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Developmental foundations of children’s fraction magnitude knowledge
Cognitive Development ( IF 1.897 ) Pub Date : 2016-07-01 , DOI: 10.1016/j.cogdev.2016.05.002
Yi Mou 1 , Yaoran Li 1 , Mary K Hoard 1 , Lara D Nugent 1 , Felicia W Chu 1 , Jeffrey N Rouder 1 , David C Geary 1
Affiliation  

The conceptual insight that fractions represent magnitudes is a critical yet daunting step in children's mathematical development, and the knowledge of fraction magnitudes influences children's later mathematics learning including algebra. In this study, longitudinal data were analyzed to identify the mathematical knowledge and domain-general competencies that predicted 8th and 9th graders' (n=122) knowledge of fraction magnitudes and its cross-grade gains. Performance on the fraction magnitude measures predicted 9th grade algebra achievement. Understanding and fluently identifying the numerator-denominator relation in 7th grade emerged as the key predictor of later fraction magnitudes knowledge in both 8th and 9th grades. Competence at using fraction procedures, knowledge of whole number magnitudes, and the central executive contributed to 9th but not 8th graders' fraction magnitude knowledge, and knowledge of whole number magnitude contributed to cross-grade gains. The key results suggest fluent processing of numerator-denominator relations presages students' understanding of fractions as magnitudes and that the integration of whole number and fraction magnitudes occurs gradually.

中文翻译:

儿童分数大小知识的发展基础

分数代表大小的概念性洞察是儿童数学发展中关键但令人生畏的一步,分数大小的知识影响儿童以后的数学学习,包括代数。在本研究中,对纵向数据进行了分析,以确定预测 8 年级和 9 年级学生 (n=122) 分数大小及其跨年级增益的数学知识和领域通用能力。分数幅度测量的表现预测了 9 年级代数成绩。理解并流利地识别 7 年级的分子-分母关系成为 8 年级和 9 年级以后分数大小知识的关键预测因素。使用分数程序的能力,整数幅度的知识,中央执行器对 9 年级学生的分数级知识有贡献,但不是 8 年级学生的分数级知识,整数级知识有助于跨年级的收益。主要结果表明,分子-分母关系的流畅处理预示着学生将分数理解为大小,并且整数和分数大小的整合逐渐发生。
更新日期:2016-07-01
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