Percent: A Privileged Proportion

Why is percent, a ubiquitous mathematical concept, so hard to learn? This question motivates our review. We argue that asking the question is worthwhile because percent is universal and because it forms a bridge between real-world situations and mathematical concepts of multiplicative structures. The answer involves explaining the long history of the percent concept from its early roots in Babylonian, Indian, and Chinese trading practices and its parallel roots in Greek proportional geometry to its modern multifaceted meanings. The answer also involves specifying what percent is: its meaning (fraction or ratio) and its sense (function or statistic). Finally, the answer involves understanding the privileged language of percent—an extremely concise language that has lost its explicit referents, has misleading additive terminology for multiplicative meanings, and has multiple uses for the preposition of. The answer leads to speculation, in light of previous research, concerning what can be done to teach percent—and other multiplicative mathematical concepts—more effectively.