Processes of mathematical cognition

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。就就业机会而言，算术甚至可能比识字更关键。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。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，用于基本的算术运算，包括简单的加、减、乘和除。这些运算提供了构建高阶数学技能的概念基础。具体地说，我的研究调查了数字技能的“体系结构”(即潜在组成部分过程的功能和结构组织)，并试图确定有助于数字比较、估计和基本算术的心理代码和提取过程。基本数字认知的统一理论是本研究的最终目标，它的实现将为理解成人数字能力的个体差异和跨国差异提供科学依据。

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 employment 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. The purpose of my programme 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. Specifically, my research investigates the "architecture" of numerical skills (i.e., the functional and structural organization of the underlying component processes) and attempts to identify the mental codes and retrieval processes that subserve numerical comparison, estimation, and basic arithmetic. A unified theory of basic numerical cognition 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.