Adaptive number knowledge and its relation to arithmetic and pre-algebra knowledge
Adaptive number knowledge and its relation to arithmetic and pre-algebra knowledge
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DOI：
10.1016/j.learninstruc.2017.02.001
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发表时间：
2017-06-01
影响因子：
6.2
通讯作者：
Lehtinen, Erno
中科院分区：
文献类型：
--
作者：
McMullen, Jake;Brezovszky, Boglarka;Lehtinen, Erno
考虑到算术和代数之间的密切概念关系，传统上衡量的算术技能与后来的代数成功在预期的水平上没有关系。然而，算术的适应性可能是算术能力的一个方面，可以解释代数成绩的额外变化。考虑到这一点，本研究旨在提供证据，证明算术适应性的一个新的组成部分的存在和相关性，即适应性数字知识。特别是，我们的目标是考察适应性数字知识是否存在显著的个体差异，以及这些差异在多大程度上与算术和预代数技能和知识有关。自适应数知识被定义为关于数的特征和关系的良好连接的知识。对1065名芬兰小学后期学生进行了大样本测试，包括适应性数字知识、算术概念知识和算术流利度。三个月后，他们完成了对预代数技能的测试。潜伏期分析表明，个体在适应数知识上存在显著差异。确定的个人资料与并行算术技能和知识有关。此外，研究发现，即使考虑到算术概念知识和算术流利性，自适应数字知识也可以预测后来的预代数技能。这些结果表明，适应性数字知识是数学发展的一个相关组成部分，并可能有助于解释代数发展中的差异。(C)2017爱思唯尔有限公司。保留所有权利。
Traditionally measured skills with arithmetic are not related to later algebra success at levels that would be expected given the close conceptual relation between arithmetic and algebra. However, adaptivity with arithmetic may be one aspect of arithmetic competences that can account for additional variation in algebra attainment. With this in mind, the present study aims to present evidence for the existence and relevance of a newly acknowledged component of adaptivity with arithmetic, namely, adaptive number knowledge. In particular, we aim to examine whether there are substantial individual differences in adaptive number knowledge and to what extent these differences are related to arithmetic and pre-algebra skills and knowledge. Adaptive number knowledge is defined as the well-connected knowledge of numerical characteristics and relations. A large sample of 1065 Finnish late primary school students completed measures of adaptive number knowledge, arithmetic conceptual knowledge, and arithmetic fluency. Three months later they completed a measure of pre-algebra skills. Substantial individual differences in adaptive number knowledge were identified using latent profile analysis. The identified profiles were related to concurrent arithmetic skills and knowledge. As well, adaptive number knowledge was found to predict later pre-algebra skills, even after taking into account arithmetic conceptual knowledge and arithmetic fluency. These results suggest that adaptive number knowledge is a relevant component of mathematical development, and may help account for disparities in algebra development. (C) 2017 Elsevier Ltd. All rights reserved.