Department of Education, University of Oxford, Oxford, UK.
J Exp Child Psychol. 2012 Dec;113(4):469-86. doi: 10.1016/j.jecp.2012.07.009. Epub 2012 Sep 17.
Recent research on children's conceptual and procedural knowledge has suggested that there are individual differences in the ways that children combine these two types of knowledge across a number of mathematical topics. Cluster analyses have demonstrated that some children have more conceptual knowledge, some children have more procedural knowledge, and some children have an equal level of both. The current study investigated whether similar individual differences exist in children's understanding of fractions and searches for explanations for these differences. Grade 6 students (n=119) and Grade 8 students (n=114) were given measures of conceptual and procedural knowledge of fractions as well as measures of general fraction knowledge, general conceptual ability, and general procedural ability. Grade 6 children demonstrated a four-cluster solution reflecting those who do poorly on procedural and conceptual fraction knowledge, those who do well on both, those whose strength is procedural knowledge, and those whose strength is conceptual knowledge. Grade 8 children demonstrated a two-cluster solution reflecting those whose strength is procedural knowledge and those whose strength is conceptual knowledge. Cluster in either grade, however, did not vary in distribution across schools and was not related to general conceptual ability or general procedural ability. Overall, these results provide a more detailed picture of individual differences in conceptual and procedural knowledge in mathematical cognition.
最近关于儿童概念和程序知识的研究表明，儿童在将这两种知识结合到许多数学主题中的方式上存在个体差异。聚类分析表明，一些儿童具有更多的概念知识，一些儿童具有更多的程序知识，而一些儿童则具有两者相等的水平。本研究探讨了在儿童对分数的理解中是否存在类似的个体差异，并寻找这些差异的解释。六年级学生（n=119）和八年级学生（n=114）接受了分数的概念和程序知识的测量，以及一般分数知识、一般概念能力和一般程序能力的测量。六年级学生表现出四聚类解决方案，反映了那些在程序和概念分数知识方面表现不佳的学生、那些在两者方面表现出色的学生、那些程序知识较强的学生以及那些概念知识较强的学生。八年级学生表现出两聚类解决方案，反映了那些程序知识较强的学生和那些概念知识较强的学生。然而，无论在哪个年级，聚类在学校之间的分布都没有差异，也与一般概念能力或一般程序能力无关。总的来说，这些结果提供了数学认知中概念和程序知识个体差异的更详细图景。
