Computational Fluency, Algorithms, and Mathematical Proficiency: One Mathematician's Perspective

Abstract

In recent years, few aspects of mathematics education have been as much discussed and debated as the notions of computational fluency and algorithms. A National Research Council report, Adding It Up: Helping Children Learn Mathematics (Kilpatrick, Swafford, and Findell 2001), offers an image of what it means to have skill with mathematics, or mathematical proficiency. This concept is helpful for moving beyond these debates. Mathematical proficiency includes five components: conceptual understanding, procedural fluency, strategic competence, adaptive reasoning, and productive disposition (Kilpatrick, Swafford, and Findell 2001, p. 116). That these components are not separate but fundamentally intertwined is important to note. This article illustrates some of the ways in which the goal of computational fluency and an appreciation of mathematical algorithms are related to this larger concept of mathematical proficiency.