Skills Underlying Maths: The Role of Inhibitory Control in Learning Multiplication Tables

良好的数学技能对于现代生活中的成功很重要，但许多孩子离开学校时没有学习他们所需要的数学。了解学习数学所涉及的技能有助于为改善所有儿童的数学学习提供正确的支持。尤其是，许多孩子很难学习乘法表之类的数字知识。对数字事实的良好回忆有助于个人能够专注于数学问题解决的其他方面，例如理解涉及的概念关系，或选择适当的解决策略。因此，整体数学成绩良好的个人往往拥有良好的数字事实知识也就不足为奇了。英国政府已经认识到很好地记住乘法表的重要性，最近引入了一项新的国家乘法表测试，从2020年开始，所有8至9岁的儿童都可以参加。有多种方法可以成功地用于学习乘法表。为了帮助孩子，许多老师和家长越来越多地转向纸质或计算机化的游戏和活动。然而，目前我们对学习乘法知识的过程还不够了解，不知道如何设计这些活动来最有效地支持学习。特别是，我们不知道这些活动的特点，如儿童是否必须产生答案或从一系列答案中选择，或者产生答案是否有时间限制或没有时间限制，如何影响学习和记忆乘法事实的过程。我们也不知道这些特征是否会增加一些孩子的焦虑水平。为了对有效资源的设计提出建议，我们需要更多地了解认知技能在数字事实学习中的作用，比如抑制控制。每当我们需要忽略令人分心的信息或抑制不想要的反应时，就会涉及抑制性控制。抑制控制对于学习乘法事实可能很重要，因为当回忆一个数字事实(例如6x7)时，我们需要忽略密切相关的事实的答案(例如6x6=36，6x8=48)。然而，目前对抑制控制在数字事实学习中的作用还知之甚少。我们将进行一系列研究：1)密切跟踪新数字事实的学习过程，以确定何时以及如何参与抑制控制；2)确定学习活动的特点如何增加或减少抑制控制的需求，从而影响学习速度；3)确定独立的抑制控制训练是否从一个背景转移到另一个背景，从而支持数字事实学习。该项目将有助于更好地理解认知技能在数字事实学习中的作用。这将允许开发包含设计特征的教育资源，以最大限度地提高数字事实的学习速度。更广泛地说，这个项目将有助于揭示数学学习中涉及的技能，并提高我们对为什么这门学科对许多人来说是困难的理解。

Good mathematical skills are important for success in modern life, but many children leave school without learning the mathematics they need. Understanding the skills involved in learning mathematics can help provide the right support to improve mathematics learning for all children. In particular, many children struggle to learn number facts, such as multiplication tables. Good recall of number facts helps individuals to be able to focus on other aspects of mathematical problem solving, such as understanding the conceptual relationships involved, or selecting an appropriate solution strategy. It is therefore unsurprising that individuals with good overall mathematics achievement tend to have good number fact knowledge. The importance of good recall of multiplication tables has been recognised by the UK Government, who have recently introduced a new national multiplication tables test to be taken by all children aged 8- to 9-years old from 2020. There are a variety of approaches that can be used successfully to learn multiplication tables. To help children, many teachers and parents have increasingly turned to paper-based or computerised games and activities. However, at present we don't understand enough about the process of learning multiplication facts to know how to design these activities to be most effective in supporting learning. In particular, we don't know how features of these activities, such as whether children have to produce an answer or select from a range of answers, or whether there is a time limit or no time limit in producing answers, affect the process of learning and remembering multiplication facts. We also don't know if these features may increase anxiety levels for some children.In order to make recommendations about the design of effective resources we need to understand more about the role of cognitive skills, such as inhibitory control, in number fact learning. Inhibitory control is involved whenever we need to ignore distracting information or suppress unwanted responses. Inhibitory control is likely to be important for learning multiplication facts because when recalling a number fact (e.g. 6 x 7) we need to ignore the answers to closely related facts (e.g. 6 x 6 = 36, 6 x 8 = 48). However, at present the role of inhibitory control in number fact learning is poorly understood. We will conduct a series of studies that: 1) closely track the process of learning new number facts over time to identify when and how inhibitory control is involved; 2) identify how features of learning activities may increase or decrease the demands for inhibitory control and therefore impact the rate of learning; and 3) identify whether stand-alone inhibitory control training transfers from one context to another and could therefore support number fact learning.This project will lead to improved understanding of the role of cognitive skills in number fact learning. This will allow the development of educational resources that incorporate design features to maximise the rate of number fact learning. More generally, this project will help to reveal the skills involved in mathematics learning and improve our understanding of why this subject is difficult for many individuals.