ABSTRACT

A centra l phenomeno n o f th e 21s t centur y wil l b e change : economic, social, and technological change. Indeed, engaging students in an analysis of change and variation is a central element of nearly every chapter in this book. Today, however, the mathematics of change and variation (MCV), despite it s importance i n understanding an d controllin g thi s ubiquitou s phenomenon, is packed away in a course, Calculus, that sits at the end of a long series of prerequisite s that flter ou t 90% of th e population. This is especially true for student s from economicall y poorer neighborhood s and families. Additionally, the 10% who do have nominal access to MCV in calculus courses develop mostly symbol manipulation skil l but littl e understanding (Tucker, 1990). The tradi-tional curriculum thus excludes most childre n fro m th e concept s o f rat e o f change , accumulation , approximation, continuity, and limit (among others). These are the very concepts children most need not only to participate in the physical, social, and life sciences of the 21st century, but also to make informed decision s in thei r persona l an d politica l lives . Even thoug h MC V concept s hav e

been at the heart of mathematics and science historically (Bochner, 1966), in educatio n th e opposit e i s mor e nearl y true . Conventional curricul a neglect, delay, or deny students’ access to MCV.