关于古代术数中内算与外算易位问题的探讨

在古代,传统术数(也称数术)中的内算与外算是一个整体。在两千多年的历史时期中,从教育史、从业者的身份认同与知识结构,以及史籍对二者的记载和二者在数术整体功能中的权重等方面来看,"外算"是以"内算"的婢女身份出现的。从《四库全书》起,这一观念发生改变,而在阮元等人所编《畴人传》中,内算与外算之关系发生了易位。通过对晚明前清中西术数、中西文化会通的考察而发现,这一易位有其必然性。但是从人类文化的未来发展来看,二者关系及各自前景值得深入思考。     

The relationships between quantity‐number competencies,working memory,and phonological awareness in 5‐ and 6‐year‐olds

In this study, the interdependencies among phonological awareness, verbal working memory components, and early numerical skills in children 1 year before school entry are addressed. Early numerical skills were conceptualized as quantity‐number competencies (QNC) at both basic (QNC Level 1) and advanced (QNC Level 2) levels. In a sample of 1,343 children aged 5 and 6, structural equation modelling provided support for the isolated number words hypothesis (Krajewski & Schneider, 2009, J. Exp. Child Psychol., 103, 516–531). This hypothesis claims that phonological awareness contributes to the acquisition of QNC Level 1, such as learning the number word sequence, but not of QNC Level 2, which requires the linkage of number words to quantities. In addition, phonological awareness relied on verbal working memory, especially with regard to the phonological loop, central executive, and episodic buffer. The results were congruent with the idea that phonological awareness mediates the impact of verbal working memory on QNCs. The relationships between verbal working memory, phonological awareness, and QNCs were comparable in monolingual and bilingual children.