Associative Mechanisms of Cognitive Arithmetic

加拿大迅速发展的知识和技术经济的成功将越来越依赖于其公民的数学能力。就社会经济机会而言，算术能力甚至可能比识字能力更重要。目前，与许多国家相比，加拿大人的基本数学技能平均相对较弱。这激发了对数学技能基础的基本认知过程的实验研究。最近的研究发现，在正常和受损的算术发展已确定易感性的记忆干扰（记忆中的相关信息的混乱）作为一个关键因素，在算术学习的个体差异。例如，加拿大学生比中国学生更容易受到算术记忆干扰的影响，而中国学生的算术技能也比加拿大学生好。因此，理解干扰过程对于理解算术技能的本质和获得至关重要。事实上，记忆干扰无疑是基本算术事实难以记忆的原因。我的研究计划的目的是开发一个详细的理论和计算机模型的成年人的记忆系统的基本算术运算，包括简单的加法，减法，乘法和除法。这些操作提供了高阶数学技能建立的概念基础。我的研究将调查组织的基本算术记忆的组件过程，以及这些是如何与干扰的问题。详细了解干扰的机制，因为它们表现在成年人的算术性能将揭示如何减轻学习过程中的干扰。一个全面的理论熟练的联想记忆的所有四个基本算术运算是本研究的最终目标，它的实现将提供一个严格的科学基础，认知算术理论和未来的进展，在加拿大的基础数学教育。

The success of Canada's rapidly evolving knowledge- and technology-based economies will depend increasingly upon the mathematical competence of its citizens. Numeracy may be more critical even than literacy in terms of socio-economic opportunities. At present, Canadians' basic mathematical skills are, on average, relatively weak compared to many countries. This motivates experimental research into the basic cognitive processes that underlie mathematical skills. Recent findings in both normal and impaired arithmetic development have identified susceptibility to memory interference (confusions of related information in memory) as a critical factor in individual differences in arithmetic learning. For example, Canadian students are more susceptible to arithmetic memory interference effects than are Chinese students, who also generally have better arithmetic skills compared to Canadians. Understanding the interference process therefore is central to understanding the nature and acquisition of arithmetic skills. Indeed, memory interference undoubtedly is the reason that the basic arithmetic facts are notoriously difficult to memorize. The purpose of my program of research is to develop a detailed theory and computer model of adults' memory systems for the fundamental arithmetic operations, including simple addition, subtraction, multiplication and division. These operations provide the conceptual foundations upon which higher-order mathematical skills are built. My research will investigate the organization of the component processes for elementary arithmetic memory and how these are related to the problem of interference. A detailed understanding of the mechanisms of interference as they are manifest in adults' arithmetic performance will shed light on ways to mitigate interference during learning. A comprehensive theory of skilled associative memory for all four elementary arithmetic operations is the ultimate goal of this research, and its realization will provide a rigorous scientific foundation for cognitive arithmetic theory and for future advances in basic mathematics education in Canada.