Distinguishing variables from parameters
The blog post addresses the common confusion between variables and parameters in mathematics. It highlights how teachers often define a parameter as a "constant that can vary," leading students to question the distinction. The author notes this is a frequently recurring source of confusion in mathematical instruction.
Background
John D. Cook is a mathematician, programmer, and longtime blogger who writes accessible explanations of technical topics in math, statistics, and software engineering. This post addresses a classic source of confusion in mathematics and programming: the fuzzy line between a variable (something that changes) and a parameter (something that is fixed for a given scenario but can be changed across scenarios). The joke “a parameter is a constant that can vary” captures the dilemma — parameters are treated as fixed within a problem but become variables when you zoom out. The distinction matters in fields like calculus (differentiating with respect to a variable vs. treating a parameter as constant), statistics (model parameters vs. data variables), and software (function arguments vs. configuration settings). Cook’s post likely unpacks why this ambiguity is both inevitable and useful.