arithmetic not nonsymbolic. Our experiments empirically demonstrate that the symbolic number system is modulated more by development and education than the nonsymbolic system. Also, in contrast to the nonsymbolic system, the symbolic system is modulated by language.
使用阿拉伯数字进行的大数象征性（即近似）算术是数学的一个重要预测指标。此前有证据表明，这种算术能力在幼儿园阶段正式上学之前就已出现（吉尔摩等人，2007年），并且被认为是映射到预先存在的非象征性（即抽象数量）表征上。通过一项纵向研究（实验1），我们首次表明，非象征性和象征性算术呈现出不同的发展轨迹。与吉尔摩等人（2007年）的研究结果相反，实验1表明，象征性算术在一年级随着正式上学开始时才出现，而非更早。吉尔摩等人（2007年）研究的是说英语的儿童，而我们评估的是一个说荷兰语的大样本。例如，由于20以上数字的倒置特性，荷兰语中的数字在认知上可能要求更高。因此，比如数字48在荷兰语中被称为“achtenveertig”（八和四十），而不是“forty eight”。为了研究数字语言的影响，我们对社会经济地位和数学成绩技能相似的说英语和荷兰语的儿童进行了一项跨文化研究（实验2）。结果表明，说荷兰语的幼儿园儿童在象征性算术方面落后于说英语的儿童，而非象征性算术方面则不然，并且在象征性算术中表现出工作记忆过载，而非象征性算术中则没有。此外，我们首次表明，说出两位数的能力与象征性近似算术高度相关，而非非象征性算术。我们的实验通过实证证明，象征性数字系统比非象征性系统更多地受到发展和教育的调节。而且，与非象征性系统不同，象征性系统受到语言的调节。
