Department of Psychology, University of Kentucky, Lexington, KY 40506, USA.
Department of Psychology, University of Kentucky, Lexington, KY 40506, USA.
J Exp Child Psychol. 2023 Dec;236:105743. doi: 10.1016/j.jecp.2023.105743. Epub 2023 Jul 17.
This study examined whether different types of commonly used mathematical tasks affect how children think about whole number division problems. Prior research suggested that children tend to rely on the partitive model to understand whole number division, which is likely problematic when students transition to learning about fraction division. We assessed variability in correct whole number division problem-solving strategies among 63 elementary school children (41.5% female, 58.5% male, 0% nonbinary/gender expansive; 69.2% White, 10.7% multiracial, 6.1% Black, 4.6% Latino, 3.3% other/unidentified, 6.1% preferred not to answer). Each participant was asked to demonstrate four whole number division problems in each of three contexts (within participants): objects, story problems, and number lines. Most children displayed understanding of multiple conceptual models of division, but strategies varied by context. Story problems elicited partitive models, number lines elicited quotative models, and objects elicited both. Finally, elementary school children used strategies adaptively. Number line representations may afford conceptual connections between earlier-learned whole number concepts and analogous later-learned fraction concepts, supporting the integration of children's whole number and fraction knowledge.
这项研究考察了不同类型的常用数学任务是否会影响儿童对整数除法问题的思考方式。先前的研究表明，儿童倾向于依赖部分模型来理解整数除法，而当学生过渡到学习分数除法时，这可能会出现问题。我们评估了 63 名小学生（41.5%女性，58.5%男性，0%非二元/性别扩展；69.2%白人，10.7%多种族，6.1%黑人，4.6%拉丁裔，3.3%其他/未识别，6.1%选择不回答）在正确解决整数除法问题策略方面的可变性。每个参与者都被要求在三个情境（参与者内）中演示四个整数除法问题：物体、故事问题和数轴。大多数儿童表现出对多种除法概念模型的理解，但策略因情境而异。故事问题引发部分模型，数轴引发定量模型，而物体则引发两者。最后，小学生能够自适应地使用策略。数轴表示可能在早期学习的整数概念和类似的后期学习的分数概念之间提供概念联系，从而支持儿童整数和分数知识的整合。
