Processes of mathematical cognition

加拿大快速发展的以知识和技术为基础的经济的成功将越来越依赖于其公民的数学能力。就就业机会而言，计算能力甚至可能比识字更重要。目前，加拿大人的基本数学技能与许多国家相比，平均而言相对较弱。这激发了对数学技能背后的基本认知过程的实验研究。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人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。这些运算提供了建立高阶数学技能的概念基础。具体来说，我的研究调查了数字技能的“体系结构”（即，底层组成过程的功能和结构组织），并试图确定为数字比较、估计和基本算术服务的心理代码和检索过程。统一的基本数字认知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.