Skills underlying mathematics: Executive functions and components of mathematics

This data collection contains data from a large battery of mathematics and executive function tasks administered to a sample of 403 participants aged between 5 and 25 years of age. The data collection includes standardised assessments of mathematics, the Numerical Operations and Mathematical Reasoning subtests from the Weschler Individual Achievement Test (WIAT-II UK), in addition to age appropriate experimental mathematics tests of factual knowledge, procedural skill and conceptual understanding in the domain of arithmetic. Executive functions were assessed with experimental tasks measuring verbal and visuospatial short-term and working memory, inhibitory control, cognitive flexibility and selective attention. Questionnaire measures of mathematics anxiety and the Behavior Rating Inventory of Executive Function were also administered. These data underpin the following papers:

Gilmore, C., Keeble, S., Richardson, S., & Cragg, L. (2015). The role of cognitive inhibition in different components of arithmetic. ZDM, 1–12. (see Related Resources)

Gilmore, C., Keeble, S., Richardson, S., & Cragg, L. (submitted). The interaction of procedural skill, conceptual understanding and executive functions in early mathematics achievement.

Cragg, L., Keeble, S., Richardson, S., Roome, H., & Gilmore, C. (in preparation). Direct and indirect influences of executive functions on mathematics achievement.

<p>A high proportion of children and adults struggle with learning and doing maths. To help them we need to have a clear understanding of the processes involved in mathematics. There are lots of different skills involved in successful maths performance including maths specific knowledge such as knowledge of facts, procedures, and concepts as well as other more general skills. These include holding and manipulating information in mind (working memory), flexible thinking (shifting), and focusing on relevant information and ignoring distractions (inhibition). These skills are often termed 'executive function' skills and are thought to be particularly important for learning maths. To date, this basic understanding of the importance of executive function skills has not been exploited in the classroom because our understanding is not detailed enough.

This project will explore the relationship between maths and executive function skills in greater depth using a variety of different research methods. This research will reveal the ways in which executive function skills are involved in learning and doing maths and help us to understand why some children find maths easy, and other children struggle.These findings will be used to raise teachers’ awareness of the importance of considering executive functions skills when teaching maths.</p>

这个数据集包含对403名年龄在5至25岁之间的参与者进行的一系列大量数学与执行功能（executive function）任务的数据。该数据集包括标准化数学评估（韦氏个体成就测验（Weschler Individual Achievement Test, WIAT-II UK）中的数字运算和数学推理子测验），以及适龄的算术领域事实性知识、程序性技能和概念理解的实验性数学测试。执行功能通过实验任务进行评估，这些任务测量言语和视空间短时记忆与工作记忆（working memory）、抑制控制（inhibitory control）、认知灵活性（cognitive flexibility）和选择性注意（selective attention）。此外，还采用了数学焦虑问卷和执行功能行为评定量表（Behavior Rating Inventory of Executive Function）进行测量。这些数据支撑了以下论文：

Gilmore, C., Keeble, S., Richardson, S., & Cragg, L. (2015). The role of cognitive inhibition in different components of arithmetic. ZDM, 1–12. (see Related Resources)

Gilmore, C., Keeble, S., Richardson, S., & Cragg, L. (submitted). The interaction of procedural skill, conceptual understanding and executive functions in early mathematics achievement.

Cragg, L., Keeble, S., Richardson, S., Roome, H., & Gilmore, C. (in preparation). Direct and indirect influences of executive functions on mathematics achievement.

<p>相当一部分儿童和成人在学习与运用数学时面临困难。为了帮助他们，我们需要清晰理解数学学习所涉及的过程。成功的数学表现涉及多种技能，包括数学特定知识（如事实、程序和概念知识）以及其他更通用的技能，例如在脑中保持和处理信息（工作记忆）、灵活思维（转换）和专注于相关信息并忽略干扰（抑制）。这些技能常被称为“执行功能”技能，且被认为对数学学习尤为重要。迄今为止，由于我们的理解不够深入，这种关于执行功能技能重要性的基本认知尚未在课堂教学中得到应用。</p>

<p>本项目将采用多种研究方法，更深入地探索数学与执行功能技能之间的关系。该研究将揭示执行功能技能参与数学学习与运用的方式，并帮助我们理解为何部分儿童觉得数学容易，而另一些则感到困难。这些发现将用于提高教师在数学教学中考虑执行功能技能重要性的意识。</p>