Processes of Mathematical Cognition

加拿大快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，计算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而言相对较弱。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乱）的敏感性是算术学习个体差异的关键因素。了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成人记忆系统的详细理论和计算机模型，用于基本算术运算，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。我的研究将调查基本算术存储器的组件过程的组织以及它们如何与干扰问题相关。详细了解成人算术表现中所体现的干扰机制将有助于减轻学习过程中的干扰。这项研究的最终目标是建立一个适用于所有四种基本算术运算的熟练记忆的统一理论，其实现将为理解成人数字能力的个体和跨国差异提供科学基础。

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. Understanding the interference process 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 unified theory of skilled memory for all four basic arithmetic operations is the ultimate goal of this research, and its realization will provide a scientific basis for understanding individual and cross-national differences in adults' numerical competencies.