Associative Mechanisms of Cognitive Arithmetic

加拿大迅速发展的以知识和技术为基础的经济的成功将越来越取决于其公民的数学能力。就社会经济机会而言，算术甚至可能比识字更重要。目前，与许多国家相比，加拿大人的基本数学技能相对较弱。这激发了对构成数学技能基础的基本认知过程的实验研究。最近对正常和受损算术发展的研究发现，对记忆干扰(记忆中相关信息的混淆)的敏感性是算术学习个体差异的关键因素。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，中国学生通常也比加拿大人拥有更好的算术技能。因此，理解干扰过程对于理解算术技能的本质和习得至关重要。事实上，记忆干扰无疑是众所周知的基本算术事实难于记忆的原因。我的研究项目的目的是开发成人记忆系统的详细理论和计算机模型，用于基本的算术运算，包括简单的加法、减法、乘法和除法。这些运算提供了构建高阶数学技能的概念基础。我的研究将调查初级算术记忆的组成过程的组织，以及这些过程与干扰问题的关系。对成人算术表现中干扰机制的详细了解将有助于揭示在学习过程中减少干扰的方法。四种初等算术运算熟练联想记忆的综合理论是本研究的最终目标，它的实现将为认知算术理论和加拿大基础数学教育的未来发展提供严密的科学基础。

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.