Abstract

Little is known about whether manipulatives can support children’s inferences of the mathematical structure of word problems. The objective was to test the effects of using manipulatives during problem solving on students’ understanding of the additive relationships in word problems. Third and fifth graders (N = 45) solved one-step addition and subtraction word problems that described either a mathematical action or relation. Children in each grade were randomly assigned to either a manipulatives or a paper-and-pencil condition. Problem structure understanding was assessed by the degree to which students’ strategies and verbal justifications reflected the quantitative relationships described in the problem text. Performance of the fifth graders was not impacted by the use of manipulatives, but in the third grade, strategy performance with manipulatives was superior to performance without manipulatives on Relation problems. The degree to which the third graders’ justifications were aligned with corresponding problem structure was positively impacted by manipulatives regardless of problem type.

摘要

关于操作是否可以支持儿童对单词问题的数学结构的推断知之甚少。目的是测试在问题解决过程中使用操作对学生理解单词问题中附加关系的影响。三、五年级学生（N = 45) 解决了描述数学动作或关系的一步加法和减法单词问题。每个年级的孩子被随机分配到操作或纸笔条件。问题结构的理解通过学生的策略和口头论证反映问题文本中描述的定量关系的程度来评估。五年级学生的表现不受操纵的影响，但在三年级，在关系问题上，有操纵的策略表现优于没有操纵的表现。无论问题类型如何，三年级学生的理由与相应问题结构一致的程度都受到操纵因素的积极影响。