ABSTRACT Mathematical reasoning requires perseverance to overcome the cognitive and affective difficulties encountered whilst pursuing a reasoned line of enquiry. The aims of the study were: to understand how children’s perseverance in mathematical reasoning (PiMR) manifests in reasoning activities, and to examine how PiMR can be facilitated through a focus on children’s active goals. The article reports on children aged 10–11 from two English schools, purposively selected for their limited PiMR. Data relating to their cognitive and affective responses and the focus of their attention, a conative component, were collected by observation and interview. The study defines the construct perseverance in mathematical reasoning. Conative characteristics of PiMR were used to analyse the cognitive–affective interplay during reasoning. It revealed the role that children’s active goals play in restricting and enabling PiMR. The article offers new approaches to designing pedagogic interventions and collecting and analysing data relating to perseverance in vivo.

中文翻译：

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数学推理中的毅力：儿童意念专注在认知和情感之间的生产性相互作用中的作用

摘要 数学推理需要坚持不懈地克服在追求合理的探究路线时遇到的认知和情感困难。该研究的目的是：了解儿童的数学推理 (PiMR) 毅力如何体现在推理活动中，并研究如何通过关注儿童的积极目标来促进 PiMR。这篇文章报道了来自两所英语学校的 10-11 岁儿童，他们因有限的 PiMR 而被故意挑选出来。通过观察和访谈收集与他们的认知和情感反应以及他们的注意力焦点（意念成分）相关的数据。该研究定义了数学推理中的结构毅力。PiMR 的意动特征用于分析推理过程中的认知-情感相互作用。它揭示了儿童的积极目标在限制和启用 PiMR 方面的作用。本文提供了设计教学干预措施以及收集和分析与体内毅力相关的数据的新方法。