Students' Conceptions of the Mathematics of Change and Variation'...

点击翻译按钮获取中文摘要

This research project examines how elementary, high school, and college students develop intuitive conceptions about calculus--which in this case is broadly defined as the mathematics of change and variation. The central assumption is that, from an early age, people develop models about how things change. Mathematics instruction must build upon these intuitive models. The method of investigation involves sequences of teaching interviews in which individual students are presented with problems about situations of change such as the motion of cars, flow of water, or plant growth. They are given physical materials and software tools to help them experiment with the problems. Researchers observe and videotape the ensuing discussion, use of materials, and student-constructed representations of the solution. Subsequent analysis focuses on students' constructions of the problem, the ideas that guide their predictions, the resources they use, and the principles they generate to verify predictions and explanations. The project's findings will help mathematics educators rethink the ways in which calculus is currently taught, as well as the age levels at which key calculus ideas are introduced. Results will also feed directly into a major elementary mathematics curriculum, in the form of a curriculum strand about "change."