Associative Mechanisms of Cognitive Arithmetic

点击翻译按钮获取中文摘要

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.